ACTIVIDAD_2_PROBLEMA_3
JOHN WILMAR VARGAS MENDEZ
2023-09-15
Problema 3: Teorema del limite central
Para este ejercicio se hace la sigueinte funcion:
ademas se desarrolla el punto c
p3<- function(n) {
Teorema<-matrix(,n,n)
exito<-rep(1,500)
fracaso<-rep(0,500)
lote<-c(exito,fracaso)
for (i in 1:n) {
Teorema[i,]=sample(lote, n, replace = FALSE, prob = NULL)
}
pi<-rowSums(Teorema)/n
promedio<-(mean(pi))
#print(pi)
#print(pi)
print(shapiro.test(pi))
print(qqnorm(pi))
print(promedio)
}
p3(100)##
## Shapiro-Wilk normality test
##
## data: pi
## W = 0.98885, p-value = 0.5727
## $x
## [1] -1.10306256 -1.05812162 -1.81191067 -0.42614801 -0.11303854 -0.39885507
## [7] -0.08784484 -1.31057911 -0.93458929 1.81191067 -2.57582930 -0.06270678
## [13] -0.89647336 -0.37185609 -1.01522203 0.45376219 1.95996398 -0.03760829
## [19] -0.62800601 -1.69539771 -0.59776013 0.29237490 -0.72247905 -0.34512553
## [25] -0.85961736 -1.25356544 -1.59819314 -0.31863936 1.51410189 0.85961736
## [31] -0.29237490 0.48172685 0.51007346 1.59819314 0.89647336 1.20035886
## [37] -0.56805150 -1.20035886 -0.53883603 0.93458929 0.13830421 0.97411388
## [43] 1.25356544 -0.97411388 0.16365849 2.17009038 -1.51410189 0.18911843
## [49] -0.69030882 -0.65883769 -0.26631061 -2.17009038 0.31863936 -0.24042603
## [55] -0.82389363 0.34512553 -0.01253347 0.01253347 1.31057911 0.53883603
## [61] 1.37220381 0.69030882 0.72247905 0.03760829 0.75541503 1.43953147
## [67] -1.95996398 -0.21470157 -0.78919165 0.56805150 0.37185609 0.39885507
## [73] 1.01522203 1.05812162 0.78919165 -0.18911843 -1.37220381 0.21470157
## [79] -1.15034938 0.06270678 0.82389363 -1.43953147 -0.16365849 1.69539771
## [85] -0.75541503 0.59776013 0.62800601 2.57582930 -0.13830421 0.42614801
## [91] 1.10306256 1.15034938 -0.51007346 0.08784484 -0.48172685 0.11303854
## [97] -0.45376219 0.24042603 0.65883769 0.26631061
##
## $y
## [1] 0.45 0.45 0.41 0.49 0.50 0.49 0.50 0.44 0.46 0.60 0.38 0.50 0.46 0.49 0.45
## [16] 0.53 0.60 0.50 0.48 0.42 0.48 0.52 0.47 0.49 0.46 0.44 0.42 0.49 0.57 0.55
## [31] 0.49 0.53 0.53 0.57 0.55 0.56 0.48 0.44 0.48 0.55 0.51 0.55 0.56 0.45 0.51
## [46] 0.62 0.42 0.51 0.47 0.47 0.49 0.40 0.52 0.49 0.46 0.52 0.50 0.50 0.56 0.53
## [61] 0.56 0.54 0.54 0.50 0.54 0.56 0.40 0.49 0.46 0.53 0.52 0.52 0.55 0.55 0.54
## [76] 0.49 0.43 0.51 0.44 0.50 0.54 0.42 0.49 0.57 0.46 0.53 0.53 0.62 0.49 0.52
## [91] 0.55 0.55 0.48 0.50 0.48 0.50 0.48 0.51 0.53 0.51
##
## [1] 0.5014Por lo anterior, se tiene que el estimador tiende a el parametro poblacional ya que la cantidad de obervaciones, este es la regla de oro del teorema del limite centrar ya que por esto entre mas grande la muestra los estimadores seran muy cercanos a los parametros poblacionales.
