Lab 8-2021

Task 1

getwd()

## [1] "C:/Users/Caleb/Documents/Civil Engineering degree coursework/Applied Statistical Methods/Labs/Lab 8"

Task 2

sample <- runif(10,0,5)

a=0
b=5
mean=(a+b)/2
mean

## [1] 2.5

var=((b-a)^2)/12
var

## [1] 2.083333

mean(sample)

## [1] 2.417656

(sd(sample))^2

## [1] 2.381815

\(\bar x\) and \(s^2\) are close to the values of \(\mu\) and \(\sigma^2\) but not exact.

\(Y_i \sim Uniform(0,5)\) \(\mu_i=2.5\) \(\sigma^2 _i=2.083\)

The sum \(T\):

\[E(T)=E(Y_1 +Y_2+...+Y_n)=E(Y_1)+E(Y_2)+...+E(Y_n)=n*E(Y_i)=n*\mu_i=2.5*n\] \[V(T)=V(Y_1 +Y_2+...+Y_n)=1^2*V(Y_1)+1^2*V(Y_2)+...+1^2*V(Y_n)=n*V(Y_i)=n*\sigma^2_i=2.083*n\]

The mean \(\bar Y\)

\[E(\bar Y)=E(\frac{Y_1+Y_2+...+Y_n}{n})=\frac{nE(Y_i)}{n}=E(Y_i)=\mu_i=2.5\] \[V(\bar Y)=V(\frac{T}{n})=\frac{1}{n^2}V(T)=\frac{nV(Y_i)}{n^2}=\frac{V(Y_i)}{n}=\frac{\sigma^2_i}{n}=\frac{2.083}{n}\]

myclt=function(n,iter,a=0,b=5){
y=runif(n*iter,a,b)
data=matrix(y,nr=n,nc=iter,byrow=TRUE)
sm=apply(data,2,sum)
h=hist(sm)
#hist(sm,col=rainbow(length(h$mids)),freq=FALSE,main="Distribution of the sum of uniforms")
#curve(dnorm(x,mean=n*(a+b)/2,sd=sqrt(n*(b-a)^2/12)),add=TRUE,lwd=2,col="Blue")
sm
}
w=myclt(n=50,iter=10000,a=5,b=10)

Line A forms a sample with n*iter values from the uniform distribution between 0 and 5.

Line B creates a matrix named data using the sample y formed in line A and the matrix has n rows and iter columns. Then it fills the matrix by row.

Line C creates a vector named sm by applying the function sum to the columns of the data matrix.

Line D runs the command with n=10 and iter=10000.

mean(w)

## [1] 374.9148

var(w)

## [1] 106.0505

myclt=function(n,iter,a=0,b=5){
y=runif(n*iter,a,b)
data=matrix(y,nr=n,nc=iter,byrow=TRUE)
sm=apply(data,2,mean)
h=hist(sm)
sm
print(sm)
}
w=myclt(n=50,iter=10000,a=5,b=10)

