mvtnorm
2023-03-30
HELLO!
Teknik Informatika UIN MAULANA MALIK IBRAHIM MALANG|| Lalu Egiq Fahalik Anggara_220605110066 | linier algebra
by Prof. Dr. Suhartono, M.Kom
library(mvtnorm)
library(ggplot2)
library(MASS)##Standar deviation
sigma <- matrix(c(4,2,2,3), ncol = 2, nrow = 2)
##mean
mu <- c(1,2)
n <- 1000
set.seed(123)x <- rmvnorm(n = n, mean = mu, sigma = sigma)
d <- data.frame(x)
d## X1 X2
## 1 -0.205156592 1.307822329
## 2 4.031369338 2.991770505
## 3 2.212307319 4.882440535
## 4 1.173488321 0.186586732
## 5 -0.568859453 0.883752746
## 6 3.551737218 3.277617451
## 7 1.831449504 2.406630823
## 8 0.937685108 4.614989617
## 9 0.849985521 -0.941995922
## 10 2.080369843 1.619715404
## 11 -1.172083277 1.042598089
## 12 -1.379038272 0.229082932
## 13 -1.147886254 -1.114656027
## 14 2.694241593 2.722246451
## 15 -0.479645074 3.414275955
## 16 1.652660790 1.756334982
## 17 3.211733394 3.941841839
## 18 2.964047158 3.590054111
## 19 2.028365830 2.209966687
## 20 0.198856570 1.204678655
## 21 -0.450281636 1.268830087
## 22 -0.209438285 4.841993107
## 23 2.687144008 0.839111301
## 24 -0.035622743 1.008997772
## 25 2.450170974 2.301890441
## 26 1.470162825 2.095640269
## 27 1.687102058 4.218055112
## 28 1.419176035 4.357483962
## 29 -1.643971532 2.087100548
## 30 1.359117335 2.423400090
## 31 1.446276290 1.390474520
## 32 -0.212158696 0.143968016
## 33 -0.886525125 1.894737208
## 34 1.890075942 2.338805601
## 35 3.922663410 5.877085893
## 36 -1.240612301 -2.059110884
## 37 2.531689414 1.403524931
## 38 0.256004392 3.293397119
## 39 -0.232833609 -0.159969668
## 40 1.269907272 1.874380120
## 41 1.227656386 2.634438135
## 42 0.650816448 2.847296385
## 43 0.763323224 2.419601425
## 44 3.349881134 3.329558903
## 45 1.020242354 3.698841346
## 46 3.215189408 3.456945841
## 47 1.105224063 1.105520847
## 48 3.274142502 1.781522928
## 49 6.059879105 5.740498774
## 50 -0.029417541 0.185930305
## 51 -0.219118051 2.021479041
## 52 0.331130233 1.291944855
## 53 -0.851817493 1.391261199
## 54 -1.444184634 -1.173807306
## 55 0.786837816 3.291823317
## 56 0.237477485 2.672574211
## 57 -2.136544235 0.999449920
## 58 2.166231676 2.785368701
## 59 0.842646058 1.009751220
## 60 -1.206627342 -0.155488750
## 61 0.693165757 0.513907334
## 62 -0.085526423 1.304672621
## 63 4.172539772 1.968485218
## 64 1.495620170 2.260048903
## 65 -0.886242101 1.342451047
## 66 4.026443458 3.551772769
## 67 0.841626329 1.331011211
## 68 -2.304929812 2.699176128
## 69 -1.387527083 2.391115220
## 70 3.852556041 0.707736167
## 71 2.199581595 1.964968341
## 72 -2.869019608 -1.365262876
## 73 -2.372393357 0.229891328
## 74 -1.418918244 2.305247125
## 75 4.307348632 1.072098725
## 76 2.944291052 3.702750120
## 77 1.070739976 0.534749515
## 78 0.613097090 1.473480973
## 79 1.871209323 1.706335958
## 80 2.664591617 1.935555596
## 81 2.430723480 0.872954943
## 82 0.403313985 6.601314644
## 83 0.367552122 2.254236166
## 84 1.949843563 1.565291147
## 85 2.199467937 2.895031656
## 86 0.623311722 1.985888054
## 87 2.131162735 5.467851438
## 88 -1.039030699 -0.212306595
## 89 1.247072505 2.529898291
## 90 1.580169401 1.494468722
## 91 -0.330788096 3.471683404
## 92 -0.157671793 0.385483734
## 93 0.435646808 1.544141300
## 94 3.177979930 2.762786609
## 95 2.166618539 1.605925082
## 96 1.229070585 1.588627698
## 97 0.678194635 0.586314883
## 98 -0.393135848 4.535105046
## 99 1.449553756 0.287765538
## 100 -0.839491539 -0.285728586
## 101 5.958119998 5.386205293
## 102 0.796456613 2.740848280
## 103 -0.063001365 0.986844417
## 104 -0.847893005 0.582521348
## 105 4.138322651 2.839576186
## 106 1.365868834 2.466264574
## 107 3.075457023 1.847402334
## 108 0.037040886 4.187305968
## 109 -0.253239136 0.567406117
## 110 -2.095088254 -0.799720542
## 111 0.245747478 2.689764370
## 112 3.527989176 3.783151311
## 113 0.335598140 1.893450247
## 114 -0.755576485 0.428892395
## 115 2.127033114 0.833496973
## 116 4.702149787 2.951237288
## 117 0.996600937 0.910690989
## 118 -0.842848106 -0.480546610
## 119 0.884438271 2.583576017
## 120 1.183102920 0.901937305
## 121 -0.795974859 0.733918175
## 122 3.232130778 0.977816058
## 123 1.725783831 5.015946544
## 124 0.041731579 -0.284566611
## 125 -0.003025144 2.421607067
## 126 -0.036788996 0.868336051
## 127 0.390771401 1.954919265
## 128 4.018334744 2.753537948
## 129 3.429040352 3.640944959
## 130 -0.079866956 -0.575209585
## 131 -0.275604961 0.904498239
## 132 1.821438362 4.156599988
## 133 6.271260259 5.824471696
## 134 -0.243031162 -0.952539413
## 135 0.303938721 1.927586433
## 136 3.162992850 4.051931946
## 137 1.529059858 0.098845823
## 138 2.379735197 1.746056866
## 139 1.377420734 2.220404509
## 140 1.835680233 2.281126764
## 141 -1.786459546 2.269184319
## 142 1.591585075 1.781800179
## 143 1.302114962 2.286010224
## 144 2.346650546 4.812417988
## 145 0.674043353 2.152194987
## 146 3.835184422 4.383874601
## 147 2.873544267 1.697776690
## 148 4.880994377 3.235009057
## 149 3.823735907 0.836328104
## 150 1.742938750 4.059508029
## 151 -0.795950122 0.364796536
## 152 -1.393089872 -0.251930475
## 153 0.347109627 2.296806997
## 154 -2.746838188 1.214956329
## 155 4.519093503 6.033340181
## 156 3.922868434 3.971291129
## 157 -2.652376148 0.043848015
## 158 0.719793536 2.954660371
## 159 0.089604451 -0.121425722
## 160 4.745404750 4.440053336
## 161 2.140498819 4.129080595
## 162 -1.198104933 2.329991783
## 163 0.380720507 2.826202249
## 164 1.239091476 3.002775483
## 165 3.567445320 2.762730189
## 166 2.284966314 0.625050914
## 167 0.469034517 4.083242162
## 168 0.570649015 -1.149962402
## 169 -1.730959978 0.904244265
## 170 2.604471885 2.319801145
## 171 2.737167548 3.922019622
## 172 4.238856650 3.031186850
## 173 -0.085388477 -0.901518657
## 174 0.869169471 1.118987650
## 175 -0.970618598 1.157704720
## 176 1.827785408 -0.694112770
## 177 0.245464576 1.950881396
## 178 -0.526682234 2.044893103
## 179 1.771112673 2.177170738
## 180 -2.287366302 4.826519662
## 181 0.972036448 2.951424859
## 182 2.101497895 3.832606137
## 183 2.451448437 2.115962784
## 184 1.194362553 0.663748668
## 185 2.385567272 1.726425287
## 186 4.710503558 0.653753150
## 187 0.573441877 3.091365044
## 188 1.647742920 1.321045066
## 189 -0.831967228 1.676332342
## 190 -0.033902268 -0.941027509
## 191 1.173257781 2.331074322
## 192 0.742265733 0.369811092
## 193 2.688863784 4.526153213
## 194 1.237291676 0.396068702
## 195 0.358405734 2.322108599
## 196 -1.454879839 -1.898580874
## 197 2.230894100 1.138180961
## 198 0.744574653 4.141374323
## 199 -0.010423142 2.950345696
## 200 -1.619024656 0.710442621
## 201 0.201839156 0.044069260
## 202 -0.234528051 1.595913450
## 203 1.359424461 -0.327014914
## 204 0.753922077 3.042585457
## 205 0.093604572 2.069466156
## 206 2.095335381 2.715504883
## 207 2.184857517 2.166210088
## 208 -1.279893752 -2.562777798
## 209 1.063505008 2.652678798
## 210 1.715465884 1.391282624
## 211 4.576536327 3.469625640
## 212 1.957675653 4.155341802
## 213 -0.632166150 0.858319007
## 214 5.607845179 3.366006863
## 215 3.326731390 0.561663401
## 216 0.847066826 2.512862122
## 217 1.010545964 0.521157346
## 218 0.431272808 0.245708835
## 219 2.977765732 4.177826685
## 220 -2.575896758 2.773593804
## 221 -1.126361257 2.047362916
## 222 2.154222744 2.043501215
## 223 -0.145271373 1.908179096
## 224 2.338819385 3.693788907
## 225 -3.859107902 -1.834610394
## 226 4.333848150 4.518800744
## 227 2.237530120 3.416369503
## 228 1.264505279 -1.843732574
## 229 2.858382945 1.829617548
## 230 1.276709448 1.646094183
## 231 2.477719351 1.919296000
## 232 1.775567389 1.651434981
## 233 -0.417227844 3.368006231
## 234 3.391385518 5.241337851
## 235 1.757496219 3.879698530
## 236 4.633311501 2.649373005
## 237 -1.673783436 0.864152329
## 238 0.674446648 2.128167929
## 239 4.103191819 2.428289799
## 240 1.587935455 1.836681205
## 241 1.215805963 2.526011566
## 242 3.617531546 2.945435126
## 243 2.806056466 3.676729894
## 244 2.432877712 1.573237558
## 245 3.908418257 2.290468321
## 246 1.586275391 4.240760727
## 247 2.871060664 0.941780881
## 248 -1.439213084 -0.715729255
## 249 1.441699784 2.372284620
## 250 2.009275440 3.109283763
## 251 -0.713879460 0.033676489
## 252 3.392999878 3.807676718
## 253 -1.950131860 0.995714649
## 254 -1.883764386 -1.896147150
## 255 1.243605081 1.954621861
## 256 0.934627060 2.299380662
## 257 2.809354202 2.832921354
## 258 -0.596247539 0.449650815
## 259 0.921304230 2.433799559
## 260 -1.099139866 1.113573871
## 261 2.795668117 2.366374683
## 262 -0.495652754 1.155293543
## 263 3.448636296 3.527747916
## 264 3.451829981 2.923102560
## 265 1.473520739 