Ademas por viendo la normalidad de los datos se ve que se cumple con este supuesto ya que el p valor es mayor al 5%.
punto D
p3(5)##
## Shapiro-Wilk normality test
##
## data: pi
## W = 0.88104, p-value = 0.314
## $x
## [1] 0.0000000 -1.1797611 1.1797611 0.4972006 -0.4972006
##
## $y
## [1] 0.6 0.4 0.8 0.6 0.4
##
## [1] 0.56p3(10)##
## Shapiro-Wilk normality test
##
## data: pi
## W = 0.91416, p-value = 0.3108
## $x
## [1] -0.1225808 -0.6554235 1.0004905 0.1225808 -1.5466353 -0.3754618
## [7] 0.3754618 1.5466353 -1.0004905 0.6554235
##
## $y
## [1] 0.5 0.4 0.6 0.5 0.2 0.4 0.5 0.8 0.2 0.5
##
## [1] 0.46p3(15)##
## Shapiro-Wilk normality test
##
## data: pi
## W = 0.96631, p-value = 0.8002
## $x
## [1] -0.7279133 -0.5244005 0.7279133 -0.3406948 0.1678940 -0.1678940
## [7] 0.3406948 -1.8339146 1.8339146 0.0000000 0.5244005 0.9674216
## [13] -1.2815516 1.2815516 -0.9674216
##
## $y
## [1] 0.4000000 0.4000000 0.6000000 0.4000000 0.5333333 0.4666667 0.5333333
## [8] 0.2666667 0.7333333 0.4666667 0.5333333 0.6000000 0.3333333 0.6000000
## [15] 0.3333333
##
## [1] 0.48p3(20)##
## Shapiro-Wilk normality test
##
## data: pi
## W = 0.95937, p-value = 0.5314
## $x
## [1] 1.43953147 0.59776013 -0.93458929 -0.06270678 -0.75541503 -1.43953147
## [7] -0.59776013 -1.15034938 -0.45376219 0.31863936 1.95996398 -0.31863936
## [13] 0.45376219 0.06270678 -0.18911843 0.75541503 -1.95996398 0.93458929
## [19] 1.15034938 0.18911843
##
## $y
## [1] 0.70 0.55 0.35 0.45 0.35 0.30 0.40 0.30 0.40 0.50 0.70 0.40 0.50 0.45 0.40
## [16] 0.55 0.25 0.55 0.60 0.45
##
## [1] 0.4575p3(30)##
## Shapiro-Wilk normality test
##
## data: pi
## W = 0.97654, p-value = 0.7281
## $x
## [1] -0.3853205 0.4770404 2.1280452 0.0417893 0.5729675 -1.0364334
## [7] 1.1918162 -2.1280452 -0.9027348 0.9027348 -0.2967378 0.1256613
## [13] -0.6744898 -0.5729675 -0.7835004 0.6744898 0.7835004 -1.6448536
## [19] 1.3829941 0.2104284 -1.3829941 -1.1918162 -0.4770404 0.2967378
## [25] 1.0364334 1.6448536 -0.2104284 0.3853205 -0.1256613 -0.0417893
##
## $y
## [1] 0.5000000 0.5666667 0.6666667 0.5333333 0.5666667 0.4333333 0.6333333
## [8] 0.3333333 0.4333333 0.6000000 0.5000000 0.5333333 0.4666667 0.4666667
## [15] 0.4333333 0.5666667 0.5666667 0.4000000 0.6333333 0.5333333 0.4000000
## [22] 0.4000000 0.4666667 0.5333333 0.6000000 0.6333333 0.5000000 0.5333333
## [29] 0.5000000 0.5000000
##
## [1] 0.5144444p3(50)##
## Shapiro-Wilk normality test
##
## data: pi
## W = 0.98022, p-value = 0.5613
## $x
## [1] 1.88079361 -0.67448975 -1.88079361 -0.17637416 1.12639113 0.95416525
## [7] -0.12566135 1.22652812 -1.03643339 0.33185335 1.34075503 0.38532047
## [13] 0.43991317 -0.95416525 -0.07526986 -0.02506891 -0.61281299 -1.34075503
## [19] -1.22652812 0.07526986 0.12566135 -0.87789630 0.49585035 0.02506891
## [25] -1.12639113 0.17637416 0.55338472 0.61281299 -0.55338472 -0.80642125
## [31] 1.47579103 -0.73884685 -0.49585035 0.67448975 -0.43991317 -0.38532047
## [37] -0.33185335 0.73884685 -0.27931903 -1.64485363 -2.32634787 1.03643339
## [43] 1.64485363 -0.22754498 0.80642125 2.32634787 0.22754498 -1.47579103
## [49] 0.27931903 0.87789630