##     [1] 7.576480 7.680168 7.758707 7.042635 7.454525 7.276094 7.495523 7.181072
##     [9] 7.490062 7.290826 7.278234 7.359053 7.578756 7.732485 7.452447 7.331399
##    [17] 7.946037 7.489058 7.826808 7.469666 7.538737 7.519072 7.300201 7.365497
##    [25] 7.299807 7.733841 7.499567 7.466549 7.249810 7.518430 7.798028 7.440867
##    [33] 7.249816 7.537518 7.626283 7.346116 7.422635 7.314365 7.216328 7.499699
##    [41] 7.108990 7.695684 7.600303 7.324378 7.157626 7.754649 7.197636 7.702563
##    [49] 7.162330 7.320616 7.810300 7.238927 7.360835 7.351163 7.829971 7.410381
##    [57] 7.392386 7.468977 7.232580 7.024616 7.789211 7.439854 7.297115 7.791645
##    [65] 7.825647 7.585601 7.584782 7.475896 7.415078 7.663248 7.753481 7.775080
##    [73] 7.260658 7.476687 7.392883 7.672974 7.358100 7.405913 7.572136 7.646518
##    [81] 7.324670 7.436125 7.175050 7.305153 6.999653 7.557219 7.693265 7.280418
##    [89] 7.241777 7.383221 7.179979 7.511131 7.468403 7.578525 7.842627 7.840327
##    [97] 7.482988 7.889248 7.280816 7.467312 7.598942 7.550218 7.407751 7.083206
##   [105] 7.522420 7.130745 7.358619 7.494304 7.676806 7.312911 7.225572 7.442917
##   [113] 7.401130 7.565034 7.579608 7.043936 7.347603 7.455988 7.489902 7.677352
##   [121] 7.462081 7.601654 7.070779 7.305379 7.346596 7.526010 7.329239 7.782853
##   [129] 7.449006 7.611759 7.667783 7.565140 7.420099 7.415993 7.433683 7.503862
##   [137] 7.437875 7.666627 7.369021 7.248061 7.411072 7.553631 7.364561 7.277006
##   [145] 7.443766 7.232350 7.507141 7.443378 7.181982 7.560104 7.628209 7.247177
##   [153] 7.381266 7.238678 7.358846 7.263602 7.620622 7.387409 7.615782 7.292318
##   [161] 7.367499 7.559650 7.470254 7.383438 7.322649 7.954208 7.226631 7.051776
##   [169] 7.411230 7.811903 7.769594 7.474323 7.132581 7.876803 7.539592 7.515294
##   [177] 7.286068 7.419394 7.738975 7.629279 7.553569 7.411506 7.836360 7.236756
##   [185] 7.383076 7.539673 7.812485 7.769869 7.329427 7.182216 7.469744 7.430145
##   [193] 7.549609 7.038021 7.627732 7.400022 7.537906 7.480739 7.570445 7.412054
##   [201] 7.657513 7.602431 7.813359 7.350878 7.629494 7.630692 7.727765 7.697387
##   [209] 7.357879 7.195408 7.493696 7.169361 7.463354 7.621111 7.633164 7.829797
##   [217] 7.490490 7.164327 7.471041 7.571420 7.636959 7.116013 7.346035 7.282208
##   [225] 7.588362 7.461155 7.204341 7.399429 7.398082 7.751286 7.422065 7.185100
##   [233] 7.588485 7.629983 7.657356 7.425021 7.754403 7.442534 7.744923 7.772111
##   [241] 7.717704 7.528800 7.734163 7.529596 7.491503 7.516495 8.046051 7.507492
##   [249] 7.543172 7.701821 7.822122 7.397485 7.818908 7.259716 7.614923 7.478294
##   [257] 7.471967 7.446409 7.449000 7.255031 7.710155 7.514721 7.446843 7.772429
##   [265] 7.780137 7.566835 7.465586 7.335903 7.302774 7.708839 7.330288 7.383790
##   [273] 7.323562 7.710466 7.617600 7.404890 7.313046 7.631784 7.492004 7.552434
##   [281] 7.293481 7.372589 7.568822 7.266688 7.682548 7.454647 7.405899 7.554515
##   [289] 7.457186 7.367804 7.303328 7.493986 7.478255 7.338392 7.507342 7.497668
##   [297] 7.283273 7.723241 7.486295 7.854349 7.538428 7.660054 7.411285 7.336998
##   [305] 7.184214 7.511088 7.655498 7.532798 7.701845 7.403728 7.456433 7.793859
##   [313] 7.609700 7.317894 7.467347 7.358659 7.487035 7.299183 7.346758 7.108567
##   [321] 7.734782 7.818874 6.902675 7.621739 7.559594 7.510465 7.667905 7.623809
##   [329] 7.471198 7.641548 7.562446 7.485479 7.494082 7.552184 7.569204 7.644632
##   [337] 7.519766 7.541476 7.852028 7.416555 7.393815 7.512376 7.324658 7.592091
##   [345] 7.542419 7.710343 7.685701 7.305047 7.610799 7.579752 7.271285 7.467276
##   [353] 7.422695 7.209054 7.553294 7.334628 7.259888 7.200357 7.409996 7.496475
##   [361] 7.652169 7.502142 7.425347 7.571031 7.611258 7.635103 7.279056 7.519509
##   [369] 7.276894 7.645300 7.621733 7.377348 7.493200 7.209622 7.399229 7.222343
##   [377] 7.505663 7.677959 7.517657 7.479646 7.690690 7.702323 7.676703 7.431719
##   [385] 7.293073 7.667804 7.019478 7.590500 7.919409 7.630866 7.500707 7.437658
##   [393] 7.875841 7.439898 7.338494 7.102899 7.489168 8.005876 7.563514 7.537389
##   [401] 7.335051 7.978984 7.381835 7.140580 7.636569 7.306240 7.614295 7.658525
##   [409] 7.548930 7.730349 7.464958 7.527604 7.529569 7.125368 7.404903 7.452200
##   [417] 7.318866 7.663768 7.366618 7.922398 7.643265 7.524180 7.481256 7.840123
##   [425] 7.562592 7.409461 7.405112 7.460785 7.285996 7.605661 7.837450 7.599699
##   [433] 7.849334 7.433705 7.625674 7.508264 7.437581 7.630639 7.649431 7.640615
##   [441] 7.165004 7.606991 7.249632 7.804820 7.362314 7.650474 7.831500 7.711582
##   [449] 7.642789 7.721402 7.070368 7.491192 7.690582 7.412361 7.453675 7.531340
##   [457] 7.115819 7.226818 7.525112 7.639351 7.274427 7.365447 7.381213 7.501567
##   [465] 7.229475 7.339702 7.475994 7.397343 7.357681 7.465580 7.585158 7.646379
##   [473] 7.584867 7.666803 7.705012 7.367974 7.740384 7.299840 7.869966 7.609787
##   [481] 7.844525 7.517718 7.584673 7.335670 7.566507 7.826981 7.623896 7.390615
##   [489] 7.398141 7.445783 7.770482 7.583784 7.341678 7.023039 7.508120 7.769089
##   [497] 7.380094 7.828541 7.236932 7.373034 7.605874 7.494617 7.451717 7.546166
##   [505] 7.709182 7.229121 7.581242 7.378839 7.725907 7.503699 7.619991 7.276540
##   [513] 7.591096 7.312756 7.705851 7.139799 7.447407 7.668975 7.234825 7.463928
##   [521] 7.443640 7.150646 7.682771 7.161299 7.407854 7.715228 7.627465 7.411971
##   [529] 7.627078 7.476328 7.404624 7.534338 7.652649 7.347434 7.645508 7.809771
##   [537] 7.605006 7.330264 7.385762 7.416715 7.446059 7.653669 7.681611 7.594689
##   [545] 7.271061 7.277888 7.549434 7.415525 7.709416 7.918735 7.521532 7.131678
##   [553] 7.910789 7.695302 7.777622 7.507116 7.533396 7.563964 7.614339 7.551315
##   [561] 7.498999 7.274431 7.546153 7.147473 7.526330 7.748940 7.593885 7.427507
##   [569] 7.169938 7.674221 7.523092 7.420884 7.862712 7.543145 7.815651 7.807347
##   [577] 7.460053 7.507303 7.930128 7.557958 7.607314 7.483884 7.645170 7.072799
##   [585] 7.210421 7.461448 7.288156 7.332506 7.152105 7.583779 7.541168 7.744637
##   [593] 7.234191 7.365291 7.474147 7.390661 7.457115 7.762513 7.370512 7.412948
##   [601] 7.761847 7.446497 7.488690 7.483080 7.256461 7.461269 7.410512 7.664092
##   [609] 7.412677 7.577762 7.960428 7.279195 7.142045 7.480874 7.580171 7.330191
##   [617] 7.337360 7.383548 7.548731 7.687643 7.211430 7.468041 7.842607 7.847426
##   [625] 7.485900 7.631393 7.500654 7.477959 7.685612 7.114723 7.259007 7.568420
##   [633] 7.833906 7.786498 7.265850 7.314090 7.346522 7.534484 7.578958 7.488065
##   [641] 7.519369 7.019100 7.575066 7.425225 7.494346 7.939791 7.756373 7.615118
##   [649] 7.488445 7.307719 7.678055 7.272034 7.531911 7.772655 7.588102 7.433731
##   [657] 7.487427 7.582004 7.406821 7.897957 7.671828 7.497645 7.753084 7.374903
##   [665] 7.644055 7.344277 7.447466 7.360291 7.631346 7.367673 7.393893 7.333448
##   [673] 7.643483 7.314956 7.408049 7.337493 7.875996 7.434033 7.573447 7.343597
##   [681] 7.257197 7.304452 7.358104 7.259604 7.552651 7.651086 7.890093 7.575265
##   [689] 7.757180 7.846238 7.572914 7.832795 7.592311 7.542570 7.613129 7.731251
##   [697] 7.707945 7.635370 7.503555 7.355642 7.762071 7.362886 7.390670 7.573740
##   [705] 7.521765 7.197317 7.374602 7.465947 7.288836 7.792982 7.305778 7.366773
##   [713] 7.098002 7.449060 7.307008 7.946669 7.778374 7.796920 7.632687 7.766475
##   [721] 7.654707 7.747443 7.371630 7.504715 7.777334 7.629952 7.322989 7.590665
##   [729] 7.700558 7.276415 7.448658 7.162787 7.570832 7.112239 7.490943 7.106850
##   [737] 7.636941 7.422725 7.487761 7.287892 7.617867 7.467039 7.441529 7.512310
##   [745] 7.880596 7.536462 7.823272 7.256498 7.155649 7.391017 7.373402 7.793580
##   [753] 7.321570 7.398718 7.511965 7.575450 7.648959 7.530350 7.414637 7.592332
##   [761] 7.787781 7.444281 7.508761 7.368587 7.322046 7.271983 7.463218 7.336559
##   [769] 7.599138 7.528539 7.683887 7.422904 7.575497 7.542088 7.483447 7.743529
##   [777] 7.390449 7.479565 7.446169 7.571723 7.497735 7.319775 7.592700 7.423655
##   [785] 7.403496 7.480931 7.657261 7.389365 7.481717 7.707300 7.663442 7.420376
##   [793] 7.327917 7.582940 7.118784 7.167753 7.325565 7.750436 7.760039 7.300056
##   [801] 7.607619 7.506605 7.309028 7.553023 7.490259 7.806400 7.299866 7.552787
##   [809] 7.020760 7.606003 7.627067 7.570761 7.379174 7.449093 7.255706 7.657829
##   [817] 7.692273 7.324413 7.641225 7.662683 7.783585 7.407339 7.215989 7.363504
##   [825] 7.791848 7.212407 7.751643 7.378466 7.570200 7.308914 7.415820 7.633596
##   [833] 7.447810 7.215709 7.532615 7.404533 7.069444 7.662836 7.301034 7.050065
##   [841] 7.338258 7.340613 7.423394 7.885646 7.497456 7.410451 7.552585 7.308412
##   [849] 7.564355 7.502255 7.334846 7.415283 7.669613 7.840094 7.418935 7.598404
##   [857] 7.113643 7.378152 7.533609 7.649982 7.152446 7.760339 7.495818 7.283800
##   [865] 7.326626 7.677220 7.305377 7.425570 7.241153 7.498210 7.259116 7.408088
##   [873] 7.500191 7.617324 7.420902 7.546665 7.395887 7.670099 7.541657 7.438015
##   [881] 7.350231 7.829744 7.537606 7.580185 7.635990 7.729100 7.643636 7.330295
##   [889] 7.350619 7.175402 7.645725 7.591526 7.460789 7.349682 7.656793 7.140383
##   [897] 7.498520 7.710655 7.687540 7.655372 7.582800 7.229640 7.707755 7.761281
##   [905] 7.364390 7.281415 7.728334 7.617400 7.545708 7.496200 7.491588 7.330433
##   [913] 7.704828 7.366434 7.403386 7.516324 7.649461 8.013260 7.721093 7.696393
##   [921] 7.784504 8.090756 7.447213 7.332966 7.553659 7.852571 7.329824 7.387926
##   [929] 7.536312 7.450025 7.397013 7.577652 7.549652 7.816283 7.381591 7.460027
##   [937] 7.502925 7.111528 7.621106 7.765915 7.322257 7.549703 7.612993 7.717258
##   [945] 7.314780 7.862473 7.622641 7.317746 7.566087 7.396111 7.552786 7.667085
##   [953] 7.269101 7.725004 7.248226 7.296397 7.506832 7.432792 7.585745 7.464518
##   [961] 7.681389 7.616863 7.469456 7.505520 7.574076 7.715486 7.504414 7.592494
##   [969] 7.592751 7.616713 7.435904 7.448156 7.588751 7.465855 7.766634 7.609755
##   [977] 7.236756 7.600260 7.418946 7.914276 7.644287 7.470504 7.571393 7.628614
##   [985] 7.569570 7.653090 7.191478 7.571641 7.271536 7.055000 7.220122 7.514934
##   [993] 7.207928 7.152907 7.434554 7.421907 7.271785 7.132457 7.395384 8.120313
##  [1001] 7.786281 7.309761 7.889888 7.746384 7.124530 7.127359 7.394043 7.818449
##  [1009] 7.789195 7.892276 7.533705 7.882460 7.133107 7.322158 7.282419 7.434304
##  [1017] 7.541824 7.376238 7.695382 7.204523 7.749562 7.594045 7.380814 7.425811
##  [1025] 7.450214 7.543381 7.569663 7.607294 7.208542 7.463727 7.739322 7.703801
##  [1033] 7.331196 7.600996 7.823527 7.494351 7.223259 7.631867 7.649412 7.943659
##  [1041] 7.646869 7.528833 7.598231 7.463670 7.556692 7.590944 7.657592 7.609007
##  [1049] 7.517199 7.342088 7.495390 7.815013 7.392526 7.345574 7.445627 7.810973
##  [1057] 7.489502 7.440009 7.392421 7.494332 7.517136 7.291161 7.209820 7.570697
##  [1065] 7.049232 7.556977 7.261455 7.705590 7.731596 7.573557 7.813525 7.305164
##  [1073] 7.593886 7.725147 7.494448 7.526588 7.833426 7.426646 7.474096 7.412643
##  [1081] 7.618805 7.810610 7.376177 7.457568 7.558177 7.209953 7.474583 7.815964
##  [1089] 7.447445 7.429518 7.277479 7.446226 7.597568 7.385092 7.771805 7.529773
##  [1097] 7.243967 7.367531 7.778691 7.498625 7.720001 7.683066 7.720341 7.371176
##  [1105] 7.339871 7.345374 7.418352 7.497220 7.604700 7.355363 7.498401 7.475490
##  [1113] 7.448112 7.538460 7.117489 7.409424 7.606021 7.143881 7.784915 7.284438
##  [1121] 7.542174 7.521621 7.373433 7.729246 7.229591 7.736406 7.255434 7.782574
##  [1129] 7.580351 7.867679 7.464401 7.570819 7.558798 7.581641 7.721056 7.568747
##  [1137] 7.558296 7.796486 7.410151 7.439940 7.550801 7.185994 7.540898 7.811524
##  [1145] 7.286338 7.573987 7.498468 7.567136 7.517761 7.748679 7.391817 7.878374
##  [1153] 7.290972 7.584218 7.488996 7.483658 7.433268 7.530519 7.402072 7.388245
##  [1161] 7.525916 7.390652 7.791370 7.482970 7.404873 7.413701 7.451271 7.254439
##  [1169] 7.819663 7.468401 7.349569 7.752558 7.682519 7.444690 7.578573 7.529875
##  [1177] 7.474968 7.605822 7.425779 7.425837 7.202414 7.162992 7.429661 7.483539
##  [1185] 7.580691 7.549565 7.311763 7.313921 7.354063 7.974352 7.630622 7.438581
##  [1193] 7.458764 7.684959 7.320280 7.383211 7.607578 7.779729 7.262286 7.764105
##  [1201] 7.270809 7.981541 7.561699 7.522555 7.157952 7.372359 7.526866 7.304813
##  [1209] 7.994615 7.232213 7.459799 7.679209 7.558526 7.633884 7.379261 7.691808
##  [1217] 7.620930 7.676697 7.224771 7.392093 7.764233 7.387946 7.526082 7.423348
##  [1225] 7.469395 7.477992 6.959474 7.576590 7.375144 7.319260 7.419678 7.390047
##  [1233] 7.651970 7.799244 7.751566 7.294828 7.367337 7.476754 7.473362 7.593719
##  [1241] 7.638501 7.493502 7.583936 7.592081 7.396134 7.096951 7.683322 7.225019
##  [1249] 7.560438 7.203376 7.514694 7.755094 7.485347 7.152866 7.338221 7.586877
##  [1257] 7.786887 7.777667 7.591069 7.429372 7.731950 7.732750 7.762918 7.173717
##  [1265] 7.669903 7.890629 7.429508 7.413295 7.198831 7.506234 7.348699 7.430461
##  [1273] 7.786096 7.868855 7.489823 7.232289 7.337538 7.620971 7.608909 7.469141
##  [1281] 7.363442 7.479385 7.426345 6.998302 7.562521 7.063797 7.377493 7.695847
##  [1289] 7.532424 7.390870 7.192586 7.571667 7.612214 7.888743 7.246171 7.565771
##  [1297] 7.796518 7.686272 7.697553 7.492675 7.284213 7.342673 7.346891 7.355523
##  [1305] 7.669480 7.775500 7.675387 7.448901 8.144496 7.371827 7.788805 7.164302
##  [1313] 7.730129 7.529802 7.431861 7.382844 7.294279 7.097156 7.315809 7.336963
##  [1321] 7.474516 7.551986 7.397312 7.436647 7.583579 7.352198 7.454383 7.598151
##  [1329] 7.388276 7.387228 7.486170 7.375615 7.817838 7.401456 7.447968 7.521780
##  [1337] 7.536729 7.371352 7.618245 7.407292 7.750844 7.585307 7.392883 7.280067
##  [1345] 7.544350 7.678144 7.214179 7.585498 7.752352 7.439379 7.942142 7.265263
##  [1353] 7.644255 7.333723 7.813267 7.466913 7.732550 7.409634 7.438622 7.601588
##  [1361] 7.441339 7.188812 7.434039 7.169220 7.727373 7.087263 7.727016 7.174923
##  [1369] 7.707186 7.259911 7.282694 7.439957 7.036129 7.375615 7.059797 7.365340
##  [1377] 7.534539 7.203974 7.705271 7.610061 7.597781 7.339122 7.464804 7.455698
##  [1385] 7.799440 7.230005 7.512709 7.654003 7.560331 7.852601 7.666779 7.713285
##  [1393] 7.651567 7.753539 7.573730 7.569171 7.207245 7.385137 7.550821 7.344100
##  [1401] 7.378788 7.227600 7.597927 7.445006 7.209486 7.344941 7.604460 7.557306
##  [1409] 7.560492 7.470549 7.414311 7.337539 7.243103 7.256906 7.527632 7.524552
##  [1417] 7.718447 7.560707 7.626451 7.727904 7.702793 7.421736 7.941025 7.568231
##  [1425] 7.372320 7.338321 7.582212 7.482776 7.440338 7.333370 7.663304 7.910588
##  [1433] 7.777777 7.090557 7.371548 7.719411 7.487564 7.334267 7.482124 7.403298
##  [1441] 7.322374 7.330664 7.306087 7.877544 7.574438 7.557874 7.612416 6.897112
##  [1449] 7.509940 7.326265 7.493497 7.001257 7.433703 7.629692 7.737912 7.612566
##  [1457] 7.365596 7.133356 7.722447 7.731088 7.449993 7.462766 7.531612 7.343558
##  [1465] 7.305035 7.500737 7.306752 7.759359 7.496861 7.425527 7.049136 7.822413
##  [1473] 7.276893 7.488791 7.524008 7.347110 7.680107 7.403244 7.298747 7.321949
##  [1481] 7.433007 7.263462 7.277538 7.708347 7.544060 7.765652 7.145896 7.496256
##  [1489] 7.621938 7.562686 7.354353 7.528381 7.512652 7.692015 7.704218 7.567559
##  [1497] 7.306575 7.251093 7.400209 7.413452 7.493143 7.181471 7.234799 7.662884
##  [1505] 7.657359 7.260949 7.380048 7.497503 7.425623 7.730190 7.426597 7.721162
##  [1513] 7.408055 7.444722 7.196230 7.263392 7.750735 7.440312 7.485819 7.653649
##  [1521] 7.655006 7.401681 7.227685 7.432064 7.684788 7.683876 7.097303 7.707979
##  [1529] 7.479802 7.382520 7.491465 7.262467 7.564990 7.295092 8.108594 7.674434
##  [1537] 7.494846 7.498192 7.315312 7.540629 7.154916 7.540852 7.238655 7.523826
##  [1545] 7.534709 7.455483 7.518313 7.370746 7.592530 7.626154 7.720327 7.870464
##  [1553] 7.644684 7.600327 7.430783 7.639729 7.587124 6.932735 7.481873 7.404090
##  [1561] 7.404368 7.500025 7.956530 7.427815 7.520856 7.818199 7.591855 7.552544
##  [1569] 7.434743 7.756995 7.356536 7.585927 7.381836 7.296890 7.363436 7.650650
##  [1577] 7.380474 7.524123 7.578896 7.357216 7.369064 7.655725 7.707235 7.491635
##  [1585] 7.709020 7.521002 7.305101 7.701457 7.186545 7.589205 7.827805 7.329940
##  [1593] 7.890845 7.714094 7.399045 7.647376 7.657712 7.210262 7.280625 7.929256
##  [1601] 7.783095 7.233952 7.514647 7.585019 7.682401 7.411307 7.599829 7.596252
##  [1609] 7.504100 7.584588 7.968127 7.289765 7.246247 7.540917 7.297834 7.609755
##  [1617] 7.532005 7.388324 7.546810 7.440927 7.624215 7.422647 7.285904 7.400486
##  [1625] 7.292845 7.878977 7.606041 7.209850 7.569622 7.278371 7.356269 7.637257
##  [1633] 7.715621 7.456531 7.330970 7.203020 7.697293 7.547111 7.383673 7.636357
##  [1641] 7.277795 7.535798 7.441888 7.453114 7.459508 7.472291 7.489875 7.130617
##  [1649] 7.334012 7.602723 7.535455 7.411096 7.478417 7.293052 7.158270 7.394809
##  [1657] 7.487936 7.491255 7.717294 7.404659 7.436560 7.391050 7.451311 7.382875
##  [1665] 7.835893 7.730361 