1.315734522
## 266 1.877282697 1.510804003
## 267 -1.654631367 1.411090205
## 268 5.185050033 4.406020776
## 269 3.438285359 3.242976284
## 270 -0.281737531 1.326560436
## 271 0.212048268 1.078526213
## 272 1.678433746 0.434242944
## 273 3.148673644 3.902769302
## 274 -0.941092207 2.373839136
## 275 5.351244899 2.453323037
## 276 2.181950599 1.193512528
## 277 3.272305474 3.033691007
## 278 3.350441662 0.538451578
## 279 0.605319439 1.107910228
## 280 0.267446699 0.857676654
## 281 -0.275111050 2.479348818
## 282 -0.253188813 3.819855702
## 283 -1.219940953 1.498747190
## 284 2.352846077 3.260867751
## 285 0.465531303 1.960613931
## 286 2.026237307 0.154292257
## 287 -0.320324259 2.085439081
## 288 0.916474762 3.994409198
## 289 2.332790482 2.496712079
## 290 -1.879265333 1.195144673
## 291 0.335146087 1.654448339
## 292 -0.987514334 2.152705867
## 293 -1.121312678 1.045315363
## 294 1.291627252 0.930806596
## 295 1.378872163 0.170925449
## 296 -4.131595168 1.182179381
## 297 2.452610021 2.004230446
## 298 1.317782020 0.389687833
## 299 -0.335506687 -1.252232341
## 300 4.312703142 5.711080840
## 301 3.046048954 2.558974670
## 302 0.083740238 -0.502482572
## 303 2.398570446 2.099088483
## 304 -1.054327535 -0.682496184
## 305 -0.052670017 0.440481732
## 306 -0.446544170 -0.217969683
## 307 4.230105687 2.922494315
## 308 1.600617377 -1.658014893
## 309 -0.249587881 0.638596079
## 310 -0.477786738 3.846289373
## 311 -1.537454725 1.725984807
## 312 2.724794047 2.767766132
## 313 -0.150841074 3.049852629
## 314 0.729555111 0.353590617
## 315 -0.491085671 4.638311680
## 316 -1.345441216 -1.421382013
## 317 2.197921789 2.808026465
## 318 -2.690773945 -1.944193279
## 319 1.417306495 3.801269967
## 320 1.943840548 1.550039211
## 321 -0.448727097 1.975128612
## 322 1.656023255 3.120104213
## 323 0.745908102 3.250889505
## 324 -0.780453443 0.991418076
## 325 2.978425805 4.038315165
## 326 -2.660440793 1.085840259
## 327 1.352860862 -0.034621525
## 328 1.456922289 0.913410503
## 329 3.260956961 3.455739955
## 330 2.543957498 2.630109794
## 331 3.433740262 4.747187788
## 332 4.757986691 3.058845134
## 333 -3.299029164 0.787301043
## 334 1.307216806 1.861060814
## 335 2.658925936 3.975249239
## 336 -0.159529204 1.226995310
## 337 1.454285913 1.322233385
## 338 0.072363770 -1.162521209
## 339 -1.895920743 -0.804810217
## 340 -1.028170774 0.384291123
## 341 2.285897234 3.823897598
## 342 -0.956507437 -0.042015362
## 343 -1.232451185 0.735181560
## 344 0.813090661 2.657926777
## 345 -0.785202772 -1.585789111
## 346 1.491904113 3.893544443
## 347 2.843588037 1.377337914
## 348 -0.588903533 5.156882186
## 349 0.633468753 1.749038811
## 350 0.899872392 -0.407816816
## 351 -1.263708368 -0.933060438
## 352 -0.263488713 1.805072310
## 353 -1.287706750 2.199359880
## 354 1.047035175 0.681301731
## 355 1.854948636 3.352800328
## 356 2.916973352 2.247809789
## 357 0.771528702 1.805298123
## 358 4.399173484 4.653529783
## 359 2.439987801 1.998329858
## 360 1.943104339 2.870527886
## 361 -1.970951964 -1.417045736
## 362 1.372175317 -0.144623765
## 363 1.143913251 2.410922851
## 364 2.188757488 2.627322390
## 365 0.147889928 3.203956876
## 366 4.832446130 4.421025273
## 367 -1.943778657 3.200238711
## 368 1.187498805 2.828444331
## 369 2.139555482 2.191288985
## 370 1.428481171 3.627355338
## 371 2.922519520 4.022368883
## 372 5.947222579 4.428108276
## 373 0.155290321 -1.505055630
## 374 5.895038165 2.722438487
## 375 5.768598090 3.948774456
## 376 3.891134791 2.685121820
## 377 2.101980161 2.638056506
## 378 0.575084555 1.698129707
## 379 2.830746171 2.239339224
## 380 -3.021181343 0.533555810
## 381 2.382608180 3.313381582
## 382 1.232171798 -0.425522841
## 383 2.251851667 3.792921126
## 384 3.323755357 2.349103463
## 385 1.218587042 4.256538815
## 386 -2.446936714 0.346691705
## 387 0.968574440 -0.393197425
## 388 2.592385658 5.233667753
## 389 0.835667823 1.541531196
## 390 1.754643580 1.809782048
## 391 3.069658823 3.938988432
## 392 0.343666105 0.073760380
## 393 -1.863512897 0.287440298
## 394 1.429622209 -0.759828153
## 395 -2.988083238 -0.131509326
## 396 1.243409284 0.725038468
## 397 2.889406275 3.044656861
## 398 1.132800145 3.245542495
## 399 1.494723904 1.487759934
## 400 1.807606254 3.190734758
## 401 1.313925004 1.122285713
## 402 3.289591328 4.369602293
## 403 1.611283194 2.391397045
## 404 2.069929374 5.498493124
## 405 1.441362588 1.896005951
## 406 -4.693565387 -1.974246221
## 407 0.966888876 2.294302195
## 408 1.993245446 3.501508408
## 409 1.310154976 3.880691622
## 410 -1.448075897 -0.497817150
## 411 -0.941577660 2.525193085
## 412 1.284857654 3.247328909
## 413 0.153429852 0.879817896
## 414 -0.748487653 -1.242184049
## 415 -2.055587295 -1.019980197
## 416 2.687829660 1.614112853
## 417 3.367786795 4.928248308
## 418 0.791501958 2.357263606
## 419 -2.821170394 -0.325607768
## 420 1.276034336 2.521590750
## 421 1.051782338 5.971644074
## 422 0.156297322 1.847556167
## 423 2.232561517 2.322667180
## 424 0.352397389 3.350710938
## 425 4.084129669 2.859562865
## 426 2.024434492 2.156500349
## 427 2.300987763 0.677292441
## 428 5.115293398 2.315962337
## 429 -1.997341134 0.604977558
## 430 2.194337229 4.742423309
## 431 2.829030594 2.745641073
## 432 -2.153787196 -0.199938411
## 433 2.121829299 6.090781236
## 434 -1.934613318 2.807222928
## 435 0.924613408 4.432966882
## 436 -1.105802365 1.594871665
## 437 -0.602511479 2.862080334
## 438 4.944551264 6.029965039
## 439 3.567115210 5.468175269
## 440 3.318207604 2.484653020
## 441 1.369183757 0.675775712
## 442 1.330917543 3.896167075
## 443 2.296034602 3.053573291
## 444 -1.332392149 0.426031889
## 445 -0.245335566 2.217767834
## 446 -0.585184232 2.363948957
## 447 -0.114868021 4.368032300
## 448 1.489960667 1.110489177
## 449 1.264516999 1.558091122
## 450 1.849275374 2.607623085
## 451 -1.391308577 0.133501419
## 452 2.496454546 4.853650500
## 453 2.730664327 1.586521129
## 454 2.557944671 2.384739854
## 455 1.724698398 2.595934646
## 456 5.276897668 1.506002202
## 457 0.193053600 -0.859369509
## 458 2.748590585 4.128140815
## 459 2.692497390 -0.341222623
## 460 2.687999355 4.842434567
## 461 0.086087533 1.419690747
## 462 1.135074026 2.577463301
## 463 3.017523638 4.532893791
## 464 0.927065855 2.267878467
## 465 6.017729017 4.104937288
## 466 0.607718449 -0.092860649
## 467 0.881059037 1.639011078
## 468 0.655316892 1.051094397
## 469 -0.723447378 0.433063360
## 470 1.357409473 4.120798322
## 471 2.811214214 2.000023755
## 472 -2.710689516 -0.331435692
## 473 0.179652114 1.912449300
## 474 0.856308377 4.915010053
## 475 -0.205023322 -0.141843000
## 476 0.163674604 0.273495662
## 477 1.431061589 2.470543528
## 478 0.770743877 -0.457159671
## 479 1.598151237 2.632681676
## 480 -1.190549977 2.766254182
## 481 3.797886246 6.208260233
## 482 1.327042534 2.164656270
## 483 1.224603994 2.168594302
## 484 -3.487352019 -1.776930856
## 485 0.524516118 1.004458136
## 486 -0.081797058 -1.427982062
## 487 -2.495770568 -0.647061862
## 488 2.275069257 0.754695969
## 489 -0.489657264 1.681393606
## 490 0.462842857 2.058434441
## 491 4.792039883 1.453417830
## 492 0.123185685 0.981676997
## 493 3.470259526 1.589589461
## 494 1.284947524 3.243399567
## 495 -0.101333656 4.116536557
## 496 1.693149429 0.620040238
## 497 1.752586453 1.906092568
## 498 1.550619353 2.028682907
## 499 2.295164921 0.388328692
## 500 -0.143180044 1.297956516
## 501 -1.495932953 -0.263546377
## 502 0.891184540 1.773352009
## 503 -3.308143328 2.271589881
## 504 2.837632626 6.098815557
## 505 2.063879386 1.652952307
## 506 7.961407809 8.212590362
## 507 -1.075478626 2.083283956
## 508 0.699694262 2.187685873
## 509 0.727336100 0.060569566
## 510 2.531524043 5.026308978
## 511 0.593458840 1.640833853
## 512 4.189422272 4.258059997
## 513 -2.035577139 1.447707484
## 514 4.969387163 5.248194267
## 515 2.211488994 3.417646470
## 516 -1.128631963 1.818819741
## 517 -1.089420487 0.713075685
## 518 2.156639490 0.663416890
## 519 1.753108918 2.851781622
## 520 2.129774736 5.016127743
## 521 -0.621510856 2.418279632
## 522 0.682677822 1.522689373
## 523 1.317123058 0.589194599
## 524 -1.798974941 0.451519465
## 525 4.393612294 3.076142437
## 526 1.529417957 1.875300034
## 527 1.368042737 0.705377734
## 528 3.551157272 3.608853398
## 529 -0.517209941 1.636010565
## 530 2.688441752 3.316419881
## 531 3.499770830 1.828851380
## 532 3.724990075 4.325614961
## 533 0.139499405 0.309814498
## 534 -0.833114447 2.137699862
## 535 1.863638625 4.874685413
## 536 1.818029607 1.691487776
## 537 -1.295799214 0.469333869
## 538 1.404626707 1.454003508