##
## $y
## [1] 0.60 0.46 0.38 0.48 0.56 0.54 0.48 0.56 0.44 0.52 0.56 0.52 0.52 0.44 0.48
## [16] 0.48 0.46 0.42 0.42 0.50 0.50 0.44 0.52 0.48 0.42 0.50 0.52 0.52 0.46 0.44
## [31] 0.56 0.44 0.46 0.52 0.46 0.46 0.46 0.52 0.46 0.40 0.36 0.54 0.56 0.46 0.52
## [46] 0.64 0.50 0.40 0.50 0.52
##
## [1] 0.4872p3(60)##
## Shapiro-Wilk normality test
##
## data: pi
## W = 0.97492, p-value = 0.252
## $x
## [1] 0.14674496 -0.75541503 -1.56891963 0.50058011 -0.70095142 -1.33056151
## [7] -0.64849218 0.18911843 -0.59776013 0.75541503 0.81221780 0.54852228
## [13] -2.39397980 -0.18911843 -0.93458929 1.15034938 0.59776013 0.23183436
## [19] 0.64849218 0.87177097 -0.14674496 -1.43953147 1.95996398 -0.10463346
## [25] -1.23544034 1.23544034 -0.87177097 -0.06270678 -0.54852228 -1.15034938
## [31] 1.56891963 0.93458929 -0.50058011 2.39397980 1.00133130 0.27497775
## [37] 0.31863936 -0.45376219 0.36291730 -1.07286134 -0.02089009 1.33056151
## [43] -0.40791874 0.02089009 -1.00133130 0.70095142 -1.95996398 0.06270678
## [49] 0.40791874 1.07286134 -0.36291730 -0.31863936 0.10463346 1.73166440
## [55] 0.45376219 -0.27497775 -1.73166440 -0.23183436 -0.81221780 1.43953147
##
## $y
## [1] 0.5166667 0.4833333 0.4333333 0.5333333 0.4833333 0.4500000 0.4833333
## [8] 0.5166667 0.4833333 0.5500000 0.5500000 0.5333333 0.4166667 0.5000000
## [15] 0.4666667 0.5666667 0.5333333 0.5166667 0.5333333 0.5500000 0.5000000
## [22] 0.4333333 0.6166667 0.5000000 0.4500000 0.5666667 0.4666667 0.5000000
## [29] 0.4833333 0.4500000 0.5833333 0.5500000 0.4833333 0.6333333 0.5500000
## [36] 0.5166667 0.5166667 0.4833333 0.5166667 0.4500000 0.5000000 0.5666667
## [43] 0.4833333 0.5000000 0.4500000 0.5333333 0.4166667 0.5000000 0.5166667
## [50] 0.5500000 0.4833333 0.4833333 0.5000000 0.6000000 0.5166667 0.4833333
## [57] 0.4166667 0.4833333 0.4666667 0.5666667
##
## [1] 0.5061111p3(100)##
## Shapiro-Wilk normality test
##
## data: pi
## W = 0.98581, p-value = 0.3627
## $x
## [1] 0.01253347 1.31057911 -1.01522203 -1.81191067 0.78919165 -0.39885507
## [7] 1.37220381 0.45376219 0.03760829 -0.16365849 -0.37185609 -0.13830421
## [13] -0.69030882 -1.37220381 -0.93458929 0.97411388 -0.89647336 -0.85961736
## [19] -0.11303854 0.82389363 -0.65883769 -1.95996398 1.81191067 0.85961736
## [25] -0.62800601 0.51007346 -0.34512553 0.26631061 -0.31863936 0.06270678
## [31] 0.29237490 -0.08784484 1.43953147 0.08784484 2.17009038 0.48172685
## [37] 0.11303854 0.53883603 0.56805150 0.31863936 0.13830421 -0.06270678
## [43] 1.01522203 1.05812162 -0.29237490 0.34512553 0.89647336 -2.57582930
## [49] -0.82389363 1.51410189 0.59776013 -0.97411388 -0.59776013 0.62800601
## [55] 0.37185609 0.65883769 0.39885507 -1.25356544 0.69030882 0.93458929
## [61] -0.26631061 -0.78919165 1.59819314 1.10306256 -2.17009038 0.72247905
## [67] 1.15034938 -0.56805150 -0.53883603 1.20035886 0.16365849 -1.69539771
## [73] -0.24042603 -1.59819314 -0.51007346 -0.75541503 -1.20035886 -0.48172685
## [79] -0.72247905 0.18911843 0.21470157 1.69539771 -0.03760829 -1.15034938
## [85] 0.75541503 -1.10306256 -0.45376219 -0.42614801 1.25356544 -1.05812162
## [91] -1.51410189 -0.01253347 0.24042603 -0.21470157 -1.43953147 0.42614801
## [97] 1.95996398 -1.31057911 2.57582930 -0.18911843
##
## $y
## [1] 0.51 0.57 0.46 0.42 0.55 0.49 0.57 0.53 0.51 0.50 0.49 0.50 0.48 0.43 0.47
## [16] 0.56 0.47 0.47 0.50 0.55 0.48 0.40 0.58 0.55 0.48 0.54 0.49 0.52 0.49 0.51
## [31] 0.52 0.50 0.57 0.51 0.60 0.53 0.51 0.54 0.54 0.52 0.51 0.50 0.56 0.56 0.49
## [46] 0.52 0.55 0.37 0.47 0.57 0.54 0.46 0.48 0.54 0.52 0.54 0.52 0.45 0.54 0.55
## [61] 0.49 0.47 0.57 0.56 0.39 0.54 0.56 0.48 0.48 0.56 0.51 0.42 0.49 0.42 0.48
## [76] 0.47 0.45 0.48 0.47 0.51 0.51 0.57 0.50 0.45 0.54 0.45 0.48 0.48 0.56 0.45
## [91] 0.42 0.50 0.51 0.49 0.42 0.52 0.59 0.44 0.62 0.49
##
## [1] 0.5044p3(200)##
## Shapiro-Wilk normality test
##
## data: pi
## W = 0.99294, p-value = 0.4526
## $x
## [1] 0.905878812 1.047215930 0.590284394 -0.131980140 -1.004785806
## [6] -1.918876226 -1.494672250 0.056429069 -0.575430769 0.068986959
## [11] -0.043880072 -0.984234960 0.763777244 -1.669592577 0.285840875
## [16] 0.780664237 1.422090432 1.576111974 0.298921424 0.081555738
## [21] -0.780664237 -0.560703032 -0.392078788 -0.488776411 -0.031337982
## [26] 0.094137414 0.474701147 -0.378579699 0.924934461 0.797776846
## [31] 1.069154627 -0.365149249 -1.621082251 -2.807033768 1.091620367
## [36] -1.239933478 1.114651015 0.312053322 -0.018800820 0.605269415
## [41] 1.239933478 1.138288582 -1.114651015 -2.432379059 2.807033768
## [46] -0.763777244 -0.964091607 1.162579875 -0.944332036 1.457421739
## [51] 0.815126333 0.944332036 -0.351784345 0.620391602 -1.457421739
## [56] 0.106734011 -1.213339622 2.241402728 -0.338481986 -0.924934461
## [61] 1.267434417 -0.474701147 0.832724719 -1.422090432 -0.460719309
## [66] 1.295928846 -1.388450197 -0.905878812 0.850584865 -1.845258117
## [71] -0.006266612 -0.887146559 0.635657014 -1.780464342 0.868720547
## [76] 0.651072016 1.187577263 -0.325239256 0.119347567 -0.312053322
## [81] 0.131980140 1.918876226 0.964091607 2.432379059 -1.722383890
## [86] 0.666643306 0.887146559 0.144633812 1.621082251 0.157310685
## [91] 0.682377942 1.669592577 -0.298921424 -0.119347567 -1.091620367
## [96] -0.747105302 -1.187577263 -2.004654462 0.006266612 0.698283366
## [101] 0.325239256 -2.241402728 -0.106734011 -1.356311745 -1.162579875
## [106] -0.285840875 -0.272809053 -1.576111974 -0.259823400 0.338481986
## [111] -0.094137414 1.494672250 -0.246881415 -1.138288582 2.004654462
## [116] 1.325516200 0.488776411 0.170012889 -0.546095926 2.108358399
## [121] 0.018800820 0.502949184 0.517223714 0.351784345 -0.730638483
## [126] 0.031337982 -0.531604424 0.365149249 -0.714367440 -0.698283366
## [131] -0.233980651 0.984234960 -0.868720547 0.182742585 -1.325516200
## [136] -0.446826965 -0.221118713 -0.682377942 1.356311745 0.378579699
## [141] -1.295928846 -0.850584865 -0.208293252 1.213339622 0.195501964
## [146] 0.043880072 -0.666643306 0.208293252 0.531604424 -0.651072016
## [151] -2.108358399 -0.081555738 -0.195501964 0.392078788 0.546095926
## [156] -1.267434417 1.004785806 -0.635657014 -1.069154627 0.405649708
## [161] -0.517223714 1.722383890 0.419295753 -1.534120544 