7.470792 7.381846 7.617854 7.447951 7.582317 7.148269
##  [1673] 7.524561 7.726913 7.599611 7.604747 7.677476 7.753893 7.009628 7.927539
##  [1681] 7.658591 7.599771 7.439657 7.950717 7.877513 7.546012 7.672885 7.166990
##  [1689] 7.368844 7.456742 7.540594 7.152528 7.682195 7.558590 7.129979 7.517530
##  [1697] 7.598232 7.545085 7.704928 7.831305 7.822260 7.692072 7.494285 7.962043
##  [1705] 7.622516 7.657412 7.396540 7.599668 7.342307 7.522631 7.677003 7.040940
##  [1713] 7.642292 7.335406 7.653793 7.499451 7.379192 7.874459 7.280432 7.365451
##  [1721] 7.332126 7.404003 7.298646 7.154378 7.551113 7.303131 7.552701 7.557533
##  [1729] 7.102469 7.248790 7.344110 7.847455 7.310342 6.992857 7.023566 7.522738
##  [1737] 7.685762 7.298781 7.854085 7.491396 7.115709 7.493417 7.633673 7.420118
##  [1745] 7.545020 7.772040 7.499630 7.744362 7.597969 7.280735 7.276237 7.593512
##  [1753] 7.331803 7.367296 7.331819 7.806695 7.705575 7.351585 7.504834 7.648263
##  [1761] 8.017451 7.545148 7.393267 7.575700 7.443931 7.707663 7.814957 7.743043
##  [1769] 7.692388 7.589964 7.257279 7.797329 7.533787 7.534304 7.692521 7.347568
##  [1777] 7.331489 7.653140 7.971137 7.563212 7.524967 7.570424 8.003894 7.747580
##  [1785] 7.296108 7.402271 7.468402 7.551333 7.542872 7.366098 7.318873 7.485873
##  [1793] 7.399131 7.309872 7.277788 7.623093 7.476890 7.783075 7.361840 7.513764
##  [1801] 7.634281 7.514086 7.683704 7.730060 7.929666 7.461225 7.322206 7.497539
##  [1809] 7.685166 7.629520 7.185720 7.221966 7.307454 7.183019 7.658314 7.317007
##  [1817] 7.728029 7.748022 7.574957 7.351730 7.590784 7.626250 7.598600 7.661746
##  [1825] 7.581231 7.233609 7.457619 7.494268 7.247969 7.398273 7.335309 7.382356
##  [1833] 7.609016 7.443547 7.289121 7.858307 6.934006 7.126797 7.394048 7.497833
##  [1841] 7.411686 7.455342 7.495024 7.826114 7.409791 7.616978 7.858170 7.058688
##  [1849] 7.198107 7.485767 7.297250 7.872812 7.979714 7.465732 7.488787 7.654921
##  [1857] 7.478772 7.593952 7.727248 6.989772 7.476715 7.570393 7.544741 7.571479
##  [1865] 7.450667 7.597982 7.520318 7.325940 7.640778 7.147491 7.929134 7.225618
##  [1873] 7.313297 7.638162 7.361398 7.448381 7.269495 7.946638 7.268949 7.658408
##  [1881] 7.384142 7.559424 7.573018 7.328679 7.229884 7.795190 7.731731 7.443996
##  [1889] 7.754323 7.250648 7.649378 7.607171 7.681208 7.312434 7.890800 7.607164
##  [1897] 7.599649 7.669082 7.451878 7.820887 7.726056 7.327066 7.678902 7.421433
##  [1905] 7.598091 7.400955 7.523394 7.418847 7.639598 7.809439 7.468899 7.705905
##  [1913] 8.001484 7.324512 7.305925 7.904281 7.397659 7.651492 7.264929 7.450187
##  [1921] 7.787803 7.373414 7.383124 7.518395 7.551226 7.640498 7.681007 7.564721
##  [1929] 7.304116 7.566182 7.336597 7.500367 8.025698 7.332809 7.726951 7.740879
##  [1937] 7.752799 7.289072 7.280447 7.414859 7.910368 7.526873 7.733446 7.475500
##  [1945] 7.256743 7.071058 7.451255 7.384039 7.564689 7.746809 7.394818 7.668339
##  [1953] 7.684916 7.281397 7.362240 7.626611 7.774577 7.567976 7.103353 7.322610
##  [1961] 7.787968 7.284339 7.885857 7.580452 7.550144 7.569518 7.868432 7.639276
##  [1969] 7.600075 7.311236 7.091278 7.327472 7.446553 7.130371 7.392312 7.422368
##  [1977] 7.534004 7.593881 7.871826 7.335313 7.492317 7.436675 7.658376 7.528825
##  [1985] 7.404217 7.232278 7.487372 7.564604 7.622554 7.433743 7.511353 7.418978
##  [1993] 7.409445 7.111058 7.695448 7.291547 7.479450 7.378319 7.532235 7.560147
##  [2001] 7.490396 7.318917 7.627912 7.289869 7.344674 7.795954 7.148780 7.319266
##  [2009] 7.482831 7.215799 7.584825 7.367527 7.822696 7.697229 7.537095 7.684999
##  [2017] 7.273741 7.474463 7.250998 7.401818 7.166722 7.526110 7.546842 7.679801
##  [2025] 7.279802 7.359719 7.374070 7.263844 7.592619 7.484100 7.558048 7.553319
##  [2033] 7.448749 7.913200 7.468896 7.383789 7.706003 7.240240 7.669912 7.661245
##  [2041] 7.616321 7.457654 7.647567 7.602232 7.214186 7.491684 7.359992 7.441182
##  [2049] 7.593422 7.035294 7.182087 7.487944 7.287474 7.590801 7.522332 7.659789
##  [2057] 7.664073 7.205553 7.403191 7.369484 7.897886 7.339078 7.522426 7.561951
##  [2065] 7.520597 7.492230 7.700039 7.486952 7.711145 7.455368 7.511467 7.165590
##  [2073] 7.769819 7.574873 7.243722 7.586204 7.344541 7.783148 7.517384 7.469359
##  [2081] 7.474274 7.493683 7.800249 7.598065 7.400110 7.217526 7.527344 7.729365
##  [2089] 7.155747 7.390207 7.295593 7.868313 7.416808 7.782579 7.622405 7.604839
##  [2097] 7.542812 7.133750 7.354099 7.371291 7.364088 7.501561 7.164863 7.459083
##  [2105] 7.579009 7.578523 7.359721 7.129795 7.730693 7.719624 7.343614 7.656349
##  [2113] 7.437315 7.682836 7.396754 7.542956 7.659346 7.641266 7.441162 7.467271
##  [2121] 7.569391 7.201526 7.683571 7.569214 7.539098 7.361713 7.309884 7.801149
##  [2129] 7.561573 7.244590 7.645113 7.889690 7.500375 7.280378 7.542546 7.458495
##  [2137] 7.699414 7.605617 7.127360 7.290324 7.342150 7.557955 7.180200 7.219088
##  [2145] 7.506994 7.387188 7.462042 7.375310 7.831661 7.620740 7.705653 7.492636
##  [2153] 7.392197 7.751900 7.697753 7.598204 7.789167 7.441821 7.247279 7.461391
##  [2161] 7.586025 7.493706 7.637029 7.440350 7.512072 7.683230 7.511273 7.555102
##  [2169] 7.616283 7.629389 7.230220 7.397761 7.316418 7.411687 7.442181 7.290829
##  [2177] 7.666663 7.345607 7.445755 7.455603 7.606968 7.595000 7.366992 7.372427
##  [2185] 7.576322 7.526667 7.469482 7.250181 7.441383 7.463345 7.588331 7.270777
##  [2193] 7.410373 7.243703 7.450910 7.757205 7.149283 7.505354 7.521246 7.493445
##  [2201] 7.382897 7.525893 7.614912 7.537171 7.621729 7.715300 7.537405 7.360780
##  [2209] 7.240334 7.245917 7.345688 7.423454 7.655190 7.259639 7.267880 7.359882
##  [2217] 7.843955 7.795650 7.397079 7.933856 7.819708 7.675710 7.406873 7.580679
##  [2225] 7.488907 7.410708 7.522570 7.926943 7.683911 7.608719 7.387144 7.226506
##  [2233] 7.759333 7.481770 7.831669 7.991045 7.674116 7.705733 7.530763 7.520291
##  [2241] 7.228134 7.263339 7.373482 7.854019 7.855195 7.493757 7.387846 7.260254
##  [2249] 7.439088 7.689110 7.352405 7.360131 7.269391 7.490948 7.303438 7.560258
##  [2257] 7.450000 7.317825 7.586861 7.440762 7.414269 7.498016 7.600562 7.782355
##  [2265] 7.462471 7.671565 7.256729 7.614435 7.370384 7.734447 7.431646 7.435415
##  [2273] 7.880922 7.865641 7.333891 7.019440 7.542075 7.666751 6.961303 7.891681
##  [2281] 7.610203 7.553655 7.460199 7.448298 7.525741 7.428621 7.552196 7.424205
##  [2289] 7.753034 7.208339 7.353594 7.341923 7.691346 7.849934 7.284539 8.024990
##  [2297] 7.552614 7.413269 7.138134 7.450527 7.560623 7.674809 7.732434 7.575386
##  [2305] 7.268630 7.367564 7.772232 7.488539 7.339561 7.451508 7.504908 7.756344
##  [2313] 7.513769 7.595344 7.682834 7.495775 7.803440 7.652634 7.272722 7.563704
##  [2321] 7.445837 7.353335 7.476017 7.560839 7.769737 7.083729 7.154942 7.448808
##  [2329] 7.281950 7.417763 7.573649 7.544496 7.404047 7.379034 7.644453 7.582245
##  [2337] 7.066257 8.023123 7.628507 7.834217 7.399194 7.370505 7.615923 7.821200
##  [2345] 7.321102 7.680563 7.203083 7.883084 7.845920 7.372773 7.966424 7.716074
##  [2353] 7.659669 7.718388 7.400628 7.462329 7.582867 7.613518 7.566100 7.544509
##  [2361] 7.752566 7.428740 7.356717 7.655328 7.003074 7.254578 7.596554 7.203215
##  [2369] 6.831026 7.845365 7.417630 7.448953 7.214517 7.957328 7.408110 7.474027
##  [2377] 7.571363 7.105593 7.808029 7.744480 7.762255 7.348835 7.437126 7.426142
##  [2385] 7.393912 7.530698 7.490798 7.441024 7.645034 7.390004 7.783007 7.386719
##  [2393] 7.162924 7.702253 7.854853 7.625115 7.542870 7.400239 7.423127 7.469715
##  [2401] 7.612207 7.317059 7.300403 7.727665 7.376088 7.491118 7.509905 7.377432
##  [2409] 7.578211 7.666433 7.288397 7.145336 7.098040 7.651814 7.387981 7.267344
##  [2417] 8.028366 7.318445 7.690557 7.111005 7.540196 7.639030 7.532878 7.329411
##  [2425] 7.655747 7.686614 7.827799 7.304007 7.472903 7.519059 7.420964 7.495133
##  [2433] 7.701282 7.598807 7.556691 7.240156 7.537609 7.500024 7.440717 7.539640
##  [2441] 7.386301 7.665506 7.567633 7.774272 7.362934 7.698203 7.679094 7.196209
##  [2449] 7.542289 7.519792 7.556419 7.639398 7.524551 7.329405 7.708497 7.611207
##  [2457] 7.333343 7.676113 7.398766 7.409344 7.744421 7.951512 7.457126 7.707320
##  [2465] 7.615684 7.708619 7.763291 7.588284 7.357065 7.593786 7.692854 7.584184
##  [2473] 7.964827 7.339328 7.459122 7.465631 7.601263 7.637618 7.669487 6.899303
##  [2481] 7.653945 7.513550 7.799384 7.635699 7.596063 7.864915 7.645651 7.768242
##  [2489] 7.384399 7.644541 7.306787 7.847369 7.609270 7.419895 7.669226 7.643212
##  [2497] 7.755953 7.706741 7.662216 7.466792 7.671370 7.364183 7.294869 7.274286
##  [2505] 7.300178 7.643849 7.697281 7.553082 7.331730 7.660355 6.827972 7.344975
##  [2513] 7.406738 7.651579 7.848713 7.458374 7.668813 7.522821 7.551518 7.772347
##  [2521] 7.584728 7.660214 7.162116 7.285442 7.162663 7.461021 7.738384 7.266066
##  [2529] 7.605108 7.580549 7.184385 7.319550 7.499799 7.692632 7.449466 7.542393
##  [2537] 7.731246 7.542460 7.340982 7.501721 7.915402 7.792846 7.402777 7.360626
##  [2545] 7.661444 7.341225 7.400139 7.131124 7.492640 7.508575 7.337539 7.478933
##  [2553] 7.074761 7.649144 7.387166 7.676281 7.544112 7.822477 7.310974 7.415430
##  [2561] 7.384862 7.137939 7.336503 7.388277 7.620061 7.529243 7.552994 7.359631
##  [2569] 7.485409 7.540163 7.666861 7.773344 7.459999 7.510986 7.692751 7.325963
##  [2577] 7.063570 7.636040 7.437947 7.541889 7.593770 7.498054 7.462916 7.288996
##  [2585] 7.870669 7.221227 7.222489 7.265375 7.280146 7.675002 7.381268 7.588649
##  [2593] 7.426365 7.674301 7.031210 7.643934 7.519021 7.428868 7.531642 6.940377
##  [2601] 7.487531 7.392363 7.332227 7.590803 7.491099 7.189902 7.148809 7.583076
##  [2609] 7.683427 7.364749 7.431022 7.586511 7.630162 7.575268 7.449540 7.345286
##  [2617] 7.481162 7.684063 7.435804 7.343276 7.616023 7.749048 7.599844 7.225981
##  [2625] 7.849736 7.785070 7.627541 7.609848 7.391016 7.007167 7.620493 7.271998
##  [2633] 7.420916 7.921620 7.534734 7.646519 7.277047 7.486142 7.084347 7.683751
##  [2641] 7.050450 7.092306 7.492341 7.620997 7.485316 8.062461 7.450291 7.239290
##  [2649] 7.533603 7.550610 7.110263 7.551671 7.762448 7.212745 7.719511 7.472053
##  [2657] 7.324382 7.566681 7.542827 7.755669 7.513720 7.450029 7.527525 7.097431
##  [2665] 7.685615 7.342177 7.192437 7.721731 7.304713 6.914777 7.598852 7.577433
##  [2673] 7.575644 7.735371 7.389895 7.552304 7.507125 7.210467 7.236645 7.782840
##  [2681] 7.459180 7.680753 7.343622 7.613834 7.550338 7.778933 7.630298 7.421169
##  [2689] 7.599823 7.193120 7.324826 7.461239 7.161662 7.740536 7.496086 7.562955
##  [2697] 7.562199 7.591442 7.974822 7.472836 7.685476 6.921729 7.436910 7.830491
##  [2705] 7.476393 7.203904 7.475443 7.496481 7.700425 7.556224 7.503282 7.281412
##  [2713] 7.539230 7.608982 7.429365 7.428589 7.691261 7.641430 7.719803 7.429390
##  [2721] 7.654937 7.587932 7.464095 7.666192 7.758417 6.991456 7.261325 7.547283
##  [2729] 7.453228 7.331136 7.639642 7.250241 7.582352 7.325520 7.497181 7.188497
##  [2737] 7.584646 7.594370 7.383994 7.512323 7.102555 7.435324 7.515074 7.528277
##  [2745] 7.327060 7.474944 7.692761 7.202243 7.415351 7.233203 7.341240 7.384415
##  [2753] 7.692130 7.318935 7.537665 7.795810 7.880205 7.242995 7.412053 7.592016
##  [2761] 7.397381 7.467088 7.382081 7.830924 7.553314 7.750958 7.506040 7.598505
##  [2769] 7.422803 7.744876 7.524813 7.452331 7.975566 7.700189 7.298894 7.840038
##  [2777] 7.442669 7.518090 7.716623 7.597200 7.365526 7.578475 7.285108 7.529695
##  [2785] 7.465452 7.567483 7.481950 7.504789 7.593909 7.520353 7.209442 7.750349
##  [2793] 7.697466 7.552647 7.643348 7.210898 7.668246 7.576120 7.428778 7.421757
##  [2801] 7.393127 7.609476 7.408968 7.140772 7.780424 7.789115 7.451157 7.603444
##  [2809] 7.322049 7.573694 7.676890 7.526683 7.422852 7.550356 7.856432 7.574123
##  [2817] 7.544665 7.705819 7.588071 7.689804 7.358779 7.416614 7.906533 7.719503
##  [2825] 7.480101 7.570086 7.155717 7.461843 7.189139 7.650883 7.386259 7.532809
##  [2833] 8.067920 7.686792 7.724958 7.334712 7.336189 7.811411 7.382868 7.394208
##  [2841] 8.177505 7.362394 7.488139 7.758175 7.583305 7.422750 7.566693 7.565864
##  [2849] 7.156053 7.322123 7.142513 7.738784 7.754297 7.623421 7.637537 7.565938
##  [2857] 7.465778 7.299503 7.315364 7.225812 7.493519 7.167312 7.794287 7.870270
##  [2865] 7.993006 7.431871 7.134976 7.443337 7.510861 7.242140 7.687393 7.854814
##  [2873] 7.743203 7.341719 7.212417 7.459280 7.378135 7.181108 7.377108 7.604105
##  [2881] 7.518537 8.048836 7.374057 7.495427 7.515492 7.683804 7.254747 7.444710
##  [2889] 7.661745 7.375542 7.614883 7.316524 7.932604 7.452587 7.594437 7.147697
##  [2897] 7.307002 7.399828 7.379632 7.427450 7.504336 7.188107 7.310544 7.519612
##  [2905] 7.601835 7.128890 7.791989 7.411671 7.620699 7.550444 7.241042 7.833016
##  [2913] 7.438089 7.248659 7.829654 7.752787 7.622669 7.689548 7.202484 7.388546
##  [2921] 7.388225 7.476646 7.736284 7.615623 7.268307 7.533831 7.545841 7.118060
##  [2929] 7.301923 7.823034 7.390152 7.597923 7.209124 7.307284 7.915929 7.880228
##  [2937] 7.953211 7.469007 7.400950 7.460277 7.486297 7.388306 7.382060 7.587409
##  [2945] 7.696385 7.548343 7.270505 7.090372 7.329397 7.398112 7.744299 7.744125
##  [2953] 7.560163 7.496985 7.893646 7.527042 7.833434 7.736792 7.818014 7.384280
##  [2961] 7.603798 7.545460 7.575522 7.475318 7.407689 7.397430 7.286637 8.009067
##  [2969] 7.524296 7.657441 7.432383 7.485091 7.802797 7.267440 7.483154 7.582615
##  [2977] 7.595073 7.408068 7.646269 7.356125 7.558580 7.240188 7.517316 7.473040
##  [2985] 7.315452 7.423888 7.822244 7.737799 7.512643 6.944750 7.389649 7.472056
##  [2993] 7.282777 7.214330 7.363415 7.331022 7.286777 7.142872 7.231200 7.676330
##  [3001] 7.383644 7.174836 7.415018 7.608509 7.570052 7.300041 7.273090 7.660736
##  [3009] 7.105762 7.583974 7.552442 7.097351 7.622204 7.496458 7.289271 7.458141
##  [3017] 7.594644 7.758211 7.489567 7.592923 7.375061 7.387506 7.446084 7.653448
##  [3025] 7.355835 7.408722 7.512595 7.574042 7.474229 7.635585 7.872818 7.734801
##  [3033] 7.237807 7.748638 7.374049 7.652452 7.633192 7.311858 7.869581 7.287221
##  [3041] 7.502548 7.075196 7.485592 7.538663 7.164123 7.245645 7.660459 7.533440
##  [3049] 7.399741 7.194490 7.430579 7.404205 7.632056 7.037983 7.281397 7.201135
##  [3057] 7.284829 7.824400 7.200375 7.179831 7.583007 7.680527 7.613068 7.456775
##  [3065] 7.464318 7.409868 7.426898 7.697411 7.558462 7.714232 7.632899 7.578574
##  [3073] 7.417774 7.774562 7.376864 7.699967 7.534453 7.605200 7.759217 7.300453
##  [3081] 7.695688 7.494063 7.524986 7.789348 7.675420 7.402132 7.446305 7.214069
##  [3089] 6.922397 7.421746 7.450167 7.376753 7.569225 7.533979 7.298047 7.711332
##  [3097] 7.914302 7.395441 7.751266 7.714447 7.363302 7.354965 7.717114 7.731460
##  [3105] 7.205561 7.370170 7.576844 7.800885 7.591004 7.498294 7.784003 7.373112
##  [3113] 7.387618 7.516131 7.709333 7.419047 7.465739 7.281341 7.579733 6.850863
##  [3121] 7.518920 7.210821 7.412408 7.450491 7.960783 7.574723 7.377826 7.608118
##  [3129] 7.293516 7.300620 7.368724 7.437647 7.424745 7.345534 7.702093 7.529152
##  [3137] 7.994124 7.280173 7.790336 7.495772 7.515982 7.692076 7.453932 7.778523
##  [3145] 6.968875 7.757765 7.509517 7.274323 7.625338 7.326222 7.685636 7.279151
##  [3153] 7.284050 7.530196 7.392218 7.694635 7.417348 7.308030 7.235647 7.327356
##  [3161] 7.498276 7.618205 7.653416 7.600971 7.477069 7.582924 7.099246 7.334862
##  [3169] 7.622002 7.459159 7.354160 7.759662 7.789193 7.344296 7.859587 7.247601
##  [3177] 7.506254 7.638696 7.711044 7.693215 7.418776 7.309467 7.473547 7.623400
##  [3185] 7.706952 7.523217 7.354096 7.943046 7.040067 7.958800 7.505349 7.372753
##  [3193] 7.326423 7.511221 7.425756 7.340489 7.581936 7.673587 7.440745 7.689699
##  [3201] 7.502339 7.337579 7.313311 7.294982 7.840893 7.639983 7.463761 7.553502
##  [3209] 7.501540 7.320715 7.375816 7.271479 7.133683 7.872421 7.307827 7.356263
##  [3217] 7.270018 7.308890 7.485868 7.463316 7.545056 7.609198 7.100593 7.535942
##  [3225] 7.063782 7.705448 7.263100 7.194799 7.460635 7.429034 7.562439 7.283989
##  [3233] 7.211095 7.628293 7.221104 6.924551 7.336639 7.724084 7.672715 7.660440
##  [3241] 7.410009 7.288125 7.306495 7.473194 7.662700 7.576486 7.655390 7.512538
##  [3249] 7.776891 7.556689 7.433761 7.278152 7.348163 7.593568 7.527220 7.663845
##  [3257] 7.453794 7.965383 7.678731 7.728004 7.338763 7.645877 7.600328 7.736732
##  [3265] 7.810410 7.563127 7.507736 7.260415 7.245840 7.796594 7.274003 7.138294
##  [3273] 7.725516 7.484709 7.651328 7.492980 7.489233 7.603951 7.196808 7.551508
##  [3281] 7.277567 7.733640 7.629182 7.303302 7.272668 7.767194 7.396328 7.156013
##  [3289] 7.618088 7.692174 7.648393 7.563073 7.631898 7.551401 7.532685 7.585227
##  [3297] 7.741121 7.427384 7.556698 7.381776 7.460069 7.752575 7.700396 7.614034
##  [3305] 7.099458 7.354700 7.899144 7.822631 6.761567 7.427300 7.346139 7.755412
##  [3313] 7.197574 7.462723 7.789672 7.716854 7.512223 7.714494 7.792588 7.288642
##  [3321] 7.699511 7.579695 7.677506 7.472314 7.301062 7.662203 7.720274 7.706847
##  [3329] 7.403395 7.640370 7.642014 7.525315 7.796085 