## 539 1.799041210 1.741344586
## 540 0.386721810 0.743877107
## 541 4.843465536 3.615884943
## 542 0.491557292 -0.642091455
## 543 1.690932384 0.693931323
## 544 -0.194892976 3.003315155
## 545 -0.851779391 -1.118820053
## 546 3.060588580 -0.899875661
## 547 2.671301228 3.988557492
## 548 0.038706282 2.373156432
## 549 2.427858285 3.951699092
## 550 1.791497752 1.870957280
## 551 3.208209270 3.826587248
## 552 -1.585098384 -0.821394231
## 553 1.153618025 1.641275666
## 554 -0.844426980 1.583462256
## 555 -1.442919905 1.522072630
## 556 0.338622069 3.216788818
## 557 5.138546551 1.862341613
## 558 3.493918436 3.946413691
## 559 0.610245542 1.217338580
## 560 2.896185228 -0.399914503
## 561 -1.042275429 -0.715538133
## 562 3.570909514 2.471976472
## 563 1.782935932 6.921406578
## 564 0.654497942 1.244884374
## 565 0.693831022 -0.400945738
## 566 1.887010208 2.118090705
## 567 1.347012585 0.653990960
## 568 -1.353296788 0.288901620
## 569 0.256232931 3.696469161
## 570 3.942758409 2.630713959
## 571 0.126093861 1.259158722
## 572 1.187366722 2.197679017
## 573 1.136922173 0.939778255
## 574 0.047456179 3.485050854
## 575 0.117346295 2.188052658
## 576 0.352179198 0.398746143
## 577 2.231778353 2.615871327
## 578 3.752728701 2.979347039
## 579 0.520091206 2.269540521
## 580 -1.745498213 -0.035932817
## 581 1.792130775 1.741114192
## 582 0.808622700 1.774153208
## 583 -1.383416521 -1.672878142
## 584 2.097712299 3.443884086
## 585 -0.640156818 3.704116020
## 586 2.493482012 4.414506451
## 587 -0.743401109 1.735142840
## 588 1.240067877 3.202806600
## 589 -0.110961856 1.659726617
## 590 -2.851052716 -0.273870214
## 591 0.842913539 0.913136896
## 592 0.653320606 1.208912188
## 593 2.821809272 4.255510052
## 594 -0.751287737 1.034602716
## 595 2.527261664 -0.793065363
## 596 1.546827540 5.202763494
## 597 5.298335198 3.489716134
## 598 -0.564566549 1.785571383
## 599 0.563816281 4.013153716
## 600 -0.338295919 2.157554333
## 601 1.763870198 1.107445916
## 602 2.213924242 1.253381308
## 603 2.826170354 4.150941744
## 604 -0.274302934 3.259535344
## 605 0.225883700 2.207033320
## 606 1.147243292 1.413598963
## 607 0.822877062 0.134927187
## 608 1.202937755 3.276345733
## 609 -4.009407241 -1.659867767
## 610 -2.123520803 -1.256581567
## 611 1.247139594 0.609180719
## 612 -3.512979575 -0.261358869
## 613 0.731886463 3.184052506
## 614 -0.465663144 3.282022964
## 615 1.968307088 2.817582053
## 616 0.461983301 4.721393868
## 617 -0.341197197 -1.082043650
## 618 -0.478760194 -1.283765444
## 619 0.166654404 1.133714138
## 620 2.876188441 4.037142454
## 621 0.059508482 2.912439204
## 622 3.292975632 1.516062210
## 623 0.113644865 2.699396350
## 624 1.659840465 3.001951715
## 625 3.913709463 3.423821399
## 626 3.368777935 3.611728528
## 627 2.049321027 2.876282986
## 628 2.915082293 1.083958651
## 629 -0.788476259 2.348474310
## 630 0.811875189 2.053955505
## 631 2.846261899 3.650832576
## 632 0.320136616 1.340299929
## 633 1.738858606 3.782897071
## 634 2.623282016 4.587165074
## 635 1.618157793 3.839867004
## 636 3.038899098 3.499161674
## 637 1.638621138 1.774605891
## 638 0.919676216 2.314516820
## 639 1.624087489 3.572750866
## 640 0.750616691 1.823248076
## 641 -0.007354006 1.501096866
## 642 -0.432697597 -1.829208045
## 643 -1.660361421 1.113979603
## 644 -0.184268489 -0.116496184
## 645 -3.021706080 0.299861951
## 646 3.251157808 5.272438980
## 647 1.765609979 4.424637614
## 648 1.224298503 2.235946595
## 649 1.134046872 0.756356367
## 650 1.411435207 3.459218511
## 651 -0.619795209 1.051645979
## 652 -1.003786196 1.935287135
## 653 2.179827205 3.300984745
## 654 -1.280977616 1.489941433
## 655 -0.812208440 1.468649609
## 656 3.293920209 1.929865841
## 657 1.954136929 1.174729301
## 658 0.328165128 2.449735794
## 659 -1.260819485 -1.171711543
## 660 3.630903001 3.301605356
## 661 -1.241227505 -1.594966203
## 662 6.556999001 8.623745096
## 663 1.875966019 3.508861472
## 664 2.955846495 1.538657085
## 665 -0.645008472 -1.026941873
## 666 -0.063863533 2.605600674
## 667 0.321586482 1.485629647
## 668 -0.263739289 -1.116488338
## 669 1.796231035 0.106042368
## 670 0.353130625 1.164257932
## 671 1.401186465 4.268948217
## 672 -0.557419404 0.389849630
## 673 -2.369710862 -0.174262907
## 674 -1.009000418 2.012737424
## 675 -0.485497886 2.012951917
## 676 -0.086952548 -0.430895185
## 677 -0.019882648 3.005607801
## 678 3.860805177 5.793374874
## 679 0.152220202 -0.452597877
## 680 -0.245233801 2.237238646
## 681 4.708900758 3.248424159
## 682 3.620611369 3.899423694
## 683 -1.338189579 1.063004116
## 684 3.997788883 4.169069829
## 685 2.158413498 3.042379300
## 686 -0.684904494 -0.437777283
## 687 2.687992410 0.401529505
## 688 -0.448500078 2.502603164
## 689 -1.732857849 0.386314012
## 690 -0.921307134 2.351887975
## 691 2.093808626 2.942069280
## 692 2.162518262 3.161665401
## 693 1.120438049 -0.865794891
## 694 0.777590641 2.100587378
## 695 1.723350652 0.461954432
## 696 -0.562484702 -0.039789140
## 697 3.748286188 4.689828693
## 698 1.824642274 0.440167018
## 699 2.514208696 4.138833013
## 700 1.004090929 1.166964910
## 701 -1.458671175 0.299464549
## 702 2.129388996 1.694683462
## 703 2.164855108 4.249443642
## 704 2.877213510 4.560840070
## 705 -2.423741940 0.583597407
## 706 1.450154465 2.984471274
## 707 -0.790923039 2.663465555
## 708 1.738297686 2.604993722
## 709 1.910555263 2.095226668
## 710 3.140876542 3.582296313
## 711 1.296561235 3.619987149
## 712 1.937478672 3.260070434
## 713 0.748025878 4.255163553
## 714 1.468974911 3.386762514
## 715 0.650640406 1.485605110
## 716 1.614801278 -0.155060779
## 717 2.139410625 2.913695190
## 718 -3.966233038 1.088274340
## 719 -2.791065473 1.861927356
## 720 -0.261898702 0.606321621
## 721 1.758747112 4.245596745
## 722 0.094331033 2.557171091
## 723 0.991717668 0.259405127
## 724 -3.461828903 -2.243165147
## 725 2.038566039 2.252992153
## 726 4.874426863 3.980175771
## 727 3.381026827 4.663768634
## 728 0.325698188 2.554195018
## 729 3.437339679 4.731792184
## 730 2.700562654 3.118696592
## 731 -0.256303266 2.707136233
## 732 2.316749294 3.320314450
## 733 1.699662734 1.907492729
## 734 1.238881196 3.082884145
## 735 0.862762137 0.736534583
## 736 -0.298493491 -0.324217584
## 737 -0.937384021 1.219450760
## 738 -3.400521128 -1.777162482
## 739 2.792068675 1.675164263
## 740 -2.617522328 0.774134064
## 741 3.907914407 3.827623401
## 742 2.512641470 4.187440897
## 743 -0.070584764 2.761721770
## 744 -0.126402547 1.671210457
## 745 5.795355595 4.833110632
## 746 1.851019967 0.615997418
## 747 0.774985642 5.300027700
## 748 -0.977870560 1.736757457
## 749 3.285884944 4.170788188
## 750 2.998698419 2.345014132
## 751 -0.748504500 1.035092716
## 752 -0.378937433 2.520183229
## 753 4.346225411 6.114803416
## 754 1.210932273 0.772680262
## 755 3.474969835 4.058177892
## 756 -0.333064601 -0.686140696
## 757 3.096002588 4.277841211
## 758 0.735039311 2.712616041
## 759 0.854041880 2.962727177
## 760 0.581110014 1.369386732
## 761 1.054918825 1.598451979
## 762 -0.311988266 1.150154734
## 763 1.101000429 2.335352525
## 764 3.177857086 0.636698989
## 765 0.971880888 2.922392851
## 766 4.621455136 3.688485390
## 767 0.800703116 1.488403510
## 768 2.351226963 3.853266442
## 769 0.739170248 2.164927762
## 770 1.826357715 3.316716878
## 771 3.290081361 3.082127872
## 772 1.637837368 4.242029755
## 773 2.202821089 4.677461459
## 774 1.226276386 2.970967513
## 775 -2.030693133 0.946706844
## 776 0.531849808 0.745364643
## 777 -0.455231517 2.971004528
## 778 2.024497936 0.386223577
## 779 1.189099419 0.415910497
## 780 -0.722023441 2.269892329
## 781 0.241772805 3.241938088
## 782 1.375347366 2.900019639
## 783 -0.652212526 -0.180391257
## 784 2.889580795 2.904273684
## 785 0.580063453 1.979030394
## 786 3.152415514 1.601591572
## 787 -0.786717607 0.563601827
## 788 -1.581408538 2.451748080
## 789 1.485693471 2.447550282
## 790 0.630004038 1.139845124
## 791 -0.101554165 2.932679793
## 792 -1.489847783 1.919576331
## 793 -0.362605697 2.016921635
## 794 -0.715862793 0.726225640
## 795 4.771748676 4.089518091
## 796 -3.045777169 1.001303895
## 797 -0.506170693 -0.116108810
## 798 1.475718518 2.330855260
## 799 1.478469001 5.047167116
## 800 -2.844837993 2.109094704
## 801 0.814330240 2.913073659
## 802 -0.205240145 0.771859218
## 803 -2.400589989 0.695341653
## 804 6.314000499 5.014885378
## 805 4.730401557 4.440925780
## 806 3.703828276 4.122434908
## 807 1.584972275 1.312905006
## 808 -0.922839857 -0.922225808
## 809 1.494423807 3.470127070
## 810 3.034117717 2.735969289
## 811 1.798729997 7.082933862
## 812 