0.560703032
## [166] 1.025770021 -1.047215930 -0.433020331 -0.620391602 0.433020331
## [171] 1.534120544 -0.419295753 -0.502949184 0.221118713 -0.182742585
## [176] 0.446826965 0.714367440 -0.170012889 0.233980651 -0.068986959
## [181] -1.025770021 1.388450197 -0.605269415 0.730638483 0.246881415
## [186] 0.460719309 1.780464342 -0.157310685 -0.590284394 1.845258117
## [191] 0.575430769 0.259823400 -0.832724719 -0.815126333 -0.056429069
## [196] 0.747105302 -0.405649708 -0.144633812 -0.797776846 0.272809053
##
## $y
## [1] 0.525 0.530 0.515 0.490 0.465 0.440 0.450 0.500 0.475 0.500 0.495 0.465
## [13] 0.520 0.445 0.505 0.520 0.540 0.545 0.505 0.500 0.470 0.475 0.485 0.480
## [25] 0.495 0.500 0.510 0.485 0.525 0.520 0.530 0.485 0.445 0.420 0.530 0.455
## [37] 0.530 0.505 0.495 0.515 0.535 0.530 0.460 0.420 0.575 0.470 0.465 0.530
## [49] 0.465 0.540 0.520 0.525 0.485 0.515 0.450 0.500 0.455 0.565 0.485 0.465
## [61] 0.535 0.480 0.520 0.450 0.480 0.535 0.450 0.465 0.520 0.440 0.495 0.465
## [73] 0.515 0.440 0.520 0.515 0.530 0.485 0.500 0.485 0.500 0.555 0.525 0.565
## [85] 0.440 0.515 0.520 0.500 0.545 0.500 0.515 0.545 0.485 0.490 0.460 0.470
## [97] 0.455 0.435 0.495 0.515 0.505 0.430 0.490 0.450 0.455 0.485 0.485 0.445
## [109] 0.485 0.505 0.490 0.540 0.485 0.455 0.555 0.535 0.510 0.500 0.475 0.555
## [121] 0.495 0.510 0.510 0.505 0.470 0.495 0.475 0.505 0.470 0.470 0.485 0.525
## [133] 0.465 0.500 0.450 0.480 0.485 0.470 0.535 0.505 0.450 0.465 0.485 0.530
## [145] 0.500 0.495 0.470 0.500 0.510 0.470 0.430 0.490 0.485 0.505 0.510 0.450
## [157] 0.525 0.470 0.460 0.505 0.475 0.545 0.505 0.445 0.510 0.525 0.460 0.480
## [169] 0.470 0.505 0.540 0.480 0.475 0.500 0.485 0.505 0.515 0.485 0.500 0.490
## [181] 0.460 0.535 0.470 0.515 0.500 0.505 0.545 0.485 0.470 0.545 0.510 0.500
## [193] 0.465 0.465 0.490 0.515 0.480 0.485 0.465 0.500
##
## [1] 0.4937p3(500)##
## Shapiro-Wilk normality test
##
## data: pi
## W = 0.99588, p-value = 0.2161
## $x
## [1] 1.253565438 0.830953321 -0.568051498 0.538836030 -1.654627902
## [6] -0.184017151 1.264641136 0.184017151 -0.775574943 -2.575829304
## [11] 0.062706778 1.411830078 -0.768820293 2.575829304 -0.052663527
## [16] 1.075837361 -1.635234015 -0.178920660 -0.047643956 0.431644239
## [21] -0.323918153 0.544641655 0.437153541 0.550465695 1.170002408
## [26] -1.058121618 0.189118426 -0.671346215 0.683960672 0.690308824
## [31] -1.514101888 -0.318639364 0.556308467 -0.313369439 0.966088297
## [36] -0.404289290 0.838054670 0.313369439 -0.398855066 0.845198535
## [41] -0.950220942 0.194224628 -1.895697924 -0.308108202 0.442676144
## [46] 2.120071690 -0.042625585 1.084823128 0.199335898 1.425544037
## [51] -0.562170292 -1.616436371 1.762410298 -1.385171608 0.448212281
## [56] -0.942376333 0.852385798 0.453762190 0.067730713 0.204452382
## [61] 1.093897353 -0.037608288 1.439531471 -0.393432594 0.859617364
## [66] 0.209574223 -1.498513068 -0.556308467 1.866295743 -0.173828813
## [71] 1.103062556 0.214701568 1.180000540 -1.180000540 -0.388021666
## [76] 0.866894167 -0.934589291 -0.168741468 -0.550465695 0.974113877
## [81] -0.544641655 -0.382622075 -0.032591937 1.112321367 -1.483280127
## [86] -1.253565438 -0.538836030 -1.372203809 0.696684917 -0.926858513
## [91] -0.027576406 -0.163658486 -1.242641419 1.453806359 1.995393310
## [96] -0.762100541 -1.049387085 0.874217165 0.459326111 1.468383798
## [101] -0.533048511 1.275874179 -0.527278791 0.982202695 1.190118042
## [106] 0.219834564 -0.665078946 -1.359462745 0.464904288 0.990356294
## [111] 0.998576271 0.224973358 0.072756358 0.470496968 -1.040731886
## [116] -0.158579730 -0.521526572 -0.755415026 1.483280127 -0.919182735
## [121] -1.866295743 0.230118101 0.476104403 -1.346938626 -0.302855481
## [126] -0.297611102 0.318639364 -1.598193140 -1.231863709 1.121676528
## [131] 1.006864279 0.703089460 1.200358858 1.287270563 -0.515791557
## [136] -0.748763107 0.481726850 1.895697924 0.077783842 0.235268941
## [141] 0.487364565 0.881587347 0.562170292 -1.334622287 -1.032153958
## [146] -0.153505060 -0.911560735 2.747781385 -1.170002408 -1.160119883
## [151] 1.298836633 -0.022561568 -0.510073457 -1.023651312 1.498513068
## [156] 1.514101888 0.709522974 0.568051498 -1.580466818 -0.017547298
## [161] -0.504371986 -0.148434341 -1.015222033 2.290367878 -1.006864279
## [166] 0.323918153 -0.998576271 -0.012533470 0.493017814 -0.498686864
## [171] -0.903991328 0.573952419 1.530067588 -0.493017814 0.579873392
## [176] 0.498686864 1.210727133 1.546433122 -1.221227222 -0.007519956
## [181] 1.131130901 -0.002506631 0.715985990 -1.468383798 -0.292374896
## [186] -0.287146694 -0.896473364 -1.150349380 0.082813292 0.240426031
## [191] 0.002506631 0.329205984 0.585814766 -0.742144154 2.365618127
## [196] 1.635234015 1.654627902 0.722479052 -0.377233617 -0.658837693
## [201] -0.990356294 0.504371986 0.007519956 1.015222033 0.334503036
## [206] -0.487364565 -2.074854734 -0.481726850 -0.476104403 2.170090378
## [211] -1.838423669 1.926836573 1.140687476 0.889005731 0.729002718
## [216] 1.221227222 -0.735557557 -2.033520149 0.510073457 -0.652621998
## [221] -0.281926330 -0.276713637 -0.889005731 2.226211769 -0.646431416
## [226] -3.090232306 -0.729002718 -0.982202695 0.087844838 0.339809491
## [231] 1.310579112 1.023651312 -1.322505137 0.591776891 0.345125531
## [236] -1.210727133 -1.995393310 -0.470496968 0.012533470 -2.290367878
## [241] 0.597760126 -0.143367435 0.350451343 0.092878609 -0.464904288
## [246] 0.097914734 -0.459326111 -0.138304208 0.735557557 -0.271508452
## [251] -0.133244524 -0.453762190 0.896473364 -0.266310613 -0.371856089
## [256] -0.881587347 -0.640265509 0.603764838 -0.128188248 -1.959963985
## [261] 0.742144154 -0.448212281 -1.140687476 0.609791399 -0.366489294
## [266] 0.245589523 -0.123135248 -0.634123849 -0.442676144 -0.437153541
## [271] -0.722479052 0.102953344 -0.974113877 -0.628006014 0.355787114
## [276] -2.747781385 -0.874217165 0.250759572 0.615840189 -0.621911596
## [281] -0.615840189 -0.261119960 0.903991328 -2.457263390 -0.118085389
## [286] 0.361133034 0.107994569 -0.866894167 -0.859617364 1.032153958
## [291] 0.621911596 -0.609791399 1.322505137 0.515791557 0.017547298
## [296] 1.786613365 -1.811910673 -1.926836573 -0.431644239 -0.852385798