7.428058 7.454515 7.813231
##  [3337] 7.164141 7.140261 7.558258 7.583696 7.408929 7.546258 7.767425 7.344662
##  [3345] 7.103484 7.516178 7.137358 7.600751 7.528897 7.506157 7.509126 7.494776
##  [3353] 7.455819 7.181187 7.762806 7.298614 7.683360 7.687631 7.939282 7.518633
##  [3361] 7.347096 7.515839 7.645013 7.999855 7.372409 7.557933 7.363744 7.348792
##  [3369] 7.726835 7.378146 7.508167 7.531208 7.600812 7.541383 7.492534 7.762378
##  [3377] 7.555799 7.251566 7.683987 7.678129 7.654004 7.538537 7.360921 7.341150
##  [3385] 7.413851 7.269235 7.592278 7.599343 7.706622 7.715647 7.550222 7.546132
##  [3393] 7.754642 7.774224 7.516396 7.291332 7.230742 7.312605 7.896603 7.425071
##  [3401] 7.272701 7.493066 7.778462 7.685712 7.463566 7.667259 7.501464 7.515747
##  [3409] 7.481756 7.741821 7.646018 7.367152 7.917829 7.424155 7.485811 7.095925
##  [3417] 7.309476 7.471221 7.510823 7.806569 7.621860 7.482569 7.523233 7.691232
##  [3425] 7.293740 7.323385 7.212847 7.210980 7.402054 7.570231 7.482326 7.748728
##  [3433] 7.595736 7.445275 7.580037 7.343323 7.354545 7.474697 7.682257 7.386611
##  [3441] 7.818962 7.944143 7.126162 7.464052 7.530955 7.446032 7.424878 7.284108
##  [3449] 7.567149 7.686881 7.754648 7.485952 7.466415 7.485098 7.594137 7.540167
##  [3457] 7.540308 7.631757 7.475738 7.684374 7.535145 7.556960 7.400019 7.627793
##  [3465] 7.425063 7.122590 7.482573 7.570019 7.563268 7.219012 7.055813 7.158671
##  [3473] 7.700283 7.494309 7.322575 7.831577 7.043935 7.743742 7.477866 7.076491
##  [3481] 7.165839 7.743696 7.653802 7.488267 7.543533 7.234139 7.508819 7.583534
##  [3489] 7.655942 7.520352 7.644036 7.231685 7.507586 7.087294 7.556482 7.458206
##  [3497] 7.525914 7.443834 7.623004 7.405620 7.790941 7.572882 7.914505 7.282264
##  [3505] 7.358936 7.544258 7.241434 7.271751 7.228375 7.417058 7.726609 7.590496
##  [3513] 7.823054 7.310779 7.450685 7.677505 7.826105 7.315671 7.593047 7.663977
##  [3521] 7.119386 7.679999 7.726319 7.268589 7.342325 7.295756 7.555934 7.384149
##  [3529] 7.656301 7.324416 7.440788 7.917788 7.027021 7.887193 7.622714 7.655954
##  [3537] 7.212697 7.405387 7.589098 7.640836 7.322175 7.898522 8.113418 7.265619
##  [3545] 7.260347 7.359505 7.490298 7.637132 7.690896 7.320336 7.383577 7.527352
##  [3553] 7.248899 7.868602 7.913984 7.478413 7.781479 7.424070 7.543608 7.337803
##  [3561] 7.566533 7.466725 7.460894 7.390982 7.694810 7.138292 7.382620 7.275130
##  [3569] 7.629183 7.495805 7.359722 7.355001 7.608780 7.344318 7.533010 7.523955
##  [3577] 7.417880 7.718244 7.472260 7.477057 7.333331 7.436561 7.145385 7.590853
##  [3585] 7.528033 7.029775 7.800711 7.467408 8.029541 7.687789 7.568541 7.802992
##  [3593] 7.756225 7.120947 7.364384 7.666288 7.430776 7.314310 7.200905 7.322829
##  [3601] 7.620758 7.317693 7.286284 7.491815 7.398354 7.063145 7.688469 7.711974
##  [3609] 7.357439 7.310541 7.435178 7.541556 7.336318 7.491254 7.717333 7.948032
##  [3617] 7.521626 7.365745 7.468545 7.733532 7.312370 7.407752 7.413196 7.320995
##  [3625] 7.518247 7.506868 7.787940 7.444934 7.627017 7.087965 7.591600 7.380728
##  [3633] 7.395767 7.562504 7.572433 7.441878 7.197161 7.639232 7.460163 7.636213
##  [3641] 7.527305 7.545017 7.468700 7.212143 7.465418 7.622393 7.333066 7.655054
##  [3649] 7.218625 7.408789 7.464015 7.512829 7.688229 7.409926 7.641498 7.188650
##  [3657] 7.451584 7.481313 7.279212 7.366195 7.885306 7.617447 7.997250 7.777757
##  [3665] 7.569695 7.485703 7.558635 7.449502 7.404458 7.879184 7.411906 7.360688
##  [3673] 7.288942 7.425616 7.606136 7.434406 7.482169 7.566538 7.213461 7.546990
##  [3681] 7.721862 7.630991 7.200257 7.605773 7.368201 7.731554 7.184300 7.560702
##  [3689] 7.609056 7.025547 7.303899 7.963221 7.311644 7.400200 7.666254 7.717712
##  [3697] 7.525228 7.562297 7.802809 7.001936 7.450016 7.427941 7.723950 7.382478
##  [3705] 7.582708 7.361633 7.553204 7.326935 7.564489 7.649236 7.538482 7.129066
##  [3713] 7.374444 7.632308 7.677938 7.465782 7.606275 7.550712 7.395943 7.382064
##  [3721] 7.554929 7.934526 7.473570 7.811682 7.487473 7.343430 7.692039 7.514525
##  [3729] 7.829772 7.449421 7.813168 7.474226 7.839363 7.156969 7.443496 7.508397
##  [3737] 7.753356 7.623952 7.703778 7.196455 6.943254 7.362439 7.600876 7.651201
##  [3745] 7.662400 7.505728 7.545639 7.121715 7.362904 7.366465 7.784154 7.263774
##  [3753] 7.520215 7.346818 7.380959 7.398568 7.113275 7.432216 7.753222 7.640514
##  [3761] 7.269579 7.886821 7.638169 7.304425 7.450874 7.489409 7.455036 7.313013
##  [3769] 7.451055 7.771688 7.512968 7.591448 7.306437 7.708566 7.311746 7.359960
##  [3777] 7.176864 7.414654 7.306803 7.605488 7.591450 7.190399 7.727509 7.601473
##  [3785] 7.642418 7.566058 7.403770 7.641296 7.371837 7.616164 7.385562 7.540239
##  [3793] 7.904163 7.532459 7.603318 7.386821 7.633170 7.483756 7.456330 7.315988
##  [3801] 7.325124 7.627763 7.877686 7.179600 7.784139 7.137716 7.604875 7.728972
##  [3809] 7.590903 7.185763 7.526328 7.496087 7.559756 7.641085 7.668347 7.685306
##  [3817] 7.320836 7.444378 7.453411 7.729584 7.778141 7.515111 7.470644 7.461870
##  [3825] 7.193808 7.581021 7.137711 7.187386 7.617598 7.297799 7.576213 7.289006
##  [3833] 7.300058 7.212962 7.593847 7.842535 7.476938 7.578296 7.455009 7.268624
##  [3841] 7.382801 7.824575 7.280628 7.721983 7.734476 7.218946 7.585302 7.044141
##  [3849] 7.404968 7.778046 7.539691 7.680578 7.551899 7.457790 7.340807 7.515872
##  [3857] 7.211045 7.469013 7.374597 7.220452 7.366595 7.747876 7.149936 7.285175
##  [3865] 7.568000 7.206428 7.299745 7.484341 6.862940 7.665825 7.342955 7.900655
##  [3873] 7.460197 7.485766 7.440605 7.681023 7.520528 7.504916 7.328482 7.613194
##  [3881] 7.482936 7.525457 7.521151 7.543643 7.604691 7.404103 7.554560 7.483006
##  [3889] 7.655537 7.382141 7.472891 7.532606 7.429859 7.557526 7.527329 7.177952
##  [3897] 7.397053 7.265629 7.594449 7.250964 7.200062 7.560825 7.203421 7.016920
##  [3905] 7.954249 7.940624 7.375334 7.770647 7.265874 7.530023 7.322147 7.286684
##  [3913] 7.596632 7.764600 7.548105 7.586780 7.511574 7.854990 7.359792 7.510284
##  [3921] 7.850355 7.158225 7.577292 7.453925 7.358286 7.419415 7.142955 7.323218
##  [3929] 7.358046 7.140581 7.261142 7.456598 7.150310 7.714503 7.325572 7.253051
##  [3937] 7.575025 7.393787 7.727914 7.284863 7.600706 7.738492 7.761981 7.408257
##  [3945] 7.541509 7.391409 7.422953 7.619722 7.746862 7.802176 7.702187 7.779383
##  [3953] 7.404844 7.634753 7.777375 7.649444 7.555872 7.573611 7.092163 7.447716
##  [3961] 7.357505 7.023938 8.028326 7.410965 7.522802 7.725748 7.369163 7.295547
##  [3969] 7.491893 7.561452 7.217054 7.442260 7.472406 7.778468 7.172685 7.390917
##  [3977] 7.683865 7.477896 7.311332 7.654174 7.516308 7.522384 7.816291 7.102115
##  [3985] 7.654913 7.690754 7.519671 7.274173 7.453320 7.521322 7.413123 7.780860
##  [3993] 7.256675 7.572467 7.546885 7.520056 7.398087 7.335659 7.469416 7.774146
##  [4001] 7.289576 7.459482 7.716361 7.159414 7.285453 7.299057 7.315107 7.236540
##  [4009] 7.414136 7.256956 7.414536 7.575983 7.936456 7.345954 7.634557 7.636709
##  [4017] 7.272511 7.601790 7.567785 7.471008 7.569285 7.647521 7.563784 7.563764
##  [4025] 7.409471 7.737716 7.653524 7.624222 7.163284 7.891242 7.846271 7.517213
##  [4033] 7.416352 7.379732 7.533875 7.522968 7.536221 7.372981 7.727859 7.403737
##  [4041] 7.299820 7.487534 7.154668 7.467747 7.406440 7.375056 7.433724 7.531881
##  [4049] 7.777353 7.373048 7.422348 7.188973 7.495595 7.255701 7.620937 7.660494
##  [4057] 7.224117 7.465963 7.336483 7.737932 7.519279 7.663435 7.374021 7.542068
##  [4065] 7.632559 7.572737 7.539291 7.682535 7.482165 7.398886 7.636101 7.267056
##  [4073] 7.939570 7.711517 7.225708 7.715338 7.549596 7.642070 7.799519 7.442164
##  [4081] 7.501569 7.469688 7.491225 7.332733 7.391017 7.653001 7.450289 7.492532
##  [4089] 7.628200 7.668105 7.222678 7.408458 7.591455 7.538921 7.135893 7.464996
##  [4097] 7.706555 7.443056 7.526471 7.678188 7.454983 7.540798 7.557051 7.490014
##  [4105] 7.974193 7.655317 7.532279 7.488036 7.381480 7.476376 7.436022 7.434081
##  [4113] 7.482503 7.412153 7.337203 7.668247 7.380584 7.348869 7.437640 7.811956
##  [4121] 7.616587 7.509545 7.267543 7.597325 7.140260 7.541506 7.615828 7.507632
##  [4129] 7.215680 7.253651 7.153946 7.302314 7.355006 7.752218 7.459651 7.550790
##  [4137] 7.650196 7.635527 7.292850 7.934293 7.518951 7.571414 7.363785 7.291671
##  [4145] 7.514708 7.509577 7.190487 7.772659 7.439407 7.302407 7.565646 7.148949
##  [4153] 7.542698 7.510208 7.543013 7.399452 7.262801 7.172441 7.194689 7.783349
##  [4161] 7.459552 7.519967 7.481713 7.454463 7.508919 7.007338 7.448369 7.710689
##  [4169] 7.469138 7.578224 7.552655 7.576357 7.313061 7.234095 7.509277 7.463038
##  [4177] 7.572261 7.540840 7.329878 7.312527 7.549519 7.310156 7.498354 7.516665
##  [4185] 7.381110 7.636175 7.596368 7.557245 7.705748 7.358295 7.568913 6.998758
##  [4193] 7.667051 7.771988 7.457185 7.958866 7.553426 7.350339 7.398934 7.392254
##  [4201] 7.354725 7.439379 7.516132 7.383304 7.522868 7.310574 7.597143 7.417757
##  [4209] 7.403456 7.529075 7.393046 7.316982 7.810385 7.283662 7.643095 8.107796
##  [4217] 7.622207 7.637603 7.516091 7.602453 7.371155 6.996025 7.571116 7.226388
##  [4225] 7.536860 7.188529 7.570613 7.839828 7.553170 7.668058 7.616840 7.748960
##  [4233] 7.748700 7.724541 7.840380 7.531528 7.614002 7.447023 7.243913 7.549455
##  [4241] 7.729665 7.508610 7.402033 7.546856 7.439457 7.449661 7.428135 7.333681
##  [4249] 7.344002 7.294018 7.563226 7.719802 7.236556 7.604081 7.443892 7.263790
##  [4257] 7.771694 7.597990 7.759598 7.259855 7.481378 7.616432 7.834503 7.522319
##  [4265] 7.379896 7.422852 7.431943 7.340061 7.341423 7.594513 7.607101 7.282293
##  [4273] 7.743366 7.530548 7.275768 7.430124 7.155741 7.666155 7.475691 7.670516
##  [4281] 7.391672 7.225040 7.708616 7.422015 7.483369 7.619148 7.732739 7.648542
##  [4289] 7.301084 7.313222 7.188063 7.420457 7.677098 6.880314 7.375707 7.215852
##  [4297] 7.077257 7.337789 7.353114 7.535388 7.856871 7.484144 7.417848 7.349832
##  [4305] 7.558745 7.629558 7.913337 7.626242 7.417303 7.401178 7.343170 7.670525
##  [4313] 7.253410 7.526507 8.085651 7.690807 7.671523 7.443090 7.468474 7.312998
##  [4321] 7.202718 7.271914 7.357296 7.353725 7.180017 7.169977 7.527464 7.344476
##  [4329] 7.612962 7.491404 7.724628 7.563450 7.264792 7.583083 7.595245 7.477591
##  [4337] 7.264260 7.498249 7.555312 7.452259 7.646852 7.500235 7.578053 7.668784
##  [4345] 7.210504 7.089835 6.872295 7.453044 7.551546 7.001541 7.691510 7.251308
##  [4353] 7.464203 7.224421 7.544174 7.689100 7.403116 7.210912 7.449615 7.769978
##  [4361] 7.593271 7.225702 7.334887 7.510803 7.469662 7.381399 7.402585 7.118659
##  [4369] 7.521533 7.170515 7.509312 7.562229 7.247050 7.149595 7.751804 7.594571
##  [4377] 7.334959 7.575001 7.437827 7.642320 7.486159 7.384825 7.633948 7.085883
##  [4385] 7.568410 7.286047 7.466396 7.213082 7.404732 7.342991 7.666702 7.245224
##  [4393] 7.302783 7.635204 7.933601 7.476203 7.421732 7.621689 7.468751 7.470664
##  [4401] 7.525186 7.409704 7.202444 7.545953 7.340413 7.566289 7.675490 7.763170
##  [4409] 7.854174 7.458049 7.709024 7.890532 7.587031 7.452978 7.646106 7.162078
##  [4417] 7.252786 7.283939 7.406103 7.335498 7.256958 7.532393 7.871792 7.702366
##  [4425] 7.450569 7.392841 7.412864 7.452789 7.412696 7.412436 7.489588 7.561140
##  [4433] 7.547723 7.396966 7.569949 7.782255 7.093675 7.598837 7.977395 7.679651
##  [4441] 7.696008 7.454959 7.566535 7.606949 8.085255 7.680573 7.446291 7.622093
##  [4449] 7.648650 7.659044 7.350448 7.637631 7.295446 7.366918 7.486969 7.571974
##  [4457] 7.842032 7.653769 7.697225 7.612575 7.044378 7.297626 7.394777 8.001324
##  [4465] 7.143455 7.492706 7.746633 7.625772 7.551447 7.531514 7.673712 7.502660
##  [4473] 7.254555 7.723070 7.533349 7.485193 7.768858 7.054929 7.581851 7.492660
##  [4481] 7.880459 7.467135 7.221944 7.390430 7.174631 7.451000 7.412773 7.328993
##  [4489] 7.020805 7.585514 7.377613 7.376857 7.586007 7.667096 7.764427 7.505671
##  [4497] 8.131959 7.265879 7.719077 7.346643 7.204979 7.670014 7.686992 7.512860
##  [4505] 7.521986 7.348232 7.362148 7.273935 7.893236 7.500867 7.313871 7.625600
##  [4513] 7.493597 7.833157 7.607110 7.359579 8.150954 7.433136 7.848198 7.594936
##  [4521] 7.493722 7.309071 7.650758 7.452734 7.498570 7.598340 7.417260 7.241685
##  [4529] 7.820995 7.802106 7.827617 7.242171 7.820179 7.540071 7.278712 7.244054
##  [4537] 7.790317 7.353620 7.466240 7.516368 7.788210 7.907969 7.298017 7.123263
##  [4545] 7.192326 7.229224 7.363600 7.150600 7.663067 7.523953 7.466511 7.476257
##  [4553] 7.640188 7.365319 7.497227 7.003629 7.567447 7.416505 7.788818 7.538760
##  [4561] 7.516637 7.477195 7.471160 7.243962 7.331935 7.822358 7.689430 7.275762
##  [4569] 7.783091 7.561108 7.464278 7.237893 7.345934 7.748856 7.459446 7.655225
##  [4577] 7.202028 7.744222 7.698343 7.382342 7.252730 7.616478 7.682340 7.717231
##  [4585] 7.390200 7.464954 7.638306 7.455393 7.524278 7.738639 7.412584 7.428524
##  [4593] 7.643453 7.452715 7.807186 7.540387 7.490890 7.396016 7.515932 7.643084
##  [4601] 7.589174 7.262621 7.799501 7.659210 7.587850 7.663669 7.472586 7.151709
##  [4609] 7.477103 7.734654 7.388800 7.368069 7.578613 7.836013 7.617001 7.278108
##  [4617] 7.885503 7.544265 7.572643 7.621758 7.134025 7.783348 7.681910 7.442624
##  [4625] 7.268996 7.705066 7.433236 8.040145 7.693820 7.385040 7.564539 7.162112
##  [4633] 7.486235 7.398637 7.304566 7.483920 7.437622 7.813403 7.694829 7.561031
##  [4641] 7.409964 7.828231 7.758094 7.261117 7.405856 7.522978 7.233829 7.521360
##  [4649] 7.486700 7.245557 7.747235 7.794710 7.704802 7.332978 7.587553 7.365357
##  [4657] 7.532335 7.369119 7.543607 7.813455 7.552274 7.360903 7.469480 7.467677
##  [4665] 7.466873 7.543642 7.553483 7.655622 7.903271 7.452484 7.722517 7.851771
##  [4673] 7.734666 7.177782 7.861679 7.530709 7.326068 7.451667 7.650760 7.432293
##  [4681] 7.575006 7.420280 7.481419 7.405932 7.281783 7.229115 7.698018 7.583049
##  [4689] 7.408617 7.352213 7.329278 7.632932 7.319743 7.462568 7.663539 7.706834
##  [4697] 7.570026 7.390442 7.206800 7.693792 7.761453 7.713399 7.696708 7.641798
##  [4705] 7.466158 7.284868 7.315987 7.421786 7.799571 7.607840 7.576077 7.560965
##  [4713] 7.593465 7.675995 7.422786 7.852108 7.325521 7.381051 7.878451 7.871938
##  [4721] 7.481070 7.591808 7.428381 7.580424 7.728220 7.517902 7.198076 7.535880
##  [4729] 7.018626 7.182774 7.576078 7.145421 7.371070 7.336921 7.941591 7.406550
##  [4737] 7.603465 7.294413 7.676541 7.634533 7.620549 7.939590 7.297999 7.657688
##  [4745] 7.604583 7.536242 7.384679 7.455663 7.510615 7.512504 7.440989 7.491128
##  [4753] 7.590474 7.235330 7.249083 7.544924 7.628736 7.221713 7.560359 7.390664
##  [4761] 7.691533 6.715995 7.192406 7.936339 7.963601 7.607929 7.243368 7.441515
##  [4769] 7.521456 7.356792 7.523348 7.494236 7.416606 7.461502 7.320754 7.424109
##  [4777] 7.024131 7.534639 7.337114 7.574317 7.428195 7.111607 7.415929 7.424965
##  [4785] 7.701161 6.962354 7.755643 7.339000 7.269742 7.486899 7.261957 7.370444
##  [4793] 7.564033 7.296007 7.883256 7.445823 7.597891 7.634025 7.524604 7.307784
##  [4801] 7.087426 7.463699 7.402166 7.674957 7.217339 7.599174 7.352425 7.683105
##  [4809] 7.387487 7.331986 7.592796 7.336821 7.784014 7.574273 7.657972 7.546539
##  [4817] 7.881576 7.531630 7.425588 7.325662 7.285958 7.162189 7.731953 7.397145
##  [4825] 7.444847 7.526821 7.647784 7.386475 7.652770 7.638480 7.261918 8.010592
##  [4833] 7.348240 7.490074 7.496229 7.491715 7.668448 7.460920 7.507637 7.447232
##  [4841] 7.399973 7.220021 7.496564 7.573178 7.531825 7.541889 7.616289 7.721769
##  [4849] 7.521518 7.557554 7.245005 7.651876 7.081738 7.730312 7.097036 7.392576
##  [4857] 7.613689 7.381976 7.713357 7.428687 7.568610 7.614166 7.418259 7.128082
##  [4865] 7.333681 7.452123 7.695101 7.485730 7.413024 7.392561 7.443832 7.377825
##  [4873] 7.254261 7.493599 7.462717 7.588424 7.324672 7.096447 8.043424 7.158475
##  [4881] 7.217864 7.830444 7.360993 7.293432 7.410666 7.703569 7.741592 7.804924
##  [4889] 7.464108 7.623199 7.619990 7.740524 8.078760 7.623148 7.139625 7.314571
##  [4897] 7.815806 7.857023 7.688503 7.423059 7.318881 7.526434 7.441376 7.455847
##  [4905] 7.637390 7.614226 7.404964 6.982658 7.465031 7.793686 7.983516 7.303571
##  [4913] 7.726663 7.639019 7.554684 7.292942 7.621183 7.502100 7.472048 7.506445
##  [4921] 7.443805 7.392470 7.180972 7.105649 7.784181 7.559247 7.620495 7.425085
##  [4929] 7.044148 7.432010 7.293167 7.307652 7.844728 7.200526 7.530143 7.597723
##  [4937] 7.535072 7.299238 7.358580 7.234703 7.512541 7.757428 7.457635 7.167365
##  [4945] 7.706304 7.879152 7.557406 7.086533 7.534526 7.297194 7.273113 7.674532
##  [4953] 7.244638 7.213956 7.596982 7.062129 7.439286 7.326140 7.282810 7.603600
##  [4961] 7.446742 7.460566 7.307405 7.391207 7.294405 7.724531 7.298953 7.394212
##  [4969] 7.326448 7.412779 7.282552 7.024780 7.360407 7.458554 7.342971 7.482933
##  [4977] 7.556058 7.482829 7.638328 7.701013 7.417354 7.640427 7.680349 7.694621
##  [4985] 7.238252 7.575023 7.816233 7.524334 7.334711 7.475836 7.519253 7.495778
##  [4993] 7.515683 6.949622 7.368082 7.703889 7.568227 7.519642 7.223599 7.910419