3.212572925 4.741443967
## 813 0.330528660 1.747981047
## 814 2.803530528 4.998808325
## 815 0.882042860 3.223361188
## 816 -3.305878769 -0.008665892
## 817 -0.853939936 3.097673543
## 818 0.464898025 1.268006957
## 819 4.255337951 4.598434848
## 820 -0.483097940 2.196125748
## 821 -1.625210848 0.530214994
## 822 4.918021475 5.284507823
## 823 2.807668229 1.688155094
## 824 -3.272096925 -0.983807347
## 825 2.664956235 2.059466069
## 826 -3.252132339 0.489050349
## 827 4.068503462 3.846975819
## 828 -1.445362541 -0.994332704
## 829 -0.567036217 1.591906584
## 830 1.613963684 -0.678919982
## 831 2.966966790 2.584153881
## 832 1.164204879 -0.388185487
## 833 -0.531537217 0.890893688
## 834 3.581617384 4.271281985
## 835 2.736936619 4.872745350
## 836 0.579954586 3.369072437
## 837 0.555858707 0.886501525
## 838 3.548716390 4.781726770
## 839 2.399312986 1.659179231
## 840 0.872792637 3.992920440
## 841 2.143563999 3.557423725
## 842 1.058822037 3.875522140
## 843 -0.200743687 2.569844425
## 844 -1.952841829 -2.493781324
## 845 -1.501005964 1.468320429
## 846 1.710123652 -0.372773458
## 847 -0.409967988 4.187310370
## 848 0.451477433 2.584554200
## 849 -0.179235846 1.214610387
## 850 1.173615972 2.067004595
## 851 0.366301335 1.122089757
## 852 -3.799459748 3.347969664
## 853 3.817484962 1.202639823
## 854 1.450477665 4.158582967
## 855 3.633750100 4.652640573
## 856 0.391786381 5.619787008
## 857 -0.751695865 2.597930701
## 858 1.044206772 1.418029940
## 859 -0.285570597 0.162517210
## 860 4.164799570 3.058857331
## 861 1.615383247 2.489161923
## 862 -0.357601876 -0.068755300
## 863 0.310013871 -1.287333280
## 864 -2.327866259 -0.560915356
## 865 -1.010121236 1.569205322
## 866 3.216213919 0.416093338
## 867 2.338079416 3.717506706
## 868 -0.928956631 1.357215125
## 869 2.437171367 2.044412953
## 870 0.749420522 2.380081096
## 871 0.572441622 1.055946639
## 872 1.792421731 5.006696168
## 873 2.162731554 0.992782383
## 874 -1.591823468 0.710393379
## 875 3.714940143 3.226487045
## 876 0.149519892 3.050983728
## 877 0.114002395 0.089036606
## 878 2.742023359 4.756242933
## 879 1.941840374 2.558795351
## 880 0.059965465 2.562276975
## 881 -1.984166237 -1.310165039
## 882 0.897342766 1.918954511
## 883 4.855614008 1.336842473
## 884 1.780607894 3.414981734
## 885 3.010443172 2.573041295
## 886 -0.463562314 1.474391450
## 887 4.994482669 3.881333523
## 888 -2.123874721 3.182684315
## 889 2.018549392 2.248853982
## 890 0.881505995 1.744559920
## 891 1.209173027 1.318754070
## 892 1.008106227 0.629904031
## 893 2.006385091 3.925827502
## 894 2.558495190 3.979832823
## 895 -1.062973553 1.476513094
## 896 1.584329700 0.597306724
## 897 3.423633476 1.184946070
## 898 1.401127081 2.341231435
## 899 1.115235601 1.723664639
## 900 1.283904360 0.563603106
## 901 -1.842740116 0.202791492
## 902 1.596479078 4.026680637
## 903 4.226508109 3.415818458
## 904 1.595444305 1.815360223
## 905 0.302638925 -0.274027289
## 906 1.255417162 1.285604401
## 907 1.447870967 1.621331356
## 908 -0.393060407 1.269093885
## 909 0.911113440 3.586964371
## 910 1.644680265 2.826152984
## 911 -0.540184964 3.754645295
## 912 0.824515104 0.686763332
## 913 2.082504881 3.599752346
## 914 -0.705656594 3.991009915
## 915 1.326969009 3.747953147
## 916 0.951818007 1.496020955
## 917 -3.140366104 -0.833927275
## 918 1.386046101 3.333015120
## 919 -1.838399231 3.195537565
## 920 3.042437411 0.913395783
## 921 1.325437416 0.572121043
## 922 1.281761081 3.451027243
## 923 2.189281694 1.096966974
## 924 -0.290866019 0.183414314
## 925 0.775244389 -0.363322716
## 926 -3.220354457 2.929840037
## 927 5.107820655 2.532603668
## 928 2.456616375 2.415576763
## 929 4.141270421 3.736657578
## 930 0.379486447 -0.832998030
## 931 2.881349152 2.034007484
## 932 -1.807254985 0.880401288
## 933 1.352119875 3.664008054
## 934 -1.554150325 0.430148677
## 935 4.620046892 5.062452060
## 936 4.166692117 5.375967131
## 937 1.064492988 1.161410770
## 938 2.660821392 4.046604992
## 939 4.527992858 0.137676604
## 940 1.892544705 3.226342455
## 941 0.019445395 -0.582844787
## 942 1.985233508 1.140487397
## 943 2.481131029 3.771204805
## 944 2.588600224 0.169582013
## 945 2.650706825 1.367973609
## 946 -0.735229409 3.428579861
## 947 3.063719519 2.246972501
## 948 1.974187882 1.017534851
## 949 0.657426805 1.761549663
## 950 0.873844849 3.044836819
## 951 3.694473660 2.117557085
## 952 1.857451171 4.663109423
## 953 -1.095462211 -2.451124395
## 954 1.488177907 0.836661903
## 955 -0.117821072 3.766350042
## 956 5.114070258 1.672732944
## 957 2.925987620 2.425370034
## 958 1.959284332 4.082087362
## 959 0.931508154 0.725345288
## 960 0.482837376 2.859633160
## 961 -2.867825063 2.481120600
## 962 -1.995605591 1.154925615
## 963 1.361555393 4.011397625
## 964 1.419777997 2.273170264
## 965 1.875055936 1.037587997
## 966 1.286000180 3.819086238
## 967 1.594790946 0.294605433
## 968 1.450033177 0.101760111
## 969 0.532364842 3.647476302
## 970 -4.320686613 -2.179994164
## 971 3.039758946 1.396731929
## 972 3.292543828 2.423532711
## 973 2.278258482 3.572861962
## 974 -0.421145556 1.134903074
## 975 1.786392678 6.380183409
## 976 1.507916262 2.845496111
## 977 0.210041981 1.412317734
## 978 3.455824798 2.219906725
## 979 1.250565481 2.628890085
## 980 1.272689815 4.966796400
## 981 -0.611049644 4.492027626
## 982 1.088097464 4.025689618
## 983 -2.299673930 2.442452912
## 984 1.967553216 0.410091702
## 985 -0.365900980 1.885120063
## 986 2.764817517 1.388106778
## 987 1.453183154 4.448311591
## 988 -0.630971269 2.918993199
## 989 1.239695436 0.440648395
## 990 0.158451745 2.907774138
## 991 2.278990728 4.474669241
## 992 -1.118875961 -1.147117632
## 993 2.669014965 1.591962671
## 994 2.197370002 4.883925850
## 995 1.390476187 4.397832471
## 996 -0.585518521 2.899469574
## 997 1.059507685 0.931703879
## 998 -1.413718879 1.405982185
## 999 1.645726637 2.597981729
## 1000 1.771552340 1.547399057p2 <- ggplot(d, aes(x = X1, y = X2)) +
geom_point(alpha = .5) +
geom_density_2d()
p2
mu## [1] 1 2y <- x - mu
head (y)## [,1] [,2]
## [1,] -1.2051566 0.3078223
## [2,] 2.0313693 0.9917705
## [3,] 1.2123073 3.8824405
## [4,] -0.8265117 -1.8134133
## [5,] -1.5688595 -0.1162473
## [6,] 1.5517372 1.2776175y <- data.frame(x)
y## X1 X2
## 1 -0.205156592 1.307822329
## 2 4.031369338 2.991770505
## 3 2.212307319 4.882440535
## 4 1.173488321 0.186586732
## 5 -0.568859453 0.883752746
## 6 3.551737218 3.277617451
## 7 1.831449504 2.406630823
## 8 0.937685108 4.614989617
## 9 0.849985521 -0.941995922
## 10 2.080369843 1.619715404
## 11 -1.172083277 1.042598089
## 12 -1.379038272 0.229082932
## 13 -1.147886254 -1.114656027
## 14 2.694241593 2.722246451
## 15 -0.479645074 3.414275955
## 16 1.652660790 1.756334982
## 17 3.211733394 3.941841839
## 18 2.964047158 3.590054111
## 19 2.028365830 2.209966687
## 20 0.198856570 1.204678655
## 21 -0.450281636 1.268830087
## 22 -0.209438285 4.841993107
## 23 2.687144008 0.839111301
## 24 -0.035622743 1.008997772
## 25 2.450170974 2.301890441
## 26 1.470162825 2.095640269
## 27 1.687102058 4.218055112
## 28 1.419176035 4.357483962
## 29 -1.643971532 2.087100548
## 30 1.359117335 2.423400090
## 31 1.446276290 1.390474520
## 32 -0.212158696 0.143968016
## 33 -0.886525125 1.894737208
## 34 1.890075942 2.338805601
## 35 3.922663410 5.877085893
## 36 -1.240612301 -2.059110884
## 37 2.531689414 1.403524931
## 38 0.256004392 3.293397119
## 39 -0.232833609 -0.159969668
## 40 1.269907272 1.874380120
## 41 1.227656386 2.634438135
## 42 0.650816448 2.847296385
## 43 0.763323224 2.419601425
## 44 3.349881134 3.329558903
## 45 1.020242354 3.698841346
## 46 3.215189408 3.456945841
## 47 1.105224063 1.105520847
## 48 3.274142502 1.781522928
## 49 6.059879105 5.740498774
## 50 -0.029417541 0.185930305
## 51 -0.219118051 2.021479041
## 52 0.331130233 1.291944855
## 53 -0.851817493 1.391261199
## 54 -1.444184634 -1.173807306
## 55 0.786837816 3.291823317
## 56 0.237477485 2.672574211
## 57 -2.136544235 0.999449920
## 58 2.166231676 2.785368701
## 59 0.842646058 1.009751220
## 60 -1.206627342 -0.155488750
## 61 0.693165757 0.513907334
## 62 -0.085526423 1.304672621
## 63 4.172539772 1.968485218
## 64 1.495620170 2.260048903
## 65 -0.886242101 1.342451047
## 66 4.026443458 3.551772769
## 67 0.841626329 1.331011211
## 68 -2.304929812 2.699176128
## 69 -1.387527083 2.391115220
## 70 3.852556041 0.707736167
## 71 2.199581595 1.964968341
## 72 -2.869019608 -1.365262876
## 73 -2.372393357 0.229891328
## 74 -1.418918244 2.305247125
## 75 4.307348632 1.072098725
## 76 2.944291052 3.702750120
## 77 1.070739976 0.534749515
## 78 