## [301] 0.366489294 0.113038541 0.628006014 -0.255936332 0.255936332
## [306] 0.022561568 -1.131130901 -0.603764838 -0.250759572 -0.597760126
## [311] 0.027576406 -1.563223647 -0.361133034 0.032591937 0.634123849
## [316] 0.748763107 1.334622287 -0.245589523 0.521526572 -0.240426031
## [321] 0.371856089 -1.546433122 0.037608288 -1.453806359 -1.310579112
## [326] 0.118085389 -0.113038541 0.123135248 -1.200358858 -1.786613365
## [331] -0.235268941 0.128188248 0.755415026 -1.439531471 -0.107994569
## [336] -1.121676528 0.133244524 0.762100541 0.377233617 0.138304208
## [341] 0.382622075 1.346938626 2.457263390 1.811910673 0.261119960
## [346] 0.266310613 -0.845198535 -0.102953344 1.040731886 1.838423669
## [351] 0.271508452 0.388021666 -0.230118101 0.640265509 -0.426148008
## [356] -0.591776891 -0.420664620 -0.715985990 -0.838054670 0.393432594
## [361] -0.224973358 2.033520149 1.563223647 0.768820293 -1.762410298
## [366] -1.112321367 0.276713637 0.042625585 1.674664889 0.775574943
## [371] -0.097914734 -0.355787114 0.646431416 3.090232306 -1.103062556
## [376] -0.709522974 0.047643956 2.074854734 1.049387085 0.527278791
## [381] 0.281926330 -0.092878609 -0.219834564 0.052663527 0.057684425
## [386] -0.087844838 -0.415193851 -0.966088297 0.911560735 0.782365165
## [391] -2.226211769 0.652621998 -0.350451343 -0.082813292 -1.093897353
## [396] 0.919182735 -0.214701568 -0.345125531 -0.830953321 -1.739197665
## [401] -1.716886018 0.789191653 -0.823893630 1.580466818 0.533048511
## [406] -1.530067588 0.658837693 0.926858513 -1.425544037 -0.339809491
## [411] 0.796055117 1.058121618 -1.298836633 -0.209574223 0.934589291
## [416] 1.231863709 1.150349380 0.143367435 -0.585814766 -2.365618127
## [421] -2.170090378 0.942376333 1.359462745 -0.579873392 -0.204452382
## [426] -1.084823128 -1.287270563 -0.703089460 -1.075837361 1.372203809
## [431] -0.199335898 -1.066937632 0.148434341 -1.695397710 0.153505060
## [436] -1.275874179 -0.077783842 -0.816874766 -1.411830078 0.287146694
## [441] -1.674664889 -1.264641136 -0.334503036 0.950220942 0.292374896
## [446] 0.665078946 0.158579730 0.802956288 0.297611102 -0.194224628
## [451] -0.809895915 -0.802956288 0.302855481 0.163658486 -0.072756358
## [456] 0.398855066 0.404289290 -1.398376621 -0.958124465 0.409735480
## [461] 0.809895915 0.958124465 1.598193140 -0.696684917 1.160119883
## [466] -0.690308824 0.168741468 1.695397710 0.415193851 -0.573952419
## [471] 1.716886018 -0.796055117 1.066937632 -0.067730713 -0.683960672
## [476] 0.173828813 1.739197665 1.385171608 0.671346215 -0.409735480
## [481] 0.816874766 1.398376621 -0.789191653 -0.189118426 1.242641419
## [486] -0.782365165 -2.120071690 1.959963985 -1.190118042 -0.062706778
## [491] 0.178920660 0.308108202 0.420664620 0.677639965 0.823893630
## [496] -0.677639965 -0.329205984 0.426148008 -0.057684425 1.616436371
##
## $y
## [1] 0.522 0.514 0.492 0.510 0.474 0.498 0.522 0.504 0.488 0.464 0.502 0.524
## [13] 0.488 0.544 0.500 0.518 0.474 0.498 0.500 0.508 0.496 0.510 0.508 0.510
## [25] 0.520 0.484 0.504 0.490 0.512 0.512 0.476 0.496 0.510 0.496 0.516 0.494
## [37] 0.514 0.506 0.494 