##  [5001] 7.336097 7.483357 7.702259 7.688907 7.262540 7.272208 7.575513 7.116565
##  [5009] 7.722751 7.594197 7.512957 7.320897 7.277762 7.534003 7.859768 7.707264
##  [5017] 7.483705 7.210896 7.461045 7.071437 7.675250 7.344784 7.563415 7.408583
##  [5025] 7.553882 7.644322 7.765596 7.614653 7.314231 7.430143 7.474450 7.657203
##  [5033] 7.534623 7.478657 7.537570 7.550976 7.146835 7.653813 7.508076 7.317123
##  [5041] 7.113815 7.507746 7.196325 7.344321 7.407700 7.515530 7.259578 7.659073
##  [5049] 7.469376 7.782168 7.345883 7.599538 7.392718 7.430792 7.694018 7.706426
##  [5057] 7.948159 7.494519 7.410550 7.318562 7.783504 7.492179 7.432917 7.091250
##  [5065] 7.567402 7.644550 7.568936 7.633126 7.356115 7.486684 7.347550 7.650789
##  [5073] 7.125367 7.670804 7.704797 7.535099 7.693590 7.326506 7.354247 7.501930
##  [5081] 7.589273 7.544056 7.350344 7.388165 7.550416 7.362840 7.558015 7.500479
##  [5089] 7.675770 7.440189 7.286093 7.428153 7.128689 7.228001 7.588709 7.364280
##  [5097] 7.620183 7.417654 7.387324 7.996127 7.550466 7.481031 6.894243 7.187598
##  [5105] 7.798067 7.753794 7.509266 7.292405 7.357922 7.418080 7.673901 6.995451
##  [5113] 7.414767 7.548126 7.828921 7.243658 7.531169 7.150203 7.737168 7.158142
##  [5121] 7.635900 7.217317 7.510550 7.321815 7.378244 7.512808 7.250163 7.282583
##  [5129] 7.532491 7.940025 7.494893 7.623357 7.190365 7.727492 7.515462 7.278635
##  [5137] 7.318601 7.571556 7.717102 7.711911 7.645989 7.384414 7.560489 7.633398
##  [5145] 7.073810 7.377284 7.809805 7.563775 7.659593 7.458341 7.470697 7.653228
##  [5153] 7.620538 7.738313 7.639502 7.330156 7.626525 7.609960 7.061052 7.535716
##  [5161] 7.473689 7.396512 7.320947 7.420484 7.764236 7.514740 7.319552 7.583811
##  [5169] 7.291137 7.640808 7.510800 7.247252 7.334477 7.558518 7.802771 7.227030
##  [5177] 7.393335 7.011578 7.261452 7.704487 7.223577 7.265731 7.590367 7.878939
##  [5185] 7.598775 8.004356 7.420471 7.716586 7.806239 7.727999 7.423448 7.556942
##  [5193] 7.341524 7.531852 7.535678 7.451420 7.361532 7.377218 7.758221 7.473440
##  [5201] 7.416721 7.580707 7.506633 7.482386 7.339705 7.299276 7.409389 7.402759
##  [5209] 7.391083 7.690552 7.557314 7.379863 7.463343 7.266362 7.556524 6.859450
##  [5217] 7.470986 7.097712 7.546895 7.648096 7.756006 7.439115 7.639470 7.733191
##  [5225] 7.490866 7.508899 7.707323 7.455811 7.718722 7.524470 7.235769 7.729374
##  [5233] 7.225264 7.284264 7.799396 7.271827 7.520645 7.368247 7.404795 7.092966
##  [5241] 7.093389 7.474375 8.039728 7.581616 7.386391 7.916733 7.831061 7.580027
##  [5249] 7.584620 7.294305 7.417376 7.418211 7.737715 7.109171 7.641338 7.418074
##  [5257] 7.287625 7.436517 7.537623 7.741956 7.162779 7.757242 7.343442 7.858551
##  [5265] 7.469472 7.474494 7.491867 7.239021 7.562549 7.274655 7.471166 7.193103
##  [5273] 7.430433 7.460515 7.647289 7.370356 7.727793 7.635379 7.534525 7.709935
##  [5281] 7.668757 7.993626 7.644702 7.744653 7.661325 7.252894 7.329670 7.485827
##  [5289] 7.642489 7.687815 7.587900 7.314858 6.714962 7.995490 7.221663 7.368607
##  [5297] 7.613225 7.685242 7.555391 7.661842 7.710351 7.814638 7.563680 7.808179
##  [5305] 7.691082 7.813534 7.275027 7.347090 7.680998 7.616402 7.296298 7.307748
##  [5313] 7.517655 7.169115 7.443077 7.637925 7.914059 7.317177 7.252504 7.342505
##  [5321] 7.624064 7.639845 7.127380 7.619663 7.354874 7.583367 7.425271 7.721774
##  [5329] 7.653594 7.778019 7.385784 7.800192 7.530076 7.723207 7.491486 7.379928
##  [5337] 7.740189 7.417861 7.445619 7.522399 7.494420 7.521057 7.620052 7.600131
##  [5345] 7.597524 7.622011 7.545142 7.558419 7.312397 7.244469 7.843043 7.640985
##  [5353] 7.725691 7.489551 7.631820 7.031298 7.621996 7.312397 7.440174 7.209752
##  [5361] 7.964612 7.429074 7.765009 7.630365 7.335064 7.409659 7.542697 7.568309
##  [5369] 7.635160 7.281174 7.455143 7.549087 7.460808 7.402573 7.957623 7.242099
##  [5377] 7.636216 7.480557 7.707001 7.916467 7.266155 7.316484 7.638152 7.610611
##  [5385] 7.549462 7.585260 7.418635 7.451256 7.478946 7.539789 7.311320 7.550536
##  [5393] 7.728550 7.761308 7.559078 7.482616 7.462119 7.497690 7.475645 7.614230
##  [5401] 7.259338 7.200037 7.740726 7.611831 7.283848 6.887850 7.467079 7.318273
##  [5409] 7.511183 7.564641 7.743619 7.541820 7.446067 7.314378 6.951849 7.423617
##  [5417] 7.935060 7.530095 7.744850 7.638126 7.657185 7.515632 7.149319 7.381629
##  [5425] 7.388594 7.762244 7.550628 7.641236 7.392108 7.483093 7.490989 7.232740
##  [5433] 7.333727 7.082779 7.764141 7.358987 7.190474 7.463074 7.278398 7.801440
##  [5441] 7.408535 7.576610 7.346457 7.339109 7.377100 7.738755 7.510850 7.330964
##  [5449] 7.563428 7.085332 7.118820 7.425660 7.771096 7.392558 7.567539 7.725628
##  [5457] 7.592509 7.304896 7.546039 7.721085 7.478171 7.214295 7.676806 7.538850
##  [5465] 7.505509 7.608179 7.683328 7.417888 7.150442 7.705026 7.597169 7.710395
##  [5473] 7.551658 7.542130 7.642180 7.501659 7.524943 7.449994 7.440617 7.710216
##  [5481] 7.658400 7.527615 7.495801 7.706723 7.556189 7.540432 7.596424 7.442662
##  [5489] 7.585462 7.792822 8.101602 7.124302 7.747491 7.867947 7.607101 7.379698
##  [5497] 7.365752 7.635425 7.570276 7.413457 7.665296 7.538592 7.557966 7.690536
##  [5505] 7.401585 7.581989 7.389422 7.699392 7.633745 7.747174 7.855177 7.441749
##  [5513] 7.803850 7.519877 7.467658 7.813946 7.359546 7.488826 7.393657 7.296140
##  [5521] 7.150698 7.468241 7.471817 7.407180 7.394140 7.357397 7.770474 7.671541
##  [5529] 7.519805 7.151554 7.469447 7.560863 7.452332 7.313280 7.492762 7.261117
##  [5537] 7.419335 7.259751 7.670554 7.629054 7.878336 7.686503 7.802806 7.825366
##  [5545] 7.435668 7.424285 7.337236 7.522688 7.377580 7.420789 7.534057 7.321705
##  [5553] 7.544451 7.477905 7.381229 7.442927 7.430191 7.640720 7.549391 7.545996
##  [5561] 7.668136 7.579403 7.308278 7.548048 7.353992 7.344515 7.589023 7.130417
##  [5569] 7.470120 7.649876 7.444583 7.569896 7.781636 7.501869 7.548521 7.273238
##  [5577] 7.324405 7.286891 7.630377 7.646636 7.510752 7.539262 7.702593 7.560319
##  [5585] 7.592879 7.429470 7.108076 7.676508 7.483721 7.414675 7.672094 7.791415
##  [5593] 7.163398 7.589351 7.347427 7.178257 7.630860 7.391442 7.644357 7.425931
##  [5601] 7.670643 7.525283 7.708246 7.649309 7.346256 7.459303 7.438872 7.604316
##  [5609] 7.118384 7.437033 7.154283 7.437682 7.579347 7.218226 7.457856 7.939922
##  [5617] 7.521371 7.572303 7.716178 7.467973 7.592140 7.223998 7.619150 7.756050
##  [5625] 7.692612 7.084353 7.618936 7.285485 7.949654 7.250465 7.862142 7.410314
##  [5633] 7.619981 7.619284 8.006881 7.429945 7.382462 7.497456 7.602477 7.595780
##  [5641] 7.547984 7.727643 7.449427 7.164173 7.453914 7.189305 7.290067 7.169539
##  [5649] 7.389978 7.447023 7.307875 7.319111 7.356155 7.448072 7.419393 7.624157
##  [5657] 7.322642 7.461148 7.491399 7.578608 7.083031 7.609510 7.712884 7.725898
##  [5665] 7.396869 7.187388 7.429937 7.685895 7.463570 7.729787 7.628081 7.565167
##  [5673] 7.322463 7.556460 7.472403 7.614432 7.482097 7.567810 7.360906 7.392687
##  [5681] 7.401078 7.044268 7.567387 7.417501 7.477270 7.613036 7.583123 7.712434
##  [5689] 7.562718 7.532826 7.826528 7.152881 7.496800 7.678717 7.573545 7.461635
##  [5697] 7.354494 7.000254 7.500072 7.711485 7.341215 7.492737 7.248366 7.622678
##  [5705] 7.320545 7.363687 7.739860 6.973354 7.520078 7.504639 7.540318 7.543630
##  [5713] 7.795697 7.304438 7.405600 7.498534 7.720301 7.595848 6.770687 7.228306
##  [5721] 7.715410 7.203392 7.568371 7.826576 7.580536 7.707158 7.380230 7.563556
##  [5729] 7.675287 7.489840 7.206535 7.324011 7.281826 7.631424 7.323100 7.634223
##  [5737] 7.859644 7.408487 7.564342 7.275802 7.597950 7.829319 7.183184 7.786207
##  [5745] 7.331627 7.264661 7.355216 7.958715 7.632021 7.457308 7.705467 7.265316
##  [5753] 7.401388 7.589765 7.615038 7.483110 7.554802 7.318815 7.646053 7.434744
##  [5761] 7.688775 7.178164 7.680197 7.186751 7.187991 7.583919 7.877145 7.585057
##  [5769] 7.516603 7.226831 7.562979 7.739021 7.817998 7.583140 7.596934 7.646942
##  [5777] 7.558230 7.674592 7.543723 7.625650 7.782561 7.609528 7.320209 7.538133
##  [5785] 7.757867 7.503252 7.769720 7.594757 7.593703 7.438858 7.433857 7.289051
##  [5793] 7.568845 7.577222 7.654501 7.533791 7.361684 7.393965 7.600026 7.451429
##  [5801] 7.503235 7.718127 7.096576 7.085409 7.229455 7.159188 7.437805 7.834304
##  [5809] 7.878552 7.328456 7.689505 7.625536 7.108777 7.662186 7.294254 7.583749
##  [5817] 7.453951 7.423514 7.478980 7.413414 7.332255 7.518170 7.241203 7.255203
##  [5825] 7.412117 7.568373 7.744912 7.498567 7.482338 7.491287 7.655938 7.398299
##  [5833] 7.317849 7.453174 7.659658 7.510148 7.547218 7.530066 7.188424 7.482456
##  [5841] 8.111729 7.609043 7.560090 7.616958 7.657932 7.452674 7.552286 7.457553
##  [5849] 7.817037 7.277362 7.811468 7.480506 7.701574 7.448626 7.305942 7.448601
##  [5857] 7.593144 7.222973 7.529212 7.625763 7.628882 7.418308 7.283854 7.127764
##  [5865] 7.652497 7.576291 7.723885 7.710646 7.483847 7.350994 7.537530 7.468277
##  [5873] 7.218661 7.116426 7.266742 7.493337 7.525719 7.476884 7.332921 7.559053
##  [5881] 7.393292 7.321166 7.392947 7.343331 7.953717 7.021449 7.353038 7.257507
##  [5889] 7.538121 7.879924 7.969340 7.507461 7.320816 7.615683 7.535627 7.547179
##  [5897] 7.893114 7.311396 7.217997 7.475618 7.662605 7.065163 7.638347 7.671485
##  [5905] 7.859433 7.688226 7.603251 7.269103 7.638605 7.433648 7.625473 7.321063
##  [5913] 7.406251 7.468880 7.593721 7.238288 7.560855 7.709016 7.448195 7.843026
##  [5921] 7.534738 7.327622 7.481538 7.441727 7.611118 7.345011 7.486152 7.699327
##  [5929] 7.487077 7.795165 7.494787 7.476542 7.297754 7.834737 7.635258 7.899218
##  [5937] 7.072951 7.429718 7.200091 7.805803 7.898239 7.002170 7.682525 7.492941
##  [5945] 7.472639 7.616664 7.533087 7.231849 7.548002 7.472471 7.398742 7.574034
##  [5953] 7.845623 7.495002 7.172091 7.409337 7.215036 7.126389 7.556313 7.849608
##  [5961] 7.621527 7.326303 7.567394 7.452725 7.643724 7.605550 7.325786 7.556921
##  [5969] 7.676290 7.575233 7.375086 7.440595 7.523215 7.307307 7.655990 7.296462
##  [5977] 8.051463 7.049710 7.697959 7.652091 7.395521 7.270043 7.310411 7.323096
##  [5985] 7.674390 7.440217 7.441607 7.888256 7.908309 7.779039 7.168293 7.704104
##  [5993] 7.539396 7.551063 7.707019 7.467841 7.678008 7.578883 7.760687 7.581806
##  [6001] 7.621544 7.569884 7.441806 7.519181 7.660461 7.339419 7.906495 7.691858
##  [6009] 7.525995 7.338177 7.205626 7.062169 7.735513 7.643297 7.470198 7.422072
##  [6017] 7.344901 7.058009 7.379883 7.463849 7.536285 7.541578 7.409203 7.703458
##  [6025] 7.107402 7.723229 7.567658 7.509894 7.717435 7.429167 7.154160 7.531904
##  [6033] 7.849863 7.595942 7.459435 7.857148 7.670443 7.324055 7.604441 7.277231
##  [6041] 7.401489 7.426854 7.627807 7.318637 7.523791 7.728269 8.036774 7.637775
##  [6049] 7.496977 7.642263 7.855355 7.531325 7.718211 7.663883 7.581217 7.594549
##  [6057] 7.560374 7.370337 7.480976 7.338249 7.412762 7.293839 7.489020 7.517739
##  [6065] 7.357958 7.525620 7.457350 7.342210 7.803989 7.296498 6.939927 7.698939
##  [6073] 7.674326 7.660329 7.736510 7.583592 7.412611 7.303182 7.756089 7.572621
##  [6081] 7.652699 7.656012 7.058032 7.510803 7.644970 7.102040 7.369578 7.635242
##  [6089] 7.870691 7.640034 7.513689 7.348775 7.498681 7.975958 7.508037 7.519223
##  [6097] 7.471427 7.611922 7.757839 7.870387 7.346994 7.600135 7.405567 7.448138
##  [6105] 7.248632 7.413626 7.789410 7.437446 7.544278 7.395454 7.755592 7.608067
##  [6113] 7.639115 7.702257 7.278758 7.298651 7.316633 7.405958 7.812091 7.477132
##  [6121] 7.557333 7.380593 7.563144 7.352184 7.770331 7.372759 7.610487 7.541390
##  [6129] 7.604374 7.492618 7.634168 7.619633 7.443100 7.378839 6.927787 7.580948
##  [6137] 7.510195 7.277250 7.575154 7.292662 7.720874 7.877646 7.869221 7.705401
##  [6145] 7.576752 7.982316 7.404052 7.442821 7.439157 7.800587 7.793445 7.554571
##  [6153] 7.352200 7.496620 7.379924 7.145136 7.113474 7.388177 7.376418 7.765035
##  [6161] 7.530407 7.132972 7.414653 7.342802 7.643409 7.626315 7.278730 7.226420
##  [6169] 7.419162 7.261820 7.353874 7.314578 7.688849 7.222304 7.617542 7.818690
##  [6177] 7.626427 7.342273 7.457878 7.469590 7.363173 7.188618 7.515827 7.170170
##  [6185] 7.591270 7.268204 7.733159 7.382796 7.805892 7.496518 7.171917 7.926298
##  [6193] 7.102782 7.790664 7.512681 7.899776 7.611371 7.639053 7.856845 7.456731
##  [6201] 7.376251 7.479899 7.499751 7.456837 7.596278 7.341012 7.366018 7.401687
##  [6209] 7.529622 7.242486 7.559314 7.882297 7.491187 7.692143 7.622841 7.374409
##  [6217] 7.653277 7.212976 7.549385 7.631818 7.574203 7.515474 7.226735 7.612893
##  [6225] 7.462390 7.562132 7.396103 7.575376 7.359578 7.325304 7.643487 7.749876
##  [6233] 7.778152 7.172286 7.665748 7.671756 7.625900 7.740930 7.493071 7.513238
##  [6241] 7.267426 7.495248 7.502847 8.009492 7.291437 7.560697 7.534366 7.546897
##  [6249] 7.488972 7.701057 7.299641 7.434685 7.632822 7.657571 7.339687 7.414260
##  [6257] 7.501719 7.135679 7.479510 7.509511 7.569206 7.615290 7.657933 7.372040
##  [6265] 7.525066 7.655215 7.570324 7.642351 7.587768 7.556153 7.606102 7.505282
##  [6273] 7.354768 7.387863 7.641419 7.191018 7.537468 7.547022 7.244407 7.588523
##  [6281] 7.886508 7.695436 7.056760 7.812982 7.510200 7.485691 7.439159 7.295977
##  [6289] 7.308750 7.133626 7.256100 7.156748 7.706653 7.953012 7.534500 7.476247
##  [6297] 7.697591 7.387659 7.442305 7.386380 7.407766 7.446945 7.415288 7.536920
##  [6305] 7.501844 7.557884 7.570678 7.502238 7.586903 7.879488 7.439448 7.254640
##  [6313] 7.732678 7.182583 7.717512 7.280493 7.844761 7.438548 7.167490 7.407654
##  [6321] 7.337316 7.546408 7.431677 7.483562 7.632680 7.256754 7.348292 7.604351
##  [6329] 7.430013 7.479242 7.591277 7.502550 7.421986 7.343676 7.105570 7.347109
##  [6337] 7.514680 7.903984 7.610624 7.503953 7.560983 7.019509 7.527073 8.027470
##  [6345] 7.230424 7.734294 7.406620 7.863875 7.423543 7.627464 7.480632 7.114819
##  [6353] 7.764541 7.163185 7.553213 7.618003 7.885967 7.668409 7.398809 7.389626
##  [6361] 7.542874 7.805361 7.391376 7.966741 7.509121 7.782796 7.309550 7.499663
##  [6369] 7.886967 7.650160 7.629376 7.679143 7.571730 8.005822 7.749673 7.658676
##  [6377] 7.355607 7.445359 7.698662 7.933418 7.469844 7.298808 7.440080 7.189588
##  [6385] 7.389586 7.485364 7.703027 7.269487 7.729951 7.501637 7.135960 7.390371
##  [6393] 7.687778 7.721038 7.250980 7.204435 7.574986 7.630390 7.341232 7.507147
##  [6401] 7.601160 7.273456 7.529856 7.628819 7.401527 7.251855 7.490095 7.517642
##  [6409] 7.206549 7.687083 7.478631 7.493544 7.983872 7.611089 7.796071 7.239141
##  [6417] 7.137724 7.660677 7.421578 7.466382 7.534714 7.348021 7.110325 7.610560
##  [6425] 7.408676 7.507438 7.441574 7.169046 7.518259 7.504497 7.298028 7.401927
##  [6433] 7.256428 7.369796 7.429431 7.595787 7.312492 7.460172 7.512199 7.479822
##  [6441] 7.340004 7.866084 7.536626 7.357927 7.617457 7.715616 7.642985 7.352821
##  [6449] 7.375933 7.495646 7.603531 7.725769 7.795347 7.720048 7.706584 7.462563
##  [6457] 7.454848 7.529664 7.586114 7.418788 7.351708 7.416967 7.169067 7.446120
##  [6465] 7.421033 7.369674 7.349607 7.334873 7.432559 7.653838 7.455854 7.742942
##  [6473] 7.443526 7.493895 7.510216 7.438712 7.648945 7.737789 7.456916 7.092759
##  [6481] 7.453603 7.379258 7.715075 7.239872 7.482705 7.245299 7.461616 7.549858
##  [6489] 7.598733 7.446137 7.613025 7.259923 7.210052 7.420250 7.517966 7.407972
##  [6497] 7.454758 7.606150 7.254997 8.057762 7.520436 7.548992 7.554192 7.652667
##  [6505] 7.720876 7.208555 7.433946 7.386113 7.813619 7.648652 8.146891 7.608993
##  [6513] 7.692962 7.433390 7.645374 7.530310 7.233766 7.444638 7.561060 7.406515
##  [6521] 7.767216 7.585837 7.424669 7.683955 7.055654 7.432663 7.496938 7.776842
##  [6529] 7.552135 7.616169 7.429595 7.363330 7.591482 7.600338 7.562713 7.425901
##  [6537] 7.403098 7.208248 7.676469 7.433914 7.614454 7.156573 7.494819 7.370501
##  [6545] 7.283538 7.800402 7.389915 7.535619 7.465625 7.845450 7.354629 7.486118
##  [6553] 8.030219 7.520412 7.273431 7.307630 7.606210 7.872545 7.178002 7.607363
##  [6561] 7.527737 7.304791 7.518041 7.436248 7.743948 7.539889 7.481132 7.467570
##  [6569] 7.419209 7.285081 7.181930 7.623337 7.179751 7.269157 7.518652 7.481639
##  [6577] 7.712758 7.265256 7.717713 7.297812 7.521196 7.148920 7.578001 7.620974
##  [6585] 7.588459 7.619119 7.450108 7.717755 7.323699 7.349135 7.345408 7.671649
##  [6593] 7.498872 7.417863 7.491554 7.704307 7.359003 7.226980 7.480643 7.393972
##  [6601] 7.439852 7.284151 7.425734 7.189483 7.618943 7.377522 7.372932 7.620586
##  [6609] 7.311812 7.748752 7.596545 7.354020 7.445162 7.492211 7.471644 7.649958
##  [6617] 7.578409 7.383942 7.214130 7.689830 7.600788 7.442307 7.554380 7.312489
##  [6625] 7.475354 7.664702 7.717022 7.505237 7.424884 7.395499 7.335161 7.809137
##  [6633] 7.735672 7.459050 8.039495 7.254358 7.258335 7.091306 7.574803 7.223451
##  [6641] 7.591301 7.523287 7.204521 7.775827 7.122966 7.601434 7.440620 7.533262
##  [6649] 7.295082 7.295475 7.471412 7.480736 7.273381 7.199885 7.414901 7.598337
##  [6657] 7.680133 7.517482 7.511387 7.911409 7.570465 7.574582 7.706961 7.826002
##  [6665] 7.545069 7.553061 