0.613097090 1.473480973
## 79 1.871209323 1.706335958
## 80 2.664591617 1.935555596
## 81 2.430723480 0.872954943
## 82 0.403313985 6.601314644
## 83 0.367552122 2.254236166
## 84 1.949843563 1.565291147
## 85 2.199467937 2.895031656
## 86 0.623311722 1.985888054
## 87 2.131162735 5.467851438
## 88 -1.039030699 -0.212306595
## 89 1.247072505 2.529898291
## 90 1.580169401 1.494468722
## 91 -0.330788096 3.471683404
## 92 -0.157671793 0.385483734
## 93 0.435646808 1.544141300
## 94 3.177979930 2.762786609
## 95 2.166618539 1.605925082
## 96 1.229070585 1.588627698
## 97 0.678194635 0.586314883
## 98 -0.393135848 4.535105046
## 99 1.449553756 0.287765538
## 100 -0.839491539 -0.285728586
## 101 5.958119998 5.386205293
## 102 0.796456613 2.740848280
## 103 -0.063001365 0.986844417
## 104 -0.847893005 0.582521348
## 105 4.138322651 2.839576186
## 106 1.365868834 2.466264574
## 107 3.075457023 1.847402334
## 108 0.037040886 4.187305968
## 109 -0.253239136 0.567406117
## 110 -2.095088254 -0.799720542
## 111 0.245747478 2.689764370
## 112 3.527989176 3.783151311
## 113 0.335598140 1.893450247
## 114 -0.755576485 0.428892395
## 115 2.127033114 0.833496973
## 116 4.702149787 2.951237288
## 117 0.996600937 0.910690989
## 118 -0.842848106 -0.480546610
## 119 0.884438271 2.583576017
## 120 1.183102920 0.901937305
## 121 -0.795974859 0.733918175
## 122 3.232130778 0.977816058
## 123 1.725783831 5.015946544
## 124 0.041731579 -0.284566611
## 125 -0.003025144 2.421607067
## 126 -0.036788996 0.868336051
## 127 0.390771401 1.954919265
## 128 4.018334744 2.753537948
## 129 3.429040352 3.640944959
## 130 -0.079866956 -0.575209585
## 131 -0.275604961 0.904498239
## 132 1.821438362 4.156599988
## 133 6.271260259 5.824471696
## 134 -0.243031162 -0.952539413
## 135 0.303938721 1.927586433
## 136 3.162992850 4.051931946
## 137 1.529059858 0.098845823
## 138 2.379735197 1.746056866
## 139 1.377420734 2.220404509
## 140 1.835680233 2.281126764
## 141 -1.786459546 2.269184319
## 142 1.591585075 1.781800179
## 143 1.302114962 2.286010224
## 144 2.346650546 4.812417988
## 145 0.674043353 2.152194987
## 146 3.835184422 4.383874601
## 147 2.873544267 1.697776690
## 148 4.880994377 3.235009057
## 149 3.823735907 0.836328104
## 150 1.742938750 4.059508029
## 151 -0.795950122 0.364796536
## 152 -1.393089872 -0.251930475
## 153 0.347109627 2.296806997
## 154 -2.746838188 1.214956329
## 155 4.519093503 6.033340181
## 156 3.922868434 3.971291129
## 157 -2.652376148 0.043848015
## 158 0.719793536 2.954660371
## 159 0.089604451 -0.121425722
## 160 4.745404750 4.440053336
## 161 2.140498819 4.129080595
## 162 -1.198104933 2.329991783
## 163 0.380720507 2.826202249
## 164 1.239091476 3.002775483
## 165 3.567445320 2.762730189
## 166 2.284966314 0.625050914
## 167 0.469034517 4.083242162
## 168 0.570649015 -1.149962402
## 169 -1.730959978 0.904244265
## 170 2.604471885 2.319801145
## 171 2.737167548 3.922019622
## 172 4.238856650 3.031186850
## 173 -0.085388477 -0.901518657
## 174 0.869169471 1.118987650
## 175 -0.970618598 1.157704720
## 176 1.827785408 -0.694112770
## 177 0.245464576 1.950881396
## 178 -0.526682234 2.044893103
## 179 1.771112673 2.177170738
## 180 -2.287366302 4.826519662
## 181 0.972036448 2.951424859
## 182 2.101497895 3.832606137
## 183 2.451448437 2.115962784
## 184 1.194362553 0.663748668
## 185 2.385567272 1.726425287
## 186 4.710503558 0.653753150
## 187 0.573441877 3.091365044
## 188 1.647742920 1.321045066
## 189 -0.831967228 1.676332342
## 190 -0.033902268 -0.941027509
## 191 1.173257781 2.331074322
## 192 0.742265733 0.369811092
## 193 2.688863784 4.526153213
## 194 1.237291676 0.396068702
## 195 0.358405734 2.322108599
## 196 -1.454879839 -1.898580874
## 197 2.230894100 1.138180961
## 198 0.744574653 4.141374323
## 199 -0.010423142 2.950345696
## 200 -1.619024656 0.710442621
## 201 0.201839156 0.044069260
## 202 -0.234528051 1.595913450
## 203 1.359424461 -0.327014914
## 204 0.753922077 3.042585457
## 205 0.093604572 2.069466156
## 206 2.095335381 2.715504883
## 207 2.184857517 2.166210088
## 208 -1.279893752 -2.562777798
## 209 1.063505008 2.652678798
## 210 1.715465884 1.391282624
## 211 4.576536327 3.469625640
## 212 1.957675653 4.155341802
## 213 -0.632166150 0.858319007
## 214 5.607845179 3.366006863
## 215 3.326731390 0.561663401
## 216 0.847066826 2.512862122
## 217 1.010545964 0.521157346
## 218 0.431272808 0.245708835
## 219 2.977765732 4.177826685
## 220 -2.575896758 2.773593804
## 221 -1.126361257 2.047362916
## 222 2.154222744 2.043501215
## 223 -0.145271373 1.908179096
## 224 2.338819385 3.693788907
## 225 -3.859107902 -1.834610394
## 226 4.333848150 4.518800744
## 227 2.237530120 3.416369503
## 228 1.264505279 -1.843732574
## 229 2.858382945 1.829617548
## 230 1.276709448 1.646094183
## 231 2.477719351 1.919296000
## 232 1.775567389 1.651434981
## 233 -0.417227844 3.368006231
## 234 3.391385518 5.241337851
## 235 1.757496219 3.879698530
## 236 4.633311501 2.649373005
## 237 -1.673783436 0.864152329
## 238 0.674446648 2.128167929
## 239 4.103191819 2.428289799
## 240 1.587935455 1.836681205
## 241 1.215805963 2.526011566
## 242 3.617531546 2.945435126
## 243 2.806056466 3.676729894
## 244 2.432877712 1.573237558
## 245 3.908418257 2.290468321
## 246 1.586275391 4.240760727
## 247 2.871060664 0.941780881
## 248 -1.439213084 -0.715729255
## 249 1.441699784 2.372284620
## 250 2.009275440 3.109283763
## 251 -0.713879460 0.033676489
## 252 3.392999878 3.807676718
## 253 -1.950131860 0.995714649
## 254 -1.883764386 -1.896147150
## 255 1.243605081 1.954621861
## 256 0.934627060 2.299380662
## 257 2.809354202 2.832921354
## 258 -0.596247539 0.449650815
## 259 0.921304230 2.433799559
## 260 -1.099139866 1.113573871
## 261 2.795668117 2.366374683
## 262 -0.495652754 1.155293543
## 263 3.448636296 3.527747916
## 264 3.451829981 2.923102560
## 265 1.473520739 1.315734522
## 266 1.877282697 1.510804003
## 267 -1.654631367 1.411090205
## 268 5.185050033 4.406020776
## 269 3.438285359 3.242976284
## 270 -0.281737531 1.326560436
## 271 0.212048268 1.078526213
## 272 1.678433746 0.434242944
## 273 3.148673644 3.902769302
## 274 -0.941092207 2.373839136
## 275 5.351244899 2.453323037
## 276 2.181950599 1.193512528
## 277 3.272305474 3.033691007
## 278 3.350441662 0.538451578
## 279 0.605319439 1.107910228
## 280 0.267446699 0.857676654
## 281 -0.275111050 2.479348818
## 282 -0.253188813 3.819855702
## 283 -1.219940953 1.498747190
## 284 2.352846077 3.260867751
## 285 0.465531303 1.960613931
## 286 2.026237307 0.154292257
## 287 -0.320324259 2.085439081
## 288 0.916474762 3.994409198
## 289 2.332790482 2.496712079
## 290 -1.879265333 1.195144673
## 291 0.335146087 1.654448339
## 292 -0.987514334 2.152705867
## 293 -1.121312678 1.045315363
## 294 1.291627252 0.930806596
## 295 1.378872163 0.170925449
## 296 -4.131595168 1.182179381
## 297 2.452610021 2.004230446
## 298 1.317782020 0.389687833
## 299 -0.335506687 -1.252232341
## 300 4.312703142 5.711080840
## 301 3.046048954 2.558974670
## 302 0.083740238 -0.502482572
## 303 2.398570446 2.099088483
## 304 -1.054327535 -0.682496184
## 305 -0.052670017 0.440481732
## 306 -0.446544170 -0.217969683
## 307 4.230105687 2.922494315
## 308 1.600617377 -1.658014893
## 309 -0.249587881 0.638596079
## 310 -0.477786738 3.846289373
## 311 -1.537454725 1.725984807
## 312 2.724794047 2.767766132
## 313 -0.150841074 3.049852629
## 314 0.729555111 0.353590617
## 315 -0.491085671 4.638311680
## 316 -1.345441216 -1.421382013
## 317 2.197921789 2.808026465
## 318 -2.690773945 -1.944193279
## 319 1.417306495 3.801269967
## 320 1.943840548 1.550039211
## 321 -0.448727097 1.975128612
## 322 1.656023255 3.120104213
## 323 0.745908102 3.250889505
## 324 -0.780453443 0.991418076
## 325 2.978425805 4.038315165
## 326 -2.660440793 1.085840259
## 327 1.352860862 -0.034621525
## 328 1.456922289 0.913410503
## 329 3.260956961 3.455739955
## 330 2.543957498 2.630109794
## 331 3.433740262 4.747187788
## 332 4.757986691 3.058845134
## 333 -3.299029164 0.787301043
## 334 1.307216806 1.861060814
## 335 2.658925936 3.975249239
## 336 -0.159529204 1.226995310
## 337 1.454285913 1.322233385
## 338 0.072363770 -1.162521209
## 339 -1.895920743 -0.804810217
## 340 -1.028170774 0.384291123
## 341 2.285897234 3.823897598
## 342 -0.956507437 -0.042015362
## 343 -1.232451185 0.735181560
## 344 0.813090661 2.657926777
## 345 -0.785202772 -1.585789111
## 346 1.491904113 3.893544443
## 347 2.843588037 1.377337914
## 348 -0.588903533 5.156882186
## 349 0.633468753 1.749038811
## 350 0.899872392 -0.407816816
## 351 -1.263708368 -0.933060438
## 352 -0.263488713 