0.514 0.486 0.504 0.472 0.496 0.508 0.534 0.500 0.518
## [49] 0.504 0.524 0.492 0.474 0.528 0.478 0.508 0.486 0.514 0.508 0.502 0.504
## [61] 0.518 0.500 0.524 0.494 0.514 0.504 0.476 0.492 0.530 0.498 0.518 0.504
## [73] 0.520 0.482 0.494 0.514 0.486 0.498 0.492 0.516 0.492 0.494 0.500 0.518
## [85] 0.476 0.480 0.492 0.478 0.512 0.486 0.500 0.498 0.480 0.524 0.532 0.488
## [97] 0.484 0.514 0.508 0.524 0.492 0.522 0.492 0.516 0.520 0.504 0.490 0.478
## [109] 0.508 0.516 0.516 0.504 0.502 0.508 0.484 0.498 0.492 0.488 0.524 0.486
## [121] 0.472 0.504 0.508 0.478 0.496 0.496 0.506 0.474 0.480 0.518 0.516 0.512
## [133] 0.520 0.522 0.492 0.488 0.508 0.530 0.502 0.504 0.508 0.514 0.510 0.478
## [145] 0.484 0.498 0.486 0.544 0.482 0.482 0.522 0.500 0.492 0.484 0.524 0.524
## [157] 0.512 0.510 0.474 0.500 0.492 0.498 0.484 0.536 0.484 0.506 0.484 0.500
## [169] 0.508 0.492 0.486 0.510 0.524 0.492 0.510 0.508 0.520 0.524 0.480 0.500
## [181] 0.518 0.500 0.512 0.476 0.496 0.496 0.486 0.482 0.502 0.504 0.500 0.506
## [193] 0.510 0.488 0.542 0.526 0.526 0.512 0.494 0.490 0.484 0.508 0.500 0.516
## [205] 0.506 0.492 0.470 0.492 0.492 0.534 0.472 0.530 0.518 0.514 0.512 0.520
## [217] 0.488 0.470 0.508 0.490 0.496 0.496 0.486 0.534 0.490 0.456 0.488 0.484
## [229] 0.502 0.506 0.522 0.516 0.478 0.510 0.506 0.480 0.470 0.492 0.500 0.468
## [241] 0.510 0.498 0.506 0.502 0.492 0.502 0.492 0.498 0.512 0.496 0.498 0.492
## [253] 0.514 0.496 0.494 0.486 0.490 0.510 0.498 0.470 0.512 0.492 0.482 0.510
## [265] 0.494 0.504 0.498 0.490 0.492 0.492 0.488 0.502 0.484 0.490 0.506 0.456
## [277] 0.486 0.504 0.510 0.490 0.490 0.496 0.514 0.466 0.498 0.506 0.502 0.486
## [289] 0.486 0.516 0.510 0.490 0.522 0.508 0.500 0.528 0.472 0.470 0.492 0.486
## [301] 0.506 0.502 0.510 0.496 0.504 0.500 0.482 0.490 0.496 0.490 0.500 0.474
## [313] 0.494 0.500 0.510 0.512 0.522 0.496 0.508 0.496 0.506 0.474 0.500 0.476
## [325] 0.478 0.502 0.498 0.502 0.480 0.472 0.496 0.502 0.512 0.476 0.498 0.482
## [337] 0.502 0.512 0.506 0.502 0.506 0.522 0.542 0.528 0.504 0.504 0.486 0.498
## [349] 0.516 0.528 0.504 0.506 0.496 0.510 0.492 0.490 0.492 0.488 0.486 0.506
## [361] 0.496 0.532 0.524 0.512 0.472 0.482 0.504 0.500 0.526 0.512 0.498 0.494
## [373] 0.510 0.544 0.482 0.488 0.500 0.532 0.516 0.508 0.504 0.498 0.496 0.500
## [385] 0.500 0.498 0.492 0.484 0.514 0.512 0.468 0.510 0.494 0.498 0.482 0.514
## [397] 0.496 0.494 0.486 0.472 0.472 0.512 0.486 0.524 0.508 0.474 0.510 0.514
## [409] 0.476 0.494 0.512 0.516 0.478 0.496 0.514 0.520 0.518 0.502 0.490 0.466
## [421] 0.468 0.514 0.522 0.490 0.496 0.482 0.478 0.488 0.482 0.522 0.496 0.482
## [433] 0.502 0.472 0.502 0.478 0.498 0.486 0.476 0.504 0.472 0.478 0.494 0.514
## [445] 0.504 0.510 0.502 0.512 0.504 0.496 0.486 0.486 0.504 0.502 0.498 0.506
## [457] 0.506 0.476 0.484 0.506 0.512 0.514 0.524 0.488 0.518 0.488 0.502 0.526
## [469] 0.506 0.490 0.526 0.486 0.516 0.498 0.488 0.502 0.526 0.522 0.510 0.492
## [481] 0.512 0.522 0.486 0.496 0.520 0.486 0.468 0.530 0.480 0.498 0.502 0.504
## [493] 0.506 0.510 0.512 0.488 0.494 0.506 0.498 0.524
##
## [1] 0.500036