7.615110 7.300658 7.532186 7.736280 7.778278 7.839892
##  [6673] 7.530030 7.338589 7.750436 7.674721 7.445645 7.299452 7.219011 7.687085
##  [6681] 7.388164 7.106592 7.511780 7.282386 7.703773 7.378026 7.524991 7.073352
##  [6689] 7.357861 7.702117 7.423029 7.632976 7.312043 7.509313 7.393600 7.526213
##  [6697] 7.511281 7.280278 7.754222 7.519362 7.305840 7.512552 7.509434 7.240755
##  [6705] 7.586776 7.730189 7.600782 7.701368 7.401589 7.525002 7.728408 7.546084
##  [6713] 7.198444 7.906691 7.421266 7.422331 7.311157 7.326897 7.358704 7.514007
##  [6721] 7.590930 7.504958 7.674236 7.309240 7.587994 7.244546 6.950205 7.315047
##  [6729] 7.471292 7.449157 7.506278 7.636298 7.418754 7.504955 7.864189 7.514067
##  [6737] 7.363692 7.317019 7.517844 7.573121 7.014912 7.493046 7.452050 7.556870
##  [6745] 7.732164 7.277876 7.302113 7.399519 7.343542 7.274483 7.483868 7.319715
##  [6753] 7.585382 7.000122 7.745858 7.761648 7.617515 7.946784 7.655948 7.618183
##  [6761] 7.198554 7.702495 7.466610 7.518127 7.498557 7.873958 7.513958 7.299424
##  [6769] 7.365046 7.432018 7.418617 7.734304 7.375311 7.900640 7.447340 7.426997
##  [6777] 7.540323 7.619835 7.686490 7.690790 7.740849 7.784056 7.623730 7.467848
##  [6785] 7.313394 7.519571 6.961524 7.651571 7.231043 7.466539 7.741776 7.255289
##  [6793] 7.276416 7.497150 7.219886 7.685953 7.441464 7.639600 7.380082 7.400478
##  [6801] 7.498917 7.117677 7.660521 7.529173 7.293089 7.538340 7.514535 7.596952
##  [6809] 7.421762 7.549861 7.517984 7.875646 7.441785 7.566650 7.577302 7.614525
##  [6817] 7.689657 7.765514 7.291840 7.549806 7.633063 7.514336 7.493377 7.702781
##  [6825] 7.646212 7.666623 7.411988 7.722918 7.423841 7.585223 7.516783 6.977032
##  [6833] 7.691434 7.273153 7.442339 7.505008 7.350180 7.154785 7.519694 7.293103
##  [6841] 7.550917 7.627132 7.633053 7.476672 7.912063 7.371984 7.361415 7.784586
##  [6849] 8.053842 7.247742 7.536516 7.343859 7.773062 7.164701 7.245388 7.429214
##  [6857] 7.611540 7.562359 7.253101 7.608981 7.414566 7.402421 7.670639 7.594772
##  [6865] 7.204428 7.320754 7.568041 7.622054 7.390542 7.301064 7.674531 7.671807
##  [6873] 7.452547 7.127012 7.419599 7.596572 7.418901 7.611837 7.289654 7.630536
##  [6881] 7.196469 7.350255 7.487456 7.204832 7.402684 7.400552 7.057993 7.149401
##  [6889] 7.876691 8.089882 7.293147 7.626643 7.567571 7.097299 7.480704 7.250566
##  [6897] 7.478262 7.707131 7.644762 7.950399 7.724472 7.682506 7.428181 7.320227
##  [6905] 7.472264 7.253770 7.859691 7.421483 7.575754 7.640579 7.835116 7.623996
##  [6913] 7.931498 7.242174 7.203623 7.352677 7.699483 7.462916 7.563017 7.391036
##  [6921] 7.558860 7.651640 7.337818 7.493468 7.464571 7.388977 7.489459 7.412961
##  [6929] 7.027902 7.467693 7.229918 7.449622 7.111440 7.529912 7.337046 7.661120
##  [6937] 7.713187 7.694038 7.604129 7.567757 7.738744 7.248281 7.433566 7.382281
##  [6945] 7.647669 7.291854 7.628017 7.504806 7.301958 7.350140 7.472727 7.421591
##  [6953] 7.363215 7.687814 7.984626 7.641779 7.081876 7.341314 7.418969 7.639574
##  [6961] 7.413461 7.559252 7.559606 6.934521 7.442436 7.512435 7.767811 7.837458
##  [6969] 7.371682 7.641668 7.868209 7.505050 7.505241 7.365121 7.872880 7.603329
##  [6977] 7.356861 7.661243 7.318265 7.531472 7.398544 7.871820 7.764906 7.429248
##  [6985] 7.165748 8.014962 7.326528 7.397279 7.847719 7.503401 7.734406 7.742930
##  [6993] 7.314599 7.421926 7.452795 7.584222 7.883150 7.460158 7.266145 7.234649
##  [7001] 7.480509 7.757712 7.659414 7.457621 7.650626 7.540745 7.550940 7.607779
##  [7009] 7.361201 7.472788 7.459993 7.462496 7.426966 7.664849 7.544240 7.602317
##  [7017] 7.869905 7.437931 7.505039 7.628115 7.162167 7.408098 7.353026 7.524737
##  [7025] 7.693479 7.717693 7.689186 7.442117 7.470522 7.764928 7.281095 7.421424
##  [7033] 7.606561 7.678381 7.388602 7.339662 7.256730 7.472659 7.622500 7.636261
##  [7041] 7.014008 7.584286 7.724284 7.623058 7.427195 7.815057 7.598786 7.313147
##  [7049] 7.594691 7.613699 7.793743 7.585200 7.601970 7.278697 7.416962 7.554404
##  [7057] 7.386268 7.485420 7.651914 7.325445 7.467595 7.537353 7.682780 7.472870
##  [7065] 7.413019 7.469911 7.458005 7.444901 7.273568 8.102206 7.555112 7.512713
##  [7073] 7.577455 7.422481 7.817765 7.373435 7.823563 7.774069 7.373884 7.355812
##  [7081] 7.870271 7.641245 7.194574 7.777550 7.209149 7.380239 7.408375 7.254016
##  [7089] 7.229596 7.704086 7.282356 7.573501 7.678657 7.172598 7.241062 6.965261
##  [7097] 7.421752 7.534791 7.387419 7.409863 7.512139 7.365530 7.454317 7.708260
##  [7105] 7.620034 7.492142 7.776351 7.688170 7.379310 7.683170 7.253256 7.389567
##  [7113] 7.283723 7.725589 7.142371 7.635929 7.714016 7.229472 7.462223 7.476792
##  [7121] 7.459480 7.710683 7.319168 7.456867 7.121622 7.521233 7.822397 7.754149
##  [7129] 7.277943 7.508203 7.512523 7.670603 7.428183 7.212756 7.491841 7.630302
##  [7137] 7.132935 7.676680 7.451749 7.120320 7.243998 7.378468 7.499879 7.534966
##  [7145] 7.531162 7.762002 7.628639 7.484785 7.398130 7.553813 7.291766 7.709221
##  [7153] 7.536912 7.451883 7.681106 7.630612 7.184587 7.585880 7.787210 7.669499
##  [7161] 7.449562 7.377981 7.526783 7.546037 7.618180 7.585594 7.517204 7.124241
##  [7169] 7.813242 7.398307 7.583122 7.197618 7.452493 7.640428 7.387981 7.342804
##  [7177] 7.491106 7.363221 7.702617 7.849536 8.042663 7.393577 7.603467 7.479785
##  [7185] 7.499019 7.641717 7.556317 7.768199 7.556545 7.278520 7.375818 7.750245
##  [7193] 7.329577 7.382818 7.690813 7.466047 7.563357 7.731621 7.673492 7.742111
##  [7201] 7.349669 7.567464 7.801755 7.247164 7.625033 7.247038 7.545298 7.460138
##  [7209] 7.633527 7.408153 7.317177 7.472224 7.478704 7.169423 7.523634 7.762496
##  [7217] 7.457410 7.480358 7.328198 7.509900 7.757207 7.306998 7.726709 7.626614
##  [7225] 7.342193 7.823230 7.632412 7.334054 7.470664 7.612277 7.309905 7.531856
##  [7233] 7.399436 7.367618 7.189150 7.415470 7.499670 7.373130 7.379076 7.405076
##  [7241] 7.307779 7.387350 7.302792 7.554254 7.566799 7.324618 7.426976 7.501999
##  [7249] 7.771174 7.459209 7.865582 7.632477 7.341127 7.496406 7.662521 7.509274
##  [7257] 7.508800 7.362061 7.553061 7.460038 7.434808 6.971067 7.503975 7.767234
##  [7265] 7.757652 7.248611 7.459065 7.587671 7.249968 7.527477 7.428979 7.675443
##  [7273] 7.613850 7.524158 7.319923 7.625284 7.367112 7.996489 7.819841 7.649868
##  [7281] 7.277327 7.671248 7.512395 7.802513 7.136935 7.299729 7.207308 7.590045
##  [7289] 7.385595 7.342573 7.524282 7.510188 7.608063 7.874978 7.445143 7.393947
##  [7297] 7.654685 7.428004 7.355237 7.346044 7.456473 7.630629 7.288185 7.265285
##  [7305] 7.600521 7.451815 7.438923 7.385471 7.483721 7.680109 7.301621 7.806757
##  [7313] 7.435011 7.628693 7.569293 7.959986 7.426932 8.071063 7.332025 7.633870
##  [7321] 7.704519 7.653601 7.292282 7.785252 7.585199 7.308826 7.415543 7.435049
##  [7329] 7.373009 7.448254 7.435456 7.459083 7.227645 7.755820 7.669610 7.795347
##  [7337] 7.387051 7.234570 7.479822 7.358521 7.274109 7.756746 7.557739 7.662450
##  [7345] 7.269006 7.245230 7.455391 7.488519 7.559725 7.568774 7.904021 7.286174
##  [7353] 7.473140 7.333609 7.553390 7.325959 7.662083 7.449468 7.113897 7.197749
##  [7361] 7.215606 7.180005 7.474308 7.350189 7.580013 7.427328 7.779814 7.183173
##  [7369] 7.480650 7.495601 7.779093 7.250332 7.535556 7.437585 7.116544 7.645139
##  [7377] 7.714308 7.262275 7.656386 7.726296 7.399426 7.468492 7.667013 7.641039
##  [7385] 7.554902 7.846674 7.535999 7.398740 7.349417 7.691657 7.450299 7.590124
##  [7393] 7.851539 7.817846 7.467465 7.311354 7.702980 7.269123 7.754284 7.803294
##  [7401] 7.464645 7.468954 7.518637 7.465888 7.721075 7.442744 7.286098 7.222018
##  [7409] 7.081665 7.252788 7.653702 7.355890 7.419474 7.839273 7.780408 7.296950
##  [7417] 7.781717 7.433121 7.808655 7.839123 7.205801 7.740774 7.789677 7.656783
##  [7425] 7.773881 7.465981 7.586926 7.594586 7.556647 7.495769 7.766336 7.342430
##  [7433] 7.499371 7.264155 7.559072 7.302850 7.493544 7.363711 7.509258 7.224745
##  [7441] 7.427685 7.924968 7.070190 7.542816 7.566125 7.435925 7.118965 7.445381
##  [7449] 7.646182 7.083803 7.479579 7.312521 7.270803 7.372046 7.325194 7.714714
##  [7457] 7.499899 7.563055 7.409255 7.647349 7.482499 7.538572 7.222877 7.329503
##  [7465] 7.474844 7.324773 7.447787 7.473872 7.365715 7.280747 7.836699 7.798424
##  [7473] 7.483025 7.651361 7.487185 7.141274 7.631339 7.387273 7.442572 7.490428
##  [7481] 7.274222 7.771143 7.416411 7.493377 7.182914 7.920526 7.473296 7.347931
##  [7489] 7.598249 7.446943 7.538343 7.705154 7.515320 7.705178 7.884190 7.664762
##  [7497] 7.170796 7.119706 7.458197 7.347775 7.453475 7.302182 7.615338 7.355656
##  [7505] 7.856744 7.694793 7.522014 7.609290 7.394177 6.987915 7.606873 7.589279
##  [7513] 7.391818 7.452011 7.403466 7.239260 7.490837 7.257267 7.385589 7.549725
##  [7521] 7.561679 7.517358 7.450167 7.084900 7.507659 7.658267 7.695415 7.598694
##  [7529] 7.384349 7.413599 7.552152 7.307471 7.471674 7.493152 7.548351 7.452880
##  [7537] 7.537867 7.243876 7.500617 7.184466 7.279294 7.498943 7.292472 7.577006
##  [7545] 7.560764 7.858244 7.278683 7.339081 7.330464 7.281497 7.461045 7.511470
##  [7553] 7.905329 7.953885 7.273338 7.619018 7.505433 7.625254 7.374418 7.396349
##  [7561] 7.688577 7.588096 7.225123 7.371871 7.923139 7.470745 7.368986 7.390430
##  [7569] 7.726406 7.364575 7.635201 7.570898 7.718493 7.263846 7.807292 7.659154
##  [7577] 7.414868 7.794045 7.212734 8.025992 7.448914 7.545469 7.262162 7.156457
##  [7585] 7.438238 7.520809 7.322154 7.415935 7.128683 7.602105 7.224833 7.225324
##  [7593] 7.738734 7.555981 7.844083 7.951003 7.489634 7.593302 7.379271 7.386376
##  [7601] 7.418179 7.671193 7.469522 7.418129 7.601479 7.814343 7.869063 7.749214
##  [7609] 7.416737 7.385957 7.126574 7.441326 7.474789 7.273392 7.819880 7.657954
##  [7617] 7.536623 7.337792 7.281921 7.317100 7.659502 7.619821 7.494125 7.532130
##  [7625] 7.741543 7.472931 7.543543 7.395642 7.692313 7.554285 7.517422 7.696827
##  [7633] 7.993668 7.314172 7.602213 7.106392 7.657091 7.362257 7.410882 7.373123
##  [7641] 7.279572 7.312253 7.345363 7.460548 7.760751 7.685873 7.519540 7.401728
##  [7649] 7.603578 7.765282 7.640458 7.744553 7.209177 7.437469 7.825571 7.701807
##  [7657] 7.360148 7.447659 7.612141 7.170970 7.697801 7.878226 7.626138 7.390393
##  [7665] 7.450056 7.421605 7.817362 7.651748 7.344356 7.662245 7.199338 7.378810
##  [7673] 7.635345 7.396168 7.330566 7.366183 7.392979 7.428115 7.408488 7.658886
##  [7681] 7.444801 7.322219 7.593066 7.718251 7.386831 8.006637 7.369280 7.621404
##  [7689] 7.782747 7.423563 7.588289 7.797726 7.482411 7.682027 7.240301 7.364181
##  [7697] 7.145838 7.468979 7.672530 7.173124 7.566348 7.254424 7.252194 7.270840
##  [7705] 7.545211 7.227146 7.654585 7.735790 7.654105 7.457359 7.789572 7.165106
##  [7713] 7.559605 7.770756 7.246088 7.889862 7.541156 7.669256 7.150367 7.911741
##  [7721] 7.376390 7.523314 7.258667 7.444057 7.752705 7.547636 7.465778 7.619276
##  [7729] 7.424976 7.345556 7.405835 7.566467 7.767845 7.172546 7.405697 7.108638
##  [7737] 7.506835 7.619880 7.377098 7.325340 7.461981 7.521519 7.335249 7.370361
##  [7745] 7.859458 7.810771 7.649937 7.440783 7.386737 7.367305 7.331794 7.481662
##  [7753] 7.146730 7.605159 7.531900 7.500382 7.331879 7.309405 7.261051 7.810912
##  [7761] 7.359537 7.692112 7.861897 7.253215 7.620734 7.417155 7.540664 7.472197
##  [7769] 7.266657 7.571693 7.486637 7.373103 7.563185 7.465966 7.472456 7.788009
##  [7777] 7.074539 7.343887 7.695408 7.432750 7.310707 7.674161 7.874952 7.620897
##  [7785] 7.154619 7.352374 7.950259 7.395914 7.193894 7.957975 7.614065 7.562437
##  [7793] 7.509600 7.468681 7.760804 7.295164 7.853697 7.474268 7.422531 7.391633
##  [7801] 7.396178 7.692087 8.092272 7.196649 7.582001 7.775155 7.568126 7.426324
##  [7809] 7.361543 7.352388 7.423369 7.797796 7.385303 7.697708 7.813929 7.544300
##  [7817] 7.431904 7.401606 7.548476 7.551767 7.268945 7.459950 7.735054 7.609430
##  [7825] 7.596408 7.666367 8.072185 7.694990 7.571344 7.820872 7.560780 7.133502
##  [7833] 7.561631 7.638702 7.496565 7.527391 7.541703 7.369240 7.449755 7.115567
##  [7841] 7.776924 7.294121 7.636152 7.266758 7.417898 7.404024 7.430462 7.555527
##  [7849] 7.654048 7.317750 7.468517 7.633004 7.228511 7.227890 7.888920 7.229298
##  [7857] 7.697420 7.300605 7.544581 7.534314 7.312262 7.514978 7.555952 7.414917
##  [7865] 7.893496 7.443042 7.351781 7.726336 7.071902 7.386226 7.303225 7.149546
##  [7873] 7.626874 7.759787 7.515563 7.025607 7.484318 6.897159 7.387620 7.431256
##  [7881] 7.513572 7.570952 7.519672 7.630816 7.774350 7.440274 7.529592 7.483447
##  [7889] 7.362126 7.151549 7.687059 7.605483 7.128025 7.113289 7.619135 7.835247
##  [7897] 7.255770 7.068989 7.508438 7.465420 7.140904 7.678211 7.404446 7.346929
##  [7905] 7.309991 7.776438 7.201973 7.380002 7.539807 7.359874 7.388390 7.717956
##  [7913] 7.736005 7.414886 7.176114 7.198015 7.155273 7.957756 7.638323 7.597911
##  [7921] 7.245371 7.510168 7.505436 7.738778 7.448449 7.660861 7.626922 7.003766
##  [7929] 7.438689 7.821272 7.445405 7.056544 7.838519 7.180289 7.919772 7.501440
##  [7937] 7.518304 7.262852 7.570238 7.422682 7.422489 7.575726 7.393612 7.585705
##  [7945] 7.576751 7.510020 7.345354 7.432154 7.865759 7.314724 7.614812 7.498118
##  [7953] 7.337821 7.292532 7.246203 7.512348 7.493750 7.475076 7.630784 7.474693
##  [7961] 7.235211 7.558495 7.082075 7.583155 7.360744 7.099096 7.712226 7.613080
##  [7969] 7.249418 7.436584 7.740294 7.739482 7.491684 7.524180 7.517580 7.474190
##  [7977] 7.428834 7.742329 7.456707 7.716664 7.370084 7.283480 7.322175 7.592945
##  [7985] 7.644547 7.450747 7.562569 7.353016 7.660731 7.380494 7.512496 7.483495
##  [7993] 7.235523 7.298789 7.225079 7.561383 7.502745 7.373557 7.807106 7.455825
##  [8001] 7.673456 7.179889 7.630709 7.259739 7.652570 7.522985 7.514816 7.698625
##  [8009] 7.833324 7.548920 7.833270 7.441700 7.292564 7.355696 7.330502 8.036577
##  [8017] 7.432919 7.565533 7.304742 7.442847 7.138161 7.386339 7.682662 7.361609
##  [8025] 7.888900 7.202092 7.494997 7.619660 7.679294 7.208893 7.442095 8.046327
##  [8033] 7.786252 7.713535 7.575358 7.517262 7.468666 7.827613 7.862686 7.165508
##  [8041] 7.279365 7.377881 7.534074 7.569562 7.576435 7.599506 7.646343 7.724068
##  [8049] 7.563197 7.179038 7.667453 7.724450 7.899570 7.105946 7.517945 7.682750
##  [8057] 7.620253 7.873894 7.334410 7.552226 7.583957 7.466782 7.332517 7.257732
##  [8065] 7.674110 7.408647 7.414631 7.490372 7.304503 7.407503 7.538869 7.470029
##  [8073] 7.185119 7.411197 7.572225 7.256862 7.217809 7.668118 7.367052 7.517825
##  [8081] 7.504078 7.563076 7.533800 7.519410 7.545775 7.493867 7.713055 7.497943
##  [8089] 7.511221 7.370907 7.285478 7.425839 7.496725 7.568165 7.473737 7.284256
##  [8097] 7.603742 7.762223 7.422983 7.313621 7.668922 7.687638 7.383014 7.523887
##  [8105] 7.455882 7.552077 7.690580 7.601797 7.611517 7.508821 7.450053 7.714647
##  [8113] 7.828267 7.530026 7.727933 7.436468 7.520555 7.543743 7.385409 7.530678
##  [8121] 7.401641 7.526242 7.378267 7.276212 7.432741 7.379729 7.450876 7.332138
##  [8129] 7.410010 7.860690 7.725052 7.505950 7.389828 7.156561 7.347110 7.366392
##  [8137] 7.107829 7.453395 7.741193 7.546476 7.581744 7.805436 7.220380 7.699699
##  [8145] 7.713274 7.279527 7.806004 7.715792 7.338242 7.245356 7.435474 7.520488
##  [8153] 7.520979 7.495739 7.656457 7.800761 7.430630 7.729013 7.182797 7.851702
##  [8161] 7.574488 7.434991 7.555054 7.616349 7.174180 7.573721 7.292470 7.379361
##  [8169] 7.728637 7.619636 7.438723 7.453908 7.645912 7.398690 7.697420 7.632633
##  [8177] 7.718431 7.829094 7.376520 7.641260 7.408781 7.460299 7.590244 7.475169
##  [8185] 7.414755 7.453672 7.180260 7.788093 7.643975 7.498676 7.320967 7.350975
##  [8193] 7.380721 7.588583 7.952359 7.385452 7.657016 7.159178 7.597361 7.359066
##  [8201] 7.780751 7.533985 7.591012 7.691410 7.386057 7.533450 7.452479 7.621452
##  [8209] 7.660391 7.625833 7.372604 7.410496 7.476576 7.824925 7.699214 7.405563
##  [8217] 7.528210 7.849889 7.459362 7.196429 7.508244 7.541395 7.273527 7.455814
##  [8225] 7.382668 7.597695 7.595109 7.938632 7.475487 7.312533 7.526777 7.710609
##  [8233] 7.374682 7.584270 7.478885 7.418556 7.889135 7.213049 7.679350 7.856936
##  [8241] 7.724524 7.660601 7.747714 7.727023 7.368894 7.655201 7.588861 7.452820
##  [8249] 7.274508 7.139444 7.545346 7.627714 7.636109 7.322232 7.694669 7.195899
##  [8257] 7.320203 7.424794 7.481215 7.832213 7.614178 7.440909 7.321604 7.549960
##  [8265] 7.846460 7.574314 7.620600 7.480845 7.193125 7.777844 8.064345 7.566089
##  [8273] 7.669419 7.287988 7.468677 7.531378 7.719933 7.234898 7.698962 7.501206
##  [8281] 7.200292 7.440035 7.951915 7.320489 7.493927 7.254292 7.368136 7.681241
##  [8289] 7.319908 7.899332 7.283504 7.271778 7.540252 7.470382 7.744827 7.705355
##  [8297] 7.612755 7.575477 7.444728 7.468119 7.582956 7.620492 7.658909 7.327463
##  [8305] 7.657187 7.419274 7.438346 7.409365 7.686854 7.674377 7.385697 7.417919
##  [8313] 7.550202 7.748681 7.454044 7.584357 7.233484 7.399168 7.681433 7.581535
##  [8321] 7.351412 7.366386 7.579442 7.654030 7.198198 7.439836 7.562554 7.788298
##  [8329] 7.180974 7.023441 7.707680 7.656729 7.446054 