1.805072310
## 353 -1.287706750 2.199359880
## 354 1.047035175 0.681301731
## 355 1.854948636 3.352800328
## 356 2.916973352 2.247809789
## 357 0.771528702 1.805298123
## 358 4.399173484 4.653529783
## 359 2.439987801 1.998329858
## 360 1.943104339 2.870527886
## 361 -1.970951964 -1.417045736
## 362 1.372175317 -0.144623765
## 363 1.143913251 2.410922851
## 364 2.188757488 2.627322390
## 365 0.147889928 3.203956876
## 366 4.832446130 4.421025273
## 367 -1.943778657 3.200238711
## 368 1.187498805 2.828444331
## 369 2.139555482 2.191288985
## 370 1.428481171 3.627355338
## 371 2.922519520 4.022368883
## 372 5.947222579 4.428108276
## 373 0.155290321 -1.505055630
## 374 5.895038165 2.722438487
## 375 5.768598090 3.948774456
## 376 3.891134791 2.685121820
## 377 2.101980161 2.638056506
## 378 0.575084555 1.698129707
## 379 2.830746171 2.239339224
## 380 -3.021181343 0.533555810
## 381 2.382608180 3.313381582
## 382 1.232171798 -0.425522841
## 383 2.251851667 3.792921126
## 384 3.323755357 2.349103463
## 385 1.218587042 4.256538815
## 386 -2.446936714 0.346691705
## 387 0.968574440 -0.393197425
## 388 2.592385658 5.233667753
## 389 0.835667823 1.541531196
## 390 1.754643580 1.809782048
## 391 3.069658823 3.938988432
## 392 0.343666105 0.073760380
## 393 -1.863512897 0.287440298
## 394 1.429622209 -0.759828153
## 395 -2.988083238 -0.131509326
## 396 1.243409284 0.725038468
## 397 2.889406275 3.044656861
## 398 1.132800145 3.245542495
## 399 1.494723904 1.487759934
## 400 1.807606254 3.190734758
## 401 1.313925004 1.122285713
## 402 3.289591328 4.369602293
## 403 1.611283194 2.391397045
## 404 2.069929374 5.498493124
## 405 1.441362588 1.896005951
## 406 -4.693565387 -1.974246221
## 407 0.966888876 2.294302195
## 408 1.993245446 3.501508408
## 409 1.310154976 3.880691622
## 410 -1.448075897 -0.497817150
## 411 -0.941577660 2.525193085
## 412 1.284857654 3.247328909
## 413 0.153429852 0.879817896
## 414 -0.748487653 -1.242184049
## 415 -2.055587295 -1.019980197
## 416 2.687829660 1.614112853
## 417 3.367786795 4.928248308
## 418 0.791501958 2.357263606
## 419 -2.821170394 -0.325607768
## 420 1.276034336 2.521590750
## 421 1.051782338 5.971644074
## 422 0.156297322 1.847556167
## 423 2.232561517 2.322667180
## 424 0.352397389 3.350710938
## 425 4.084129669 2.859562865
## 426 2.024434492 2.156500349
## 427 2.300987763 0.677292441
## 428 5.115293398 2.315962337
## 429 -1.997341134 0.604977558
## 430 2.194337229 4.742423309
## 431 2.829030594 2.745641073
## 432 -2.153787196 -0.199938411
## 433 2.121829299 6.090781236
## 434 -1.934613318 2.807222928
## 435 0.924613408 4.432966882
## 436 -1.105802365 1.594871665
## 437 -0.602511479 2.862080334
## 438 4.944551264 6.029965039
## 439 3.567115210 5.468175269
## 440 3.318207604 2.484653020
## 441 1.369183757 0.675775712
## 442 1.330917543 3.896167075
## 443 2.296034602 3.053573291
## 444 -1.332392149 0.426031889
## 445 -0.245335566 2.217767834
## 446 -0.585184232 2.363948957
## 447 -0.114868021 4.368032300
## 448 1.489960667 1.110489177
## 449 1.264516999 1.558091122
## 450 1.849275374 2.607623085
## 451 -1.391308577 0.133501419
## 452 2.496454546 4.853650500
## 453 2.730664327 1.586521129
## 454 2.557944671 2.384739854
## 455 1.724698398 2.595934646
## 456 5.276897668 1.506002202
## 457 0.193053600 -0.859369509
## 458 2.748590585 4.128140815
## 459 2.692497390 -0.341222623
## 460 2.687999355 4.842434567
## 461 0.086087533 1.419690747
## 462 1.135074026 2.577463301
## 463 3.017523638 4.532893791
## 464 0.927065855 2.267878467
## 465 6.017729017 4.104937288
## 466 0.607718449 -0.092860649
## 467 0.881059037 1.639011078
## 468 0.655316892 1.051094397
## 469 -0.723447378 0.433063360
## 470 1.357409473 4.120798322
## 471 2.811214214 2.000023755
## 472 -2.710689516 -0.331435692
## 473 0.179652114 1.912449300
## 474 0.856308377 4.915010053
## 475 -0.205023322 -0.141843000
## 476 0.163674604 0.273495662
## 477 1.431061589 2.470543528
## 478 0.770743877 -0.457159671
## 479 1.598151237 2.632681676
## 480 -1.190549977 2.766254182
## 481 3.797886246 6.208260233
## 482 1.327042534 2.164656270
## 483 1.224603994 2.168594302
## 484 -3.487352019 -1.776930856
## 485 0.524516118 1.004458136
## 486 -0.081797058 -1.427982062
## 487 -2.495770568 -0.647061862
## 488 2.275069257 0.754695969
## 489 -0.489657264 1.681393606
## 490 0.462842857 2.058434441
## 491 4.792039883 1.453417830
## 492 0.123185685 0.981676997
## 493 3.470259526 1.589589461
## 494 1.284947524 3.243399567
## 495 -0.101333656 4.116536557
## 496 1.693149429 0.620040238
## 497 1.752586453 1.906092568
## 498 1.550619353 2.028682907
## 499 2.295164921 0.388328692
## 500 -0.143180044 1.297956516
## 501 -1.495932953 -0.263546377
## 502 0.891184540 1.773352009
## 503 -3.308143328 2.271589881
## 504 2.837632626 6.098815557
## 505 2.063879386 1.652952307
## 506 7.961407809 8.212590362
## 507 -1.075478626 2.083283956
## 508 0.699694262 2.187685873
## 509 0.727336100 0.060569566
## 510 2.531524043 5.026308978
## 511 0.593458840 1.640833853
## 512 4.189422272 4.258059997
## 513 -2.035577139 1.447707484
## 514 4.969387163 5.248194267
## 515 2.211488994 3.417646470
## 516 -1.128631963 1.818819741
## 517 -1.089420487 0.713075685
## 518 2.156639490 0.663416890
## 519 1.753108918 2.851781622
## 520 2.129774736 5.016127743
## 521 -0.621510856 2.418279632
## 522 0.682677822 1.522689373
## 523 1.317123058 0.589194599
## 524 -1.798974941 0.451519465
## 525 4.393612294 3.076142437
## 526 1.529417957 1.875300034
## 527 1.368042737 0.705377734
## 528 3.551157272 3.608853398
## 529 -0.517209941 1.636010565
## 530 2.688441752 3.316419881
## 531 3.499770830 1.828851380
## 532 3.724990075 4.325614961
## 533 0.139499405 0.309814498
## 534 -0.833114447 2.137699862
## 535 1.863638625 4.874685413
## 536 1.818029607 1.691487776
## 537 -1.295799214 0.469333869
## 538 1.404626707 1.454003508
## 539 1.799041210 1.741344586
## 540 0.386721810 0.743877107
## 541 4.843465536 3.615884943
## 542 0.491557292 -0.642091455
## 543 1.690932384 0.693931323
## 544 -0.194892976 3.003315155
## 545 -0.851779391 -1.118820053
## 546 3.060588580 -0.899875661
## 547 2.671301228 3.988557492
## 548 0.038706282 2.373156432
## 549 2.427858285 3.951699092
## 550 1.791497752 1.870957280
## 551 3.208209270 3.826587248
## 552 -1.585098384 -0.821394231
## 553 1.153618025 1.641275666
## 554 -0.844426980 1.583462256
## 555 -1.442919905 1.522072630
## 556 0.338622069 3.216788818
## 557 5.138546551 1.862341613
## 558 3.493918436 3.946413691
## 559 0.610245542 1.217338580
## 560 2.896185228 -0.399914503
## 561 -1.042275429 -0.715538133
## 562 3.570909514 2.471976472
## 563 1.782935932 6.921406578
## 564 0.654497942 1.244884374
## 565 0.693831022 -0.400945738
## 566 1.887010208 2.118090705
## 567 1.347012585 0.653990960
## 568 -1.353296788 0.288901620
## 569 0.256232931 3.696469161
## 570 3.942758409 2.630713959
## 571 0.126093861 1.259158722
## 572 1.187366722 2.197679017
## 573 1.136922173 0.939778255
## 574 0.047456179 3.485050854
## 575 0.117346295 2.188052658
## 576 0.352179198 0.398746143
## 577 2.231778353 2.615871327
## 578 3.752728701 2.979347039
## 579 0.520091206 2.269540521
## 580 -1.745498213 -0.035932817
## 581 1.792130775 1.741114192
## 582 0.808622700 1.774153208
## 583 -1.383416521 -1.672878142
## 584 2.097712299 3.443884086
## 585 -0.640156818 3.704116020
## 586 2.493482012 4.414506451
## 587 -0.743401109 1.735142840
## 588 1.240067877 3.202806600
## 589 -0.110961856 1.659726617
## 590 -2.851052716 -0.273870214
## 591 0.842913539 0.913136896
## 592 0.653320606 1.208912188
## 593 2.821809272 4.255510052
## 594 -0.751287737 1.034602716
## 595 2.527261664 -0.793065363
## 596 1.546827540 5.202763494
## 597 5.298335198 3.489716134
## 598 -0.564566549 1.785571383
## 599 0.563816281 4.013153716
## 600 -0.338295919 2.157554333
## 601 1.763870198 1.107445916
## 602 2.213924242 1.253381308
## 603 2.826170354 4.150941744
## 604 -0.274302934 3.259535344
## 605 0.225883700 2.207033320
## 606 1.147243292 1.413598963
## 607 0.822877062 0.134927187
## 608 1.202937755 3.276345733
## 609 -4.009407241 -1.659867767
## 610 -2.123520803 -1.256581567
## 611 1.247139594 0.609180719
## 612 -3.512979575 -0.261358869
## 613 0.731886463 3.184052506
## 614 -0.465663144 3.282022964
## 615 1.968307088 2.817582053
## 616 0.461983301 4.721393868
## 617 -0.341197197 -1.082043650
## 618 -0.478760194 -1.283765444
## 619 0.166654404 1.133714138
## 620 2.876188441 4.037142454
## 621 0.059508482 2.912439204
## 622 3.292975632 1.516062210
## 623 0.113644865 2.699396350
## 624 1.659840465 3.001951715
## 625 3.913709463 3.423821399
## 626 