7.739150 7.676708 7.730087
##  [8337] 7.062241 7.680039 7.673952 8.040238 7.470137 7.214066 7.224710 7.719643
##  [8345] 7.725564 7.488198 7.438009 7.393348 7.532767 7.445661 7.450750 7.969378
##  [8353] 7.329669 7.709608 7.502250 7.954948 7.415914 7.380326 7.518078 7.362454
##  [8361] 7.533971 7.573852 7.540095 7.475566 7.723366 7.427201 7.571980 7.468505
##  [8369] 7.360339 7.495961 7.653775 7.475787 7.620315 7.309332 7.637717 7.337792
##  [8377] 7.434879 7.768400 7.151648 7.480173 7.551656 7.438599 7.437341 7.767536
##  [8385] 7.359591 7.600686 7.121118 7.644171 7.620091 7.235990 7.597502 7.905964
##  [8393] 7.751681 7.432089 7.962079 7.696384 7.547969 7.217188 7.426252 7.028275
##  [8401] 7.286910 7.339076 7.493315 7.744445 7.639608 7.598656 7.821200 7.415427
##  [8409] 7.251907 7.783668 7.341472 7.497086 7.262944 7.571048 7.283265 7.332570
##  [8417] 7.088871 7.558101 7.494878 7.383377 7.188703 7.742989 7.436751 7.143879
##  [8425] 7.677409 7.257003 7.714492 7.401517 7.488091 7.489912 7.894210 7.856023
##  [8433] 7.636005 7.441362 7.629336 7.245592 7.419995 7.429331 7.495684 7.666106
##  [8441] 7.377085 7.466437 7.388852 7.197796 7.343254 7.441263 7.319825 7.341286
##  [8449] 7.281414 7.332465 7.591636 7.594407 7.263749 7.557273 7.450547 7.230775
##  [8457] 7.640281 7.804154 7.351793 7.363565 7.449200 7.463308 7.588865 7.435813
##  [8465] 7.499715 7.697227 7.579008 7.758362 7.264123 7.393897 7.515347 7.730655
##  [8473] 7.378432 7.345341 7.647007 7.735312 7.487194 7.612476 7.248440 7.498867
##  [8481] 7.004019 7.349197 7.526463 7.299905 7.338304 7.564161 7.700484 7.760028
##  [8489] 7.598280 7.422129 7.727915 7.471503 7.195925 7.880169 7.523962 7.746428
##  [8497] 7.674201 7.479584 7.579951 7.376452 7.712232 7.683762 7.621845 7.203150
##  [8505] 7.464639 7.072260 7.397321 7.508930 7.508671 7.539183 7.481885 7.730420
##  [8513] 7.610476 7.480241 7.238667 7.300844 7.383027 7.349001 7.194953 7.135340
##  [8521] 7.598219 7.127424 7.460487 7.278508 7.544642 7.579260 7.223306 7.617496
##  [8529] 7.844956 7.147130 7.471196 7.457278 7.637994 7.463514 7.589522 7.332745
##  [8537] 7.899564 7.891530 7.731576 7.211145 7.749438 7.644074 7.531621 7.122574
##  [8545] 7.586801 7.287449 7.553691 8.008064 7.831344 7.755481 7.412726 7.686725
##  [8553] 7.449128 7.373263 7.651573 6.928392 7.691415 7.286873 7.357804 7.614542
##  [8561] 7.732447 7.377995 7.169420 7.585755 7.519288 7.471730 7.683074 7.514826
##  [8569] 7.873099 7.303165 7.499032 7.633048 7.159491 7.492622 7.572136 7.232365
##  [8577] 7.402901 7.314253 7.573438 7.228645 7.413832 7.483623 7.708705 7.719514
##  [8585] 7.561602 7.234992 7.215533 7.162374 7.407446 7.411898 7.551606 7.557665
##  [8593] 7.519691 7.741461 7.595264 7.343829 7.647072 7.357614 7.341526 7.420313
##  [8601] 7.323048 7.557075 7.248805 7.782990 7.667982 7.249017 7.394728 7.748130
##  [8609] 7.216365 7.480702 7.370885 7.508694 7.646156 7.173518 7.601734 7.665442
##  [8617] 7.737735 7.358393 7.409164 7.702805 7.279659 7.466113 7.246068 7.352452
##  [8625] 7.397866 7.674080 7.716579 7.356498 7.300668 7.196567 7.552219 7.689475
##  [8633] 7.456475 7.874419 7.652376 7.508801 7.604135 7.716371 7.479745 7.541564
##  [8641] 7.863247 7.376341 7.746335 7.227333 7.285617 7.286428 7.609982 7.229072
##  [8649] 7.245368 7.355824 7.540395 7.438238 7.376064 7.387365 7.123892 7.521618
##  [8657] 7.915490 7.609174 7.243088 7.754888 7.354773 7.488612 7.298359 7.440262
##  [8665] 7.347097 7.270062 7.874094 7.643926 7.623531 7.455257 7.296709 7.169775
##  [8673] 7.636273 7.544113 7.743182 7.629905 7.729049 7.732199 7.132036 7.881037
##  [8681] 7.671032 7.374495 7.294434 7.395577 7.453848 7.430599 7.657529 7.615230
##  [8689] 7.803414 7.530514 7.291862 7.782589 7.516221 7.290228 7.476586 7.321132
##  [8697] 7.766065 7.403534 7.508469 7.562512 7.454597 7.094500 7.176446 7.530285
##  [8705] 7.761727 7.120084 7.749873 7.649364 7.114652 7.578514 7.144472 8.010831
##  [8713] 7.589377 7.511427 7.319830 7.760065 7.346119 7.623631 7.803791 7.405907
##  [8721] 7.183065 7.457295 7.555562 7.335733 7.875324 7.823884 7.614334 7.872254
##  [8729] 7.926627 7.816411 7.680151 7.447179 7.518838 7.183913 7.882752 7.493621
##  [8737] 7.394179 7.428251 7.203535 7.598743 7.446621 7.629367 7.480270 7.438563
##  [8745] 7.500937 7.407183 7.534348 7.404563 7.401206 7.474151 7.611196 7.475217
##  [8753] 7.566666 7.639660 7.660865 7.273508 7.376242 7.648456 7.228225 7.461083
##  [8761] 7.564594 7.663873 7.732917 7.689281 7.412131 7.358897 7.443445 7.154388
##  [8769] 7.678362 7.250948 7.555663 7.951953 7.593499 7.360055 7.655875 7.729384
##  [8777] 7.588378 7.511395 7.492242 7.383503 7.835915 7.260179 7.555476 7.300396
##  [8785] 7.786001 7.484317 7.918869 7.827799 7.711630 7.453352 7.402022 7.423724
##  [8793] 7.550988 7.631785 7.681858 7.570096 7.636217 7.239069 7.173246 7.389498
##  [8801] 7.399133 7.439476 7.530032 7.151605 7.172838 7.503628 7.306126 7.467021
##  [8809] 7.424440 7.731975 7.840367 7.870869 7.668710 7.684426 7.606717 7.433993
##  [8817] 7.657157 7.445558 7.750533 7.302197 7.604003 7.436543 7.428413 7.221988
##  [8825] 7.560019 7.685249 7.487825 7.756113 7.806711 7.741870 7.582345 7.369631
##  [8833] 7.549887 7.643779 7.581091 7.239133 7.659443 7.115258 7.508002 7.716266
##  [8841] 7.709844 8.023016 7.371742 7.756199 7.572881 7.384485 7.548222 7.387522
##  [8849] 7.643065 7.769908 7.354454 7.824725 7.690494 7.360122 7.542295 7.429444
##  [8857] 7.631430 7.293244 7.695822 7.313119 7.347536 7.181757 7.440233 7.328917
##  [8865] 7.349291 7.559212 7.447103 7.438764 7.525260 7.574937 7.355038 7.809337
##  [8873] 7.618292 7.332845 7.497434 7.529777 7.767153 7.876793 7.501125 7.253584
##  [8881] 7.537621 7.167118 7.120489 7.742903 7.373247 7.570791 7.534116 7.148442
##  [8889] 7.771084 7.388101 7.520164 7.740128 7.510607 7.320517 7.542888 7.715480
##  [8897] 7.420547 7.526632 7.568860 7.413295 7.819717 7.399588 7.662417 7.714430
##  [8905] 7.404142 7.893329 7.408984 7.449757 7.430226 7.819475 7.421682 7.434930
##  [8913] 7.616131 7.310518 7.405109 7.636765 7.543636 7.482719 7.331285 7.405184
##  [8921] 7.657517 7.726169 7.717519 7.570063 7.527122 7.369424 7.115915 7.389406
##  [8929] 7.157356 7.121192 7.510455 7.760938 7.719072 7.362870 7.395918 7.527627
##  [8937] 7.524676 7.474686 7.571151 7.426720 7.342399 7.520881 7.378934 7.313881
##  [8945] 7.324024 7.591664 7.585397 7.495485 7.612198 7.447515 7.476514 7.370102
##  [8953] 7.181787 7.627544 7.083836 7.681695 7.016920 7.671948 7.471496 7.631355
##  [8961] 7.594165 7.605892 7.502045 7.566167 7.364984 7.523103 7.647593 7.444694
##  [8969] 7.917788 7.470651 7.725638 7.384444 7.654833 7.714375 7.667927 7.601679
##  [8977] 7.107282 7.620819 7.950265 7.911657 7.651533 7.922787 7.402495 7.708407
##  [8985] 7.699465 7.512686 7.755529 7.495347 7.690197 7.559474 7.936657 7.701646
##  [8993] 7.726210 7.347912 7.527099 7.372877 7.484023 7.310819 7.181439 7.812983
##  [9001] 7.403854 7.371495 7.775933 7.266617 7.718607 7.628127 7.474798 7.533004
##  [9009] 7.598768 7.326627 7.815672 7.450059 7.429519 8.079808 7.437052 7.486749
##  [9017] 7.563810 7.259618 7.760564 7.377846 7.378096 7.255980 7.588819 7.567277
##  [9025] 7.196277 7.433528 7.420774 7.630951 7.470603 7.464335 7.672963 7.233534
##  [9033] 7.698668 7.502384 7.650030 7.590120 7.987403 7.658228 7.598005 7.363752
##  [9041] 7.557075 7.690319 7.836319 7.358980 7.205639 7.126205 7.533560 7.392475
##  [9049] 7.431065 7.613508 7.622059 7.472317 7.372143 7.759480 7.292832 7.596511
##  [9057] 7.723326 7.388217 7.348121 7.921928 7.634606 7.560927 7.904838 7.422397
##  [9065] 7.486658 7.184443 6.985586 7.249710 7.534896 7.452183 7.717039 7.639013
##  [9073] 7.229464 7.473682 7.489222 7.423119 7.531009 7.367349 7.633443 7.632773
##  [9081] 7.583164 7.588675 7.566714 7.747442 7.407696 7.555222 7.393622 7.535600
##  [9089] 7.353791 7.357834 7.825196 7.343624 7.694108 7.589866 7.897276 7.288424
##  [9097] 7.663101 7.395837 7.696850 7.434089 7.671738 7.933172 7.554643 7.675150
##  [9105] 7.595440 7.587366 7.627557 7.624685 7.161099 7.605715 7.744894 7.440712
##  [9113] 7.541019 7.482053 7.658874 7.227365 7.302120 7.594019 7.947472 7.506028
##  [9121] 7.416694 7.395531 7.256667 7.534679 7.125715 7.617202 7.061594 7.873729
##  [9129] 7.838744 7.141850 7.753333 7.392693 7.816238 7.716277 7.237594 7.641518
##  [9137] 7.445577 7.322583 7.639525 7.330347 7.207880 7.650389 7.588160 7.464553
##  [9145] 7.109354 7.179170 7.823295 7.461279 7.498554 7.391834 8.002096 7.629166
##  [9153] 7.414293 7.378377 7.306490 7.541657 7.898692 7.392144 7.933493 7.399667
##  [9161] 7.517928 7.731434 7.423360 7.522749 7.132833 7.672225 7.162425 7.551845
##  [9169] 7.587624 7.553460 7.247657 7.293364 7.071769 7.097920 7.881005 7.551128
##  [9177] 7.885869 7.185382 7.721389 7.641642 7.364382 7.090643 7.568536 7.445961
##  [9185] 7.262681 7.388525 7.070822 7.181893 7.544379 7.623690 7.943256 7.748063
##  [9193] 7.848886 7.750557 7.725080 7.275958 7.859574 7.614944 7.608555 7.347924
##  [9201] 7.538461 7.407283 7.834931 7.633218 7.535581 7.423741 7.647718 7.686915
##  [9209] 7.579288 7.239603 7.726426 7.158122 7.489007 7.193207 7.505421 7.519012
##  [9217] 7.055629 7.946083 7.694635 7.621509 7.286919 7.630920 7.578701 7.912904
##  [9225] 7.539013 7.695467 7.345693 7.882492 6.991191 7.342019 7.547858 7.641042
##  [9233] 7.601457 7.450140 7.676225 7.596645 7.433657 7.134690 7.634491 7.478803
##  [9241] 7.879302 7.653090 7.495732 7.585347 7.699302 7.321939 7.794091 7.365018
##  [9249] 7.692460 7.545669 7.553665 7.675605 7.395145 7.626318 7.858160 7.735580
##  [9257] 7.535902 7.510812 7.653222 7.291155 7.412343 7.613163 7.523776 7.215904
##  [9265] 7.279998 7.725828 7.296734 7.724423 7.692442 7.305200 7.472317 7.133697
##  [9273] 6.960197 7.924691 7.441837 7.393061 7.366815 7.276891 7.721248 7.634895
##  [9281] 7.462272 7.288979 7.530207 7.119239 7.061980 7.503311 7.769094 7.473997
##  [9289] 7.579405 7.461811 7.599094 7.386246 7.498182 7.947010 7.525721 7.151598
##  [9297] 7.616662 7.610629 7.656127 7.832299 7.418065 7.623850 7.685536 7.530578
##  [9305] 7.532092 7.899577 7.302284 7.077586 7.447478 7.713660 7.472241 7.252705
##  [9313] 7.336684 7.767944 7.567208 7.799499 7.497982 7.411407 7.311895 7.533898
##  [9321] 7.564284 7.664779 7.695946 7.795384 7.353374 7.389621 7.622845 7.513821
##  [9329] 7.560917 7.512433 7.197096 7.899405 7.335948 7.182571 7.489693 7.713853
##  [9337] 7.344006 7.584401 7.400325 7.751444 7.479933 7.582458 7.801318 7.610158
##  [9345] 7.231897 7.384984 7.207983 7.353908 7.118971 7.889919 7.374779 7.363951
##  [9353] 7.454241 7.490054 7.331578 7.561090 7.179749 7.252838 7.598200 7.484972
##  [9361] 7.438100 7.432333 7.650637 7.501566 6.968418 7.526456 7.513463 7.369352
##  [9369] 7.501553 7.908008 7.306475 7.620376 7.852360 7.594682 7.506731 7.383347
##  [9377] 7.545657 7.338727 7.415206 7.881717 7.194505 7.230952 7.508213 7.216090
##  [9385] 7.212473 7.366093 7.634667 7.686751 7.476740 7.892531 7.296069 7.395285
##  [9393] 7.569297 7.506161 7.592216 7.247682 7.878280 7.492707 7.103937 7.104887
##  [9401] 7.444435 7.478263 7.726055 7.345395 7.440447 7.183512 7.669695 7.411933
##  [9409] 7.531994 7.589161 7.508111 7.315483 7.406661 7.443548 7.502882 7.469338
##  [9417] 7.460549 7.488176 7.135668 7.804007 7.402821 7.379082 7.277079 7.465637
##  [9425] 7.481310 7.617532 7.408140 7.847345 7.304160 7.514265 7.536198 7.130407
##  [9433] 7.438976 7.840871 7.654359 7.376054 7.549890 7.449464 7.821870 7.573325
##  [9441] 7.165430 7.379035 7.773724 7.569158 7.307977 7.327097 7.418220 7.622092
##  [9449] 7.288854 7.285238 7.529679 7.803658 7.909028 7.561417 7.553594 7.227950
##  [9457] 7.472745 7.668480 7.605408 7.584771 7.323439 7.355490 7.383369 7.654419
##  [9465] 7.424746 7.276053 7.659489 7.528714 7.444583 7.434779 7.777684 7.531206
##  [9473] 7.638188 7.555977 7.398292 7.486353 7.945426 7.598705 7.434757 7.178803
##  [9481] 7.387503 7.294059 7.471286 7.466462 7.405608 7.407521 7.408181 7.459807
##  [9489] 7.565014 7.220398 7.411398 7.437455 7.383482 7.491534 7.366304 7.365698
##  [9497] 7.475213 7.552617 7.390716 7.662900 7.512115 7.661115 7.352402 7.461231
##  [9505] 7.670107 7.607570 7.319492 7.632510 7.368283 7.660897 7.530715 7.495354
##  [9513] 7.439513 7.254384 7.133232 7.857490 7.298297 7.474958 7.613991 7.477896
##  [9521] 7.284009 7.077126 7.547089 7.183714 7.743536 7.681913 7.485830 7.525706
##  [9529] 7.650200 7.584386 7.197017 7.357938 7.656196 7.311380 7.147797 7.580459
##  [9537] 7.392623 7.583871 7.464790 7.127267 7.650528 7.766580 7.133800 7.394819
##  [9545] 7.585650 7.636785 7.363721 7.213268 7.390294 7.689507 7.454428 7.467012
##  [9553] 7.532940 7.480067 7.557635 7.583394 7.642561 8.032516 7.531019 7.790448
##  [9561] 7.630637 7.504031 7.279093 6.994361 7.246601 7.483283 7.351086 7.658006
##  [9569] 7.637803 7.647175 7.546116 7.526390 6.994759 7.388039 7.582005 7.577603
##  [9577] 7.653883 7.951317 7.519640 7.214522 7.447122 7.271654 7.673005 7.580176
##  [9585] 7.857720 7.286094 7.382580 7.749218 7.574544 7.525048 7.424968 7.656781
##  [9593] 7.785412 7.469454 7.761695 7.428816 7.295336 7.106963 7.258329 7.316944
##  [9601] 7.842454 7.503527 7.493999 7.262111 7.563106 7.353457 7.745157 7.795106
##  [9609] 7.878582 7.454008 7.469518 7.521750 7.744759 7.708966 7.707696 7.657160
##  [9617] 7.606474 7.797107 7.337867 7.592359 7.339267 7.458212 7.638753 7.429242
##  [9625] 7.679103 7.497435 7.492510 7.327842 7.550938 7.661353 7.460428 7.339919
##  [9633] 7.282220 7.370578 7.644248 7.214226 7.650400 7.283965 7.885197 7.839921
##  [9641] 7.389896 7.253563 7.226479 7.612964 6.948594 7.610276 7.648039 7.561935
##  [9649] 7.922678 7.526190 7.449294 7.638309 7.195724 7.480792 7.824620 7.330024
##  [9657] 7.387092 7.333390 7.307286 7.721644 7.823335 7.667085 7.398447 7.570582
##  [9665] 7.128733 7.855012 7.687452 7.683215 7.375575 7.246226 7.598162 7.611514
##  [9673] 7.674150 7.273463 7.498388 7.403729 7.863362 7.327257 7.619488 7.573392
##  [9681] 7.248602 7.414662 7.210391 7.485068 7.419894 7.396574 7.815220 7.375395
##  [9689] 7.644487 7.719880 7.513648 7.307400 7.314638 7.368634 7.708211 7.490106
##  [9697] 7.526546 7.147141 7.612552 7.292958 7.756059 7.548590 7.589377 7.597215
##  [9705] 7.678773 7.426197 7.535562 7.629260 7.626610 7.508258 7.398645 7.485755
##  [9713] 7.220770 7.820930 7.786392 7.398064 7.763666 7.356022 7.597509 7.574228
##  [9721] 7.554065 7.620811 7.877495 7.302724 7.227054 7.534520 7.414410 7.098206
##  [9729] 7.553407 7.508381 7.685247 7.541552 7.221908 7.615810 7.850364 7.518906
##  [9737] 7.775945 8.111801 7.409700 7.420035 7.321447 7.441858 7.305154 7.465175
##  [9745] 7.047961 7.408831 7.440206 7.656756 7.694068 7.729411 7.287354 7.821624
##  [9753] 7.627546 7.613072 7.158745 7.466944 7.388963 7.600633 7.748760 7.701953
##  [9761] 7.079753 7.688195 7.649644 7.782726 7.498425 7.298865 7.696012 7.482454
##  [9769] 7.319813 7.480413 7.222715 7.550331 7.532214 7.378103 7.310682 7.209370
##  [9777] 7.351529 7.411127 7.812368 7.639517 7.329929 7.310467 7.495788 7.731296
##  [9785] 7.655051 7.490589 7.544094 7.527354 7.449010 7.285882 7.244250 7.539268
##  [9793] 7.393096 7.773731 7.041236 7.357172 7.441033 7.917181 7.414630 7.319278
##  [9801] 7.419914 7.379272 7.129131 7.739399 7.542930 7.783651 7.877785 7.291248
##  [9809] 7.979804 7.551911 7.150961 7.269855 7.881560 7.329114 7.671661 7.455237
##  [9817] 7.430299 7.412043 7.620166 7.422525 7.339197 7.733095 7.544867 7.480530
##  [9825] 7.108895 7.596228 7.335999 7.431544 7.610369 7.230938 7.569313 7.209497
##  [9833] 7.731969 7.516379 7.540259 7.588040 7.197067 7.455798 7.488341 7.263060
##  [9841] 7.537020 7.915219 7.471030 7.910640 7.247936 7.517608 7.627978 7.205089
##  [9849] 7.866064 7.043842 7.635781 7.601154 7.211636 7.668831 7.565204 7.507874
##  [9857] 7.721876 7.274218 7.608463 7.406895 7.616015 7.594191 7.592997 7.382669
##  [9865] 7.568033 7.643133 7.841716 7.570741 7.255270 7.543840 7.710819 7.800399
##  [9873] 7.336704 7.320697 7.293670 7.754908 7.427363 7.741849 7.756820 7.514183
##  [9881] 7.664764 7.451964 7.509687 7.886966 7.695721 7.818002 7.441121 7.655173
##  [9889] 7.539140 7.527478 7.803420 7.680150 7.908185 7.942794 7.540385 7.825924
##  [9897] 7.631056 7.666388 7.435556 7.383648 7.444049 7.809711 7.886612 7.189535
##  [9905] 7.655329 7.359670 7.410170 7.469646 7.488595 8.249679 7.625780 7.511487
##  [9913] 7.698956 7.358616 7.590177 8.003329 7.637898 7.123924 7.514784 7.609311
##  [9921] 7.699613 7.859719 7.528332 7.608313 7.417943 7.379768 7.316102 8.052786
##  [9929] 7.387386 7.485034 7.764738 7.582830 7.336849 7.389327 7.624567 7.842977
##  [9937] 7.436365 7.299009 7.333706 7.499196 7.339405 7.657543 7.485807 7.301273
##  [9945] 7.998852 7.794038 8.005363 7.646560 7.416640 7.932852 7.687021 7.324593
##  [9953] 7.304950 7.755070 7.511999 7.281953 7.679835 7.692777 7.413769 7.448791
##  [9961] 7.746220 7.311698 7.574053 7.920207 7.595034 7.400478 7.517295 7.553473
##  [9969] 7.561335 7.228140 7.631520 7.791545 7.493772 7.410120 7.634612 7.461511
##  [9977] 7.281849 7.387172 7.893659 7.560742 7.715801 7.889425 7.820679 7.615911
##  [9985] 7.797871 7.529049 7.513953 7.366364 7.482366 7.558933 7.565779 7.609574
##  [9993] 7.231302 7.239368 7.358989 7.571432 7.685935 7.374688 7.568637 7.464823