3.368777935 3.611728528
## 627 2.049321027 2.876282986
## 628 2.915082293 1.083958651
## 629 -0.788476259 2.348474310
## 630 0.811875189 2.053955505
## 631 2.846261899 3.650832576
## 632 0.320136616 1.340299929
## 633 1.738858606 3.782897071
## 634 2.623282016 4.587165074
## 635 1.618157793 3.839867004
## 636 3.038899098 3.499161674
## 637 1.638621138 1.774605891
## 638 0.919676216 2.314516820
## 639 1.624087489 3.572750866
## 640 0.750616691 1.823248076
## 641 -0.007354006 1.501096866
## 642 -0.432697597 -1.829208045
## 643 -1.660361421 1.113979603
## 644 -0.184268489 -0.116496184
## 645 -3.021706080 0.299861951
## 646 3.251157808 5.272438980
## 647 1.765609979 4.424637614
## 648 1.224298503 2.235946595
## 649 1.134046872 0.756356367
## 650 1.411435207 3.459218511
## 651 -0.619795209 1.051645979
## 652 -1.003786196 1.935287135
## 653 2.179827205 3.300984745
## 654 -1.280977616 1.489941433
## 655 -0.812208440 1.468649609
## 656 3.293920209 1.929865841
## 657 1.954136929 1.174729301
## 658 0.328165128 2.449735794
## 659 -1.260819485 -1.171711543
## 660 3.630903001 3.301605356
## 661 -1.241227505 -1.594966203
## 662 6.556999001 8.623745096
## 663 1.875966019 3.508861472
## 664 2.955846495 1.538657085
## 665 -0.645008472 -1.026941873
## 666 -0.063863533 2.605600674
## 667 0.321586482 1.485629647
## 668 -0.263739289 -1.116488338
## 669 1.796231035 0.106042368
## 670 0.353130625 1.164257932
## 671 1.401186465 4.268948217
## 672 -0.557419404 0.389849630
## 673 -2.369710862 -0.174262907
## 674 -1.009000418 2.012737424
## 675 -0.485497886 2.012951917
## 676 -0.086952548 -0.430895185
## 677 -0.019882648 3.005607801
## 678 3.860805177 5.793374874
## 679 0.152220202 -0.452597877
## 680 -0.245233801 2.237238646
## 681 4.708900758 3.248424159
## 682 3.620611369 3.899423694
## 683 -1.338189579 1.063004116
## 684 3.997788883 4.169069829
## 685 2.158413498 3.042379300
## 686 -0.684904494 -0.437777283
## 687 2.687992410 0.401529505
## 688 -0.448500078 2.502603164
## 689 -1.732857849 0.386314012
## 690 -0.921307134 2.351887975
## 691 2.093808626 2.942069280
## 692 2.162518262 3.161665401
## 693 1.120438049 -0.865794891
## 694 0.777590641 2.100587378
## 695 1.723350652 0.461954432
## 696 -0.562484702 -0.039789140
## 697 3.748286188 4.689828693
## 698 1.824642274 0.440167018
## 699 2.514208696 4.138833013
## 700 1.004090929 1.166964910
## 701 -1.458671175 0.299464549
## 702 2.129388996 1.694683462
## 703 2.164855108 4.249443642
## 704 2.877213510 4.560840070
## 705 -2.423741940 0.583597407
## 706 1.450154465 2.984471274
## 707 -0.790923039 2.663465555
## 708 1.738297686 2.604993722
## 709 1.910555263 2.095226668
## 710 3.140876542 3.582296313
## 711 1.296561235 3.619987149
## 712 1.937478672 3.260070434
## 713 0.748025878 4.255163553
## 714 1.468974911 3.386762514
## 715 0.650640406 1.485605110
## 716 1.614801278 -0.155060779
## 717 2.139410625 2.913695190
## 718 -3.966233038 1.088274340
## 719 -2.791065473 1.861927356
## 720 -0.261898702 0.606321621
## 721 1.758747112 4.245596745
## 722 0.094331033 2.557171091
## 723 0.991717668 0.259405127
## 724 -3.461828903 -2.243165147
## 725 2.038566039 2.252992153
## 726 4.874426863 3.980175771
## 727 3.381026827 4.663768634
## 728 0.325698188 2.554195018
## 729 3.437339679 4.731792184
## 730 2.700562654 3.118696592
## 731 -0.256303266 2.707136233
## 732 2.316749294 3.320314450
## 733 1.699662734 1.907492729
## 734 1.238881196 3.082884145
## 735 0.862762137 0.736534583
## 736 -0.298493491 -0.324217584
## 737 -0.937384021 1.219450760
## 738 -3.400521128 -1.777162482
## 739 2.792068675 1.675164263
## 740 -2.617522328 0.774134064
## 741 3.907914407 3.827623401
## 742 2.512641470 4.187440897
## 743 -0.070584764 2.761721770
## 744 -0.126402547 1.671210457
## 745 5.795355595 4.833110632
## 746 1.851019967 0.615997418
## 747 0.774985642 5.300027700
## 748 -0.977870560 1.736757457
## 749 3.285884944 4.170788188
## 750 2.998698419 2.345014132
## 751 -0.748504500 1.035092716
## 752 -0.378937433 2.520183229
## 753 4.346225411 6.114803416
## 754 1.210932273 0.772680262
## 755 3.474969835 4.058177892
## 756 -0.333064601 -0.686140696
## 757 3.096002588 4.277841211
## 758 0.735039311 2.712616041
## 759 0.854041880 2.962727177
## 760 0.581110014 1.369386732
## 761 1.054918825 1.598451979
## 762 -0.311988266 1.150154734
## 763 1.101000429 2.335352525
## 764 3.177857086 0.636698989
## 765 0.971880888 2.922392851
## 766 4.621455136 3.688485390
## 767 0.800703116 1.488403510
## 768 2.351226963 3.853266442
## 769 0.739170248 2.164927762
## 770 1.826357715 3.316716878
## 771 3.290081361 3.082127872
## 772 1.637837368 4.242029755
## 773 2.202821089 4.677461459
## 774 1.226276386 2.970967513
## 775 -2.030693133 0.946706844
## 776 0.531849808 0.745364643
## 777 -0.455231517 2.971004528
## 778 2.024497936 0.386223577
## 779 1.189099419 0.415910497
## 780 -0.722023441 2.269892329
## 781 0.241772805 3.241938088
## 782 1.375347366 2.900019639
## 783 -0.652212526 -0.180391257
## 784 2.889580795 2.904273684
## 785 0.580063453 1.979030394
## 786 3.152415514 1.601591572
## 787 -0.786717607 0.563601827
## 788 -1.581408538 2.451748080
## 789 1.485693471 2.447550282
## 790 0.630004038 1.139845124
## 791 -0.101554165 2.932679793
## 792 -1.489847783 1.919576331
## 793 -0.362605697 2.016921635
## 794 -0.715862793 0.726225640
## 795 4.771748676 4.089518091
## 796 -3.045777169 1.001303895
## 797 -0.506170693 -0.116108810
## 798 1.475718518 2.330855260
## 799 1.478469001 5.047167116
## 800 -2.844837993 2.109094704
## 801 0.814330240 2.913073659
## 802 -0.205240145 0.771859218
## 803 -2.400589989 0.695341653
## 804 6.314000499 5.014885378
## 805 4.730401557 4.440925780
## 806 3.703828276 4.122434908
## 807 1.584972275 1.312905006
## 808 -0.922839857 -0.922225808
## 809 1.494423807 3.470127070
## 810 3.034117717 2.735969289
## 811 1.798729997 7.082933862
## 812 3.212572925 4.741443967
## 813 0.330528660 1.747981047
## 814 2.803530528 4.998808325
## 815 0.882042860 3.223361188
## 816 -3.305878769 -0.008665892
## 817 -0.853939936 3.097673543
## 818 0.464898025 1.268006957
## 819 4.255337951 4.598434848
## 820 -0.483097940 2.196125748
## 821 -1.625210848 0.530214994
## 822 4.918021475 5.284507823
## 823 2.807668229 1.688155094
## 824 -3.272096925 -0.983807347
## 825 2.664956235 2.059466069
## 826 -3.252132339 0.489050349
## 827 4.068503462 3.846975819
## 828 -1.445362541 -0.994332704
## 829 -0.567036217 1.591906584
## 830 1.613963684 -0.678919982
## 831 2.966966790 2.584153881
## 832 1.164204879 -0.388185487
## 833 -0.531537217 0.890893688
## 834 3.581617384 4.271281985
## 835 2.736936619 4.872745350
## 836 0.579954586 3.369072437
## 837 0.555858707 0.886501525
## 838 3.548716390 4.781726770
## 839 2.399312986 1.659179231
## 840 0.872792637 3.992920440
## 841 2.143563999 3.557423725
## 842 1.058822037 3.875522140
## 843 -0.200743687 2.569844425
## 844 -1.952841829 -2.493781324
## 845 -1.501005964 1.468320429
## 846 1.710123652 -0.372773458
## 847 -0.409967988 4.187310370
## 848 0.451477433 2.584554200
## 849 -0.179235846 1.214610387
## 850 1.173615972 2.067004595
## 851 0.366301335 1.122089757
## 852 -3.799459748 3.347969664
## 853 3.817484962 1.202639823
## 854 1.450477665 4.158582967
## 855 3.633750100 4.652640573
## 856 0.391786381 5.619787008
## 857 -0.751695865 2.597930701
## 858 1.044206772 1.418029940
## 859 -0.285570597 0.162517210
## 860 4.164799570 3.058857331
## 861 1.615383247 2.489161923
## 862 -0.357601876 -0.068755300
## 863 0.310013871 -1.287333280
## 864 -2.327866259 -0.560915356
## 865 -1.010121236 1.569205322
## 866 3.216213919 0.416093338
## 867 2.338079416 3.717506706
## 868 -0.928956631 1.357215125
## 869 2.437171367 2.044412953
## 870 0.749420522 2.380081096
## 871 0.572441622 1.055946639
## 872 1.792421731 5.006696168
## 873 2.162731554 0.992782383
## 874 -1.591823468 0.710393379
## 875 3.714940143 3.226487045
## 876 0.149519892 3.050983728
## 877 0.114002395 0.089036606
## 878 2.742023359 4.756242933
## 879 1.941840374 2.558795351
## 880 0.059965465 2.562276975
## 881 -1.984166237 -1.310165039
## 882 0.897342766 1.918954511
## 883 4.855614008 1.336842473
## 884 1.780607894 3.414981734
## 885 3.010443172 2.573041295
## 886 -0.463562314 1.474391450
## 887 4.994482669 3.881333523
## 888 -2.123874721 3.182684315
## 889 2.018549392 2.248853982
## 890 0.881505995 1.744559920
## 891 1.209173027 1.318754070
## 892 1.008106227 0.629904031
## 893 2.006385091 3.925827502
## 894 2.558495190 3.979832823
## 895 -1.062973553 1.476513094
## 896 1.584329700 0.597306724
## 897 3.423633476 1.184946070
## 898 1.401127081 2.341231435
## 899 1.115235601 1.723664639
## 900 1.283904360 0.563603106
## 901 -1.842740116 0.202791492
## 902 1.596479078 4.026680637
## 903 4.226508109 3.415818458
## 904 1.595444305 1.815360223
## 905 0.302638925 -0.274027289
## 906 1.255417162 1.285604401
## 907 1.447870967 1.621331356
## 908 -0.393060407 1.269093885
## 909 0.911113440 3.586964371
## 910 1.644680265 2.826152984
## 911 -0.540184964 3.754645295
## 912 0.824515104 0.686763332
## 913 2.082504881 3.599752346
## 914 -0.705656594 3.991009915
## 915 1.326969009 3.747953147
## 916 0.951818007 1.496020955
## 917 -3.140366104 -0.833927275
## 918 1.386046101 3.333015120
## 919 -1.838399231 3.195537565
## 920 3.042437411 0.913395783
## 921 1.325437416 0.572121043
## 922 1.281761081 3.451027243
## 923 2.189281694 1.096966974
## 924 -0.290866019 0.183414314
## 925 0.775244389 -0.363322716
## 926 -3.220354457 2.929840037
## 927 5.107820655 2.532603668
## 928 2.456616375 2.415576763
## 929 4.141270421 3.736657578
## 930 0.379486447 -0.832998030
## 931 2.881349152 2.034007484
## 932 -1.807254985 0.880401288
## 933 1.352119875 3.664008054
## 934 -1.554150325 0.430148677
## 935 4.620046892 5.062452060
## 936 4.166692117 5.375967131
## 937 1.064492988 1.161410770
## 938 2.660821392 4.046604992
## 939 4.527992858 0.137676604
## 940 1.892544705 3.226342455
## 941 0.019445395 -0.582844787
## 942 1.985233508 1.140487397
## 943 2.481131029 3.771204805
## 944 2.588600224 0.169582013
## 945 2.650706825 1.367973609
## 946 -0.735229409 3.428579861
## 947 3.063719519 2.246972501
## 948 1.974187882 1.017534851
## 949 0.657426805 1.761549663
## 950 0.873844849 3.044836819
## 951 3.694473660 2.117557085
## 952 1.857451171 4.663109423
## 953 -1.095462211 -2.451124395
## 954 1.488177907 0.836661903
## 955 -0.117821072 3.766350042
## 956 5.114070258 1.672732944
## 957 2.925987620 2.425370034
## 958 1.959284332 4.082087362
## 959 0.931508154 0.725345288
## 960 0.482837376 2.859633160
## 961 -2.867825063 2.481120600
## 962 -1.995605591 1.154925615
## 963 1.361555393 4.011397625
## 964 1.419777997 2.273170264
## 965 1.875055936 1.037587997
## 966 1.286000180 3.819086238
## 967 1.594790946 0.294605433
## 968 1.450033177 0.101760111
## 969 0.532364842 3.647476302
## 970 -4.320686613 -2.179994164
## 971 3.039758946 1.396731929
## 972 3.292543828 2.423532711
## 973 2.278258482 3.572861962
## 974 -0.421145556 1.134903074
## 975 1.786392678 6.380183409
## 976 1.507916262 2.845496111
## 977 0.210041981 1.412317734
## 978 3.455824798 2.219906725
## 979 1.250565481 2.628890085
## 980 1.272689815 4.966796400
## 981 -0.611049644 4.492027626
## 982 1.088097464 4.025689618
## 983 -2.299673930 2.442452912
## 984 1.967553216 0.410091702
## 985 -0.365900980 1.885120063
## 986 2.764817517 1.388106778
## 987 1.453183154 4.448311591
## 988 -0.630971269 2.918993199
## 989 1.239695436 0.440648395
## 990 0.158451745 2.907774138
## 991 2.278990728 4.474669241
## 992 -1.118875961 -1.147117632
## 993 2.669014965 1.591962671
## 994 2.197370002 4.883925850
## 995 1.390476187 4.397832471
## 996 -0.585518521 2.899469574
## 997 1.059507685 0.931703879
## 998 -1.413718879 1.405982185
## 999 1.645726637 2.597981729
## 1000 1.771552340 1.547399057p2 <- ggplot(y, aes(x = X1, y = X2)) +
geom_point(alpha = .5) +
geom_density_2d()
p2
# Load the mvtnorm package
library(mvtnorm)
# Set mean and covariance matrix
mu <- c(1, 2)
sigma <- matrix(c(1, 0.5, 0.5, 2), nrow = 2)
# Generate 1000 random samples from the multivariate normal distribution
set.seed(123) # For reproducibility
samples <- rmvnorm(n = 1000, mean = mu, sigma = sigma)
# Plot the samples
plot(samples, main = "Random Samples from Multivariate Normal Distribution")
berikut adalah contoh program yang menggunakan fungsi rmvnorm() untuk
menghasilkan sampel dari distribusi multivariat normal:
library(mvtnorm)
# Menentukan parameter distribusi multivariat normal
mean <- c(0, 0) # rata-rata
sigma <- matrix(c(1, 0.5, 0.5, 2), nrow = 2) # matriks kovariansi
# Menghasilkan sampel dari distribusi multivariat normal
n <- 1000 # jumlah sampel yang diinginkan
sampel <- rmvnorm(n, mean = mean, sigma = sigma)
# Menampilkan scatterplot dari sampel
plot(sampel[,1], sampel[,2], main = "Sampel dari distribusi multivariat normal",
xlab = "Variabel 1", ylab = "Variabel 2", col = "blue")
Program di atas menghasilkan 1000 sampel dari distribusi multivariat normal dengan rata-rata mean = c(0, 0) dan matriks kovariansi sigma = matrix(c(1, 0.5, 0.5, 2), nrow = 2). Kemudian, program menampilkan scatterplot dari sampel dengan variabel pertama pada sumbu x dan variabel kedua pada sumbu y.
library(MASS)
# menghasilkan sampel data multivariat normal dengan mean = c(1,2) dan kovarians = matriks(2,2)
sampel <- rmvnorm(n = 100, mean = c(1, 2), sigma = matrix(c(2, 1, 1, 2), nrow = 2))
# melihat sebagian data sampel
head(sampel)## [,1] [,2]
## [1,] 1.5064499 2.9600133
## [2,] 1.4465744 0.4914124
## [3,] -0.9605118 4.2709238
## [4,] 1.4535791 2.5978315
## [5,] -0.2150833 3.1104351
## [6,] 4.0720113 4.7604046d2 <- data.frame(sampel)
d2## X1 X2
## 1 1.50644993 2.96001334
## 2 1.44657440 0.49141245
## 3 -0.96051180 4.27092385
## 4 1.45357913 2.59783146
## 5 -0.21508329 3.11043507
## 6 4.07201130 4.76040461
## 7 -2.14517828 -0.16205926
## 8 1.38864725 2.98769644
## 9 -0.05721639 0.62812283
## 10 0.96886209 0.79643300
## 11 3.12330110 0.25430140
## 12 0.96431661 -0.54080281
## 13 0.86804749 3.84670769
## 14 2.01997981 0.49835059
## 15 -0.99511920 1.53908467
## 16 -0.15326813 2.20547863
## 17 -0.93343089 -0.55961542
## 18 -0.03571366 0.17024448
## 19 2.36183318 1.94038564
## 20 1.45364014 3.87207217
## 21 3.51844989 2.60767843
## 22 1.93450873 3.91027021
## 23 0.37968656 0.51052294
## 24 1.80004798 0.28121308
## 25 0.51777902 1.36087707
## 26 -0.72197280 -1.95283722
## 27 0.66178206 3.51499523
## 28 0.13292524 0.98275271
## 29 -0.23014026 0.56125993
## 30 1.41644215 2.86320116
## 31 2.40573966 0.39094262
## 32 1.48397517 1.93538788
## 33 1.01207322 0.69506993
## 34 0.63991780 0.44079260
## 35 1.55484192 0.94894883
## 36 0.30818600 -0.88259396
## 37 1.85209976 3.63285580
## 38 2.43226903 3.71977914
## 39 -0.91422092 1.27242049
## 40 1.16839658 2.95829322
## 41 0.69640045 1.66090341
## 42 3.69167579 4.10448267
## 43 -1.54012531 0.83170853
## 44 0.73236232 5.69610554
## 45 0.74493820 3.38731251
## 46 1.17134359 2.18390255
## 47 1.62429511 1.98641466
## 48 2.34272282 3.06960960
## 49 -1.50525209 0.62423154
## 50 0.09983930 1.11708809
## 51 2.99949589 4.42123804
## 52 -0.06102438 2.40221204
## 53 -0.80183827 0.81084928
## 54 1.33856097 1.85117264
## 55 -0.38977037 0.03323129
## 56 0.59333461 1.95759919
## 57 1.44745446 1.00940383
## 58 1.37552870 0.62493317
## 59 0.41884659 2.41533578
## 60 -0.23134571 0.68157365
## 61 0.94831234 2.03107956
## 62 2.19110088 2.02323290
## 63 -1.56337313 0.48157685
## 64 -0.20249426 0.49564862
## 65 2.35543821 5.53529961
## 66 2.02817773 2.07917070
## 67 2.21611200 4.15521305
## 68 0.82074991 2.79449756
## 69 1.72268101 2.03814706
## 70 1.31585195 2.91119695
## 71 0.83988843 1.52661808
## 72 0.29509411 2.18004617
## 73 0.78877290 1.47205662
## 74 0.95826220 1.00860681
## 75 0.40663453 3.58262027
## 76 -0.08836832 2.10877580
## 77 -0.40724966 1.33052728
## 78 1.16372869 0.76382962
## 79 1.89296648 2.51684303
## 80 0.65735475 2.21942759
## 81 0.79517991 0.88048504
## 82 -0.86957788 1.63361781
## 83 -0.38536605 1.58413513
## 84 -1.59136340 0.12768027
## 85 1.75432498 3.52753696
## 86 0.86725033 0.70353680
## 87 0.83293717 3.34191069
## 88 1.99661263 3.26496871
## 89 2.49968169 2.88044872
## 90 2.15922023 1.07662627
## 91 1.28506388 1.64593630
## 92 1.76070978 3.88436886
## 93 1.45773167 1.32430149
## 94 0.17346648 0.57228197
## 95 0.69444629 1.28466365
## 96 1.90095759 1.61665729
## 97 2.23411348 3.24452890
## 98 0.92746008 3.78928204
## 99 0.79783116 1.11808843
## 100 0.73891395 0.67355208library(ggplot2)
# Membuat data frame
df <- data.frame(
x = c(1, 2, 3, 4, 5),
y = c(3, 5, 4, 6, 7)
)
# Membuat scatter plot dengan ggplot
ggplot(data = df, aes(x = x, y = y)) +
geom_point()
Program ini akan membuat scatter plot berdasarkan data frame df, dengan
sumbu x diisi oleh kolom x, dan sumbu y diisi oleh kolom y. Fungsi
geom_point() digunakan untuk membuat titik-titik pada scatter plot.
Anda dapat mengubah warna, ukuran, dan bentuk titik-titik tersebut dengan menggunakan argumen tambahan pada geom_point(). Misalnya, untuk mengubah warna titik-titik menjadi merah, ukurannya menjadi 3, dan bentuknya menjadi segitiga, dapat dilakukan seperti berikut:
ggplot(data = df, aes(x = x, y = y)) +
geom_point(color = "red", size = 3, shape = 24)