mean(w)

## [1] 7.500525

var(w)

## [1] 0.04089373

Task 3

The apply function uses the 2 to run the operation on the columns of the matrix data.

There are 100,000 values in w when mycltu(n=20,iter=100000) is called.

Standard deviation takes the form (b-a)/sqrt(12*n) because as proved in task 2 \(V(\bar Y)=\frac{\sigma^2_i}{n}=\frac{(b-a)^2}{12*n}\)

Thus, \(\sigma_{\bar Y}=\frac{b-a}{\sqrt{12*n}}\)

mycltu=function(n,iter,a=0,b=10){
## r-random sample from the uniform
y=runif(n*iter,a,b)
## Place these numbers into a matrix
## The columns will correspond to the iteration and the rows will equal the sample size n
data=matrix(y,nr=n,nc=iter,byrow=TRUE)
## apply the function mean to the columns (2) of the matrix
## these are placed in a vector w
w=apply(data,2,mean)
## We will make a histogram of the values in w
## How high should we make y axis?
## All the values used to make a histogram are placed in param (nothing is plotted yet)
param=hist(w,plot=FALSE)
## Since the histogram will be a density plot we will find the max density

ymax=max(param$density)
## To be on the safe side we will add 10% more to this
ymax=1.1*ymax
## Now we can make the histogram
hist(w,freq=FALSE,  ylim=c(0,ymax), main=paste("Histogram of sample mean",
"\n", "sample size= ",n,sep=""),xlab="Sample mean")
## add a density curve made from the sample distribution
lines(density(w),col="Blue",lwd=3) # add a density plot
## Add a theoretical normal curve 
curve(dnorm(x,mean=(a+b)/2,sd=(b-a)/(sqrt(12*n))),add=TRUE,col="Red",lty=2,lwd=3) # add a theoretical curve
## Add the density from which the samples were taken
curve(dunif(x,a,b),add=TRUE,lwd=4)

}
mycltu(n=1,iter=10000,a=0,b=10)

mycltu(n=2,iter=10000,a=0,b=10)

mycltu(n=3,iter=10000,a=0,b=10)

mycltu(n=5,iter=10000,a=0,b=10)

mycltu(n=10,iter=10000,a=0,b=10)

mycltu(n=30,iter=10000,a=0,b=10)

As n got larger the distribution went from a uniform distribution to a normal distribution which is what the Central Limit Theorem said would happen.

Task 4

mycltb=function(n,iter,p=0.5,...){

## r-random sample from the Binomial
y=rbinom(n*iter,size=n,prob=p)
## Place these numbers into a matrix
## The columns will correspond to the iteration and the rows will equal the sample size n
data=matrix(y,nr=n,nc=iter,byrow=TRUE)
## apply the function mean to the columns (2) of the matrix
## these are placed in a vector w
w=apply(data,2,mean)
## We will make a histogram of the values in w
## How high should we make y axis?
## All the values used to make a histogram are placed in param (nothing is plotted yet)
param=hist(w,plot=FALSE)
## Since the histogram will be a density plot we will find the max density

ymax=max(param$density)
## To be on the safe side we will add 10% more to this
ymax=1.1*ymax

## Now we can make the histogram
## freq=FALSE means take a density
hist(w,freq=FALSE,  ylim=c(0,ymax),
main=paste("Histogram of sample mean","\n", "sample size= ",n,sep=""),
xlab="Sample mean",...)
## add a density curve made from the sample distribution
#lines(density(w),col="Blue",lwd=3) # add a density plot
## Add a theoretical normal curve 
curve(dnorm(x,mean=n*p,sd=sqrt(p*(1-p))),add=TRUE,col="Red",lty=2,lwd=3) 

}

mycltb(n=4,iter=10000,p=0.3)

mycltb(n=5,iter=10000,p=0.3)

mycltb(n=10,iter=10000,p=0.3)

mycltb(n=20,iter=10000,p=0.3)

mycltb(n=4,iter=10000,p=0.7)

mycltb(n=5,iter=10000,p=0.7)

mycltb(n=10,iter=10000,p=0.7)

mycltb(n=20,iter=10000,p=0.7)

mycltb(n=4,iter=10000,p=0.5)

mycltb(n=5,iter=10000,p=0.5)

mycltb(n=10,iter=10000,p=0.5)

mycltb(n=20,iter=10000,p=0.5)

This shows that the Central Limit Theorem also holds true for Binomial distributions.

Task 5

mycltp=function(n,iter,lambda=10,...){

## r-random sample from the Poisson
y=rpois(n*iter,lambda=lambda)
## Place these numbers into a matrix
## The columns will correspond to the iteration and the rows will equal the sample size n
data=matrix(y,nr=n,nc=iter,byrow=TRUE)
## apply the function mean to the columns (2) of the matrix
## these are placed in a vector w
w=apply(data,2,mean)
## We will make a histogram of the values in w
## How high should we make y axis?
## All the values used to make a histogram are placed in param (nothing is plotted yet)
param=hist(w,plot=FALSE)
## Since the histogram will be a density plot we will find the max density

ymax=max(param$density)
## To be on the safe side we will add 10% more to this
ymax=1.1*ymax

## Make a suitable layout for graphing
layout(matrix(c(1,1,2,3),nr=2,nc=2, byrow=TRUE))

## Now we can make the histogram
hist(w,freq=FALSE,  ylim=c(0,ymax), col=rainbow(max(w)),
main=paste("Histogram of sample mean","\n", "sample size= ",n," iter=",iter," lambda=",lambda,sep=""),
xlab="Sample mean",...)
## add a density curve made from the sample distribution
#lines(density(w),col="Blue",lwd=3) # add a density plot
## Add a theoretical normal curve 
curve(dnorm(x,mean=lambda,sd=sqrt(lambda/n)),add=TRUE,col="Red",lty=2,lwd=3) # add a theoretical curve

# Now make a new plot
# Since y is discrete we should use a barplot
barplot(table(y)/(n*iter),col=rainbow(max(y)), main="Barplot of sampled y", ylab ="Rel. Freq",xlab="y" )
x=0:max(y)
plot(x,dpois(x,lambda=lambda),type="h",lwd=5,col=rainbow(max(y)),
main="Probability function for Poisson", ylab="Probability",xlab="y")
}


mycltp(n=2,iter=10000,lambda=4)

mycltp(n=3,iter=10000,lambda=4)

mycltp(n=5,iter=10000,lambda=4)

mycltp(n=10,iter=10000,lambda=4)

mycltp(n=20,iter=10000,lambda=4)

mycltp(n=2,iter=10000,lambda=10)

mycltp(n=3,iter=10000,lambda=10)

mycltp(n=5,iter=10000,lambda=10)

mycltp(n=10,iter=10000,lambda=10)

mycltp(n=20,iter=10000,lambda=10)

Task 6

MATH4753GRAY::mycltp

## function(n,iter,lambda=10,...){
## 
##   ## r-random sample from the Poisson
##   y=rpois(n*iter,lambda=lambda)
##   ## Place these numbers into a matrix
##   ## The columns will correspond to the iteration and the rows will equal the sample size n
##   data=matrix(y,nr=n,nc=iter,byrow=TRUE)
##   ## apply the function mean to the columns (2) of the matrix
##   ## these are placed in a vector w
##   w=apply(data,2,mean)
##   ## We will make a histogram of the values in w
##   ## How high should we make y axis?
##   ## All the values used to make a histogram are placed in param (nothing is plotted yet)
##   param=hist(w,plot=FALSE)
##   ## Since the histogram will be a density plot we will find the max density
## 
##   ymax=max(param$density)
##   ## To be on the safe side we will add 10% more to this
##   ymax=1.1*ymax
## 
##   ## Make a suitable layout for graphing
##   layout(matrix(c(1,1,2,3),nr=2,nc=2, byrow=TRUE))
## 
##   ## Now we can make the histogram
##   hist(w,freq=FALSE,  ylim=c(0,ymax), col=rainbow(max(w)),
##        main=paste("Histogram of sample mean","\n", "sample size= ",n," iter=",iter," lambda=",lambda,sep=""),
##        xlab="Sample mean",...)
##   ## add a density curve made from the sample distribution
##   #lines(density(w),col="Blue",lwd=3) # add a density plot
##   ## Add a theoretical normal curve
##   curve(dnorm(x,mean=lambda,sd=sqrt(lambda/n)),add=TRUE,col="Red",lty=2,lwd=3) # add a theoretical curve
## 
##   # Now make a new plot
##   # Since y is discrete we should use a barplot
##   barplot(table(y)/(n*iter),col=rainbow(max(y)), main="Barplot of sampled y", ylab ="Rel. Freq",xlab="y" )
##   x=0:max(y)
##   plot(x,dpois(x,lambda=lambda),type="h",lwd=5,col=rainbow(max(y)),
##        main="Probability function for Poisson", ylab="Probability",xlab="y")
## }
## <bytecode: 0x0000000013562cc8>
## <environment: namespace:MATH4753GRAY>