概率上机作业1

第一次作业

注：无水印的图去gaygreen

第一题

a)产生 1000 个随机 变量服从标准正态变量服从标准正态 分布 N( 0,1)。

> a=rnorm(1000,0,1)
> a
   [1] -1.272286767 -1.439739546 -1.577142197 -0.300379649 -0.387413411 -0.509719565
   [7]  2.234016094 -0.517060159 -1.159488740  0.532285889  1.384123653 -2.156119304
  [13]  1.934877252 -0.416573079  0.753170480  1.163331357  0.535230122  1.893866142
  [19]  0.248060526  1.265366376 -1.205032371 -0.203918793  0.626720277  0.950830735
  [25] -0.054668383  1.241737166  1.952999501 -0.351648892 -0.320895556  0.194871766
  [31]  0.495396884  2.423603449  0.298776210 -0.394155104  0.163242161 -1.722109994
  [37]  0.366315833  1.079698903 -0.996532110  0.408726683  0.276217164  0.660126040
  [43]  0.042697891  1.104820456  0.038558481 -1.526068380  0.400393212 -0.635627673
  [49] -1.652228842  0.387953327  0.899609544  0.473605568 -1.044460226 -0.563788055
  [55]  1.032030206 -0.090326257  0.861538218  1.161182846  0.652539601 -0.759387236
  [61]  1.922426503  1.910906110  0.619312665  3.675403495  0.677236233  0.907365142
  [67]  0.643993868 -0.633543862 -0.547898546  1.811072668 -1.245436532  0.570818408
  [73] -0.347689102  0.348830250 -0.537999204 -0.515857817 -1.519002673  1.228815997
  [79]  0.726364197  0.258797413  0.312679505 -1.871756710  1.649968602 -0.055699846
  [85] -1.199011327  2.415859892 -0.676721194  0.252711508  0.567077894 -1.297131069
  [91]  0.813267248  1.753766094  0.268584479 -0.029634093  0.434472820 -0.938886823
  [97]  1.769771993 -0.918349719 -0.421328022 -0.934935727  0.797206021 -0.311129170
 [103] -0.432498212 -1.031555253  3.662155819 -1.051073014  1.582430632 -0.236138191
 [109] -0.903966312 -1.040797255  0.190056167 -1.729560416 -0.091065989 -0.603043795
 [115]  0.433050397 -0.314143431 -0.762582959 -0.616916601  1.274955553 -0.928284058
 [121]  0.029715039  0.995469296  0.537534011  1.122533628 -0.969147180  0.428755906
 [127] -0.923467910 -0.317074797  0.809059096  1.048178925  0.771069547 -0.121466524
 [133]  0.481577079  1.903278910 -0.741412680 -0.193808990  2.759233454  0.381091861
 [139] -0.098734410  1.150007372  1.991844540  0.632345647  0.652173007  1.652752458
 [145]  1.618808156 -0.314635273 -1.728593240  0.317859676  0.021012868 -0.957592831
 [151] -0.818949800  0.327500077  0.329610851 -0.418392592  1.335397091 -0.230914551
 [157] -0.163820774 -0.920054280  1.464718051  0.576030944  0.220831747 -1.956442373
 [163] -1.478659530 -1.765911128 -0.373186042  1.225792588 -0.880840921  1.674643932
 [169]  0.783303930  0.209124430 -1.058991965 -2.505622710 -0.952361372  2.027198185
 [175] -0.146310187 -1.162935911  0.961050338 -0.301433667 -0.574748939 -0.228265463
 [181]  1.623661300  0.187524226  0.592027436  0.881106140  1.134874529  0.174880300
 [187] -1.116992875  0.016806795  1.012467428  0.251642191 -0.949530254 -0.769395758
 [193] -0.060733206 -0.789349142  0.969786115  2.695756149  0.399772077 -0.166640400
 [199]  2.295457281 -0.358020039 -0.751267966  0.158392782  0.084682042 -1.167772988
 [205] -0.637696759 -0.038831797  0.918799299 -0.509328397  0.965082515 -0.677876832
 [211] -0.816962307 -0.149335459  1.118557382  1.334138598  0.334839418  1.120496242
 [217]  0.372316515  0.119065046 -0.834492403 -0.259465125 -0.644209355 -1.232253366
 [223]  0.319012566 -0.574453997  0.598214352  1.586703298  1.467603558  0.817424938
 [229]  0.127032005 -1.630726420 -0.783776500 -1.574442306 -1.013964734 -1.188493745
 [235] -0.365051690  1.206665388  0.864213791 -1.980124106 -0.366312657  0.347644187
 [241] -0.894354355  1.197637153  1.842008699 -0.262478225 -1.021994843  2.404768567
 [247] -0.960654784  0.833447978  0.228983764 -0.020433970 -0.841881665 -0.668943205
 [253]  1.486886686  1.267051547  0.132294153 -1.694114946  1.489866038 -0.238547090
 [259]  1.266807352  0.798635306  1.410428678  0.251018035  1.007938728  2.243341859
 [265]  0.250256140  0.835844329 -0.427025552 -0.607903233 -0.794513278 -1.038708620
 [271]  0.869818038  1.135413036  1.356658793  1.648940953 -0.997868005  0.823923123
 [277]  1.570619199 -0.651017506  0.580658610  0.730145762  0.399115100 -0.565259962
 [283] -1.097983512  1.379685989  0.476303881  1.661758328  1.996289804 -0.168065786
 [289] -0.483423417  1.132545764 -0.821477395 -2.034219131  0.251253275  0.638334027
 [295] -0.058918963 -0.838995160  1.045562862 -1.285182557 -1.609981599 -0.053890019
 [301]  1.674979679  0.346602959 -0.441414370 -0.113649263  0.011942163  0.066772730
 [307] -1.513366389  1.641209114  0.428330237 -0.126714256 -1.458876881 -0.312872702
 [313] -0.477847148 -0.421003871  0.770735345 -2.573116861 -0.594991163  0.685085872
 [319] -0.837718330 -0.801681458 -0.560372074  0.569993327  0.739636170 -0.598815039
 [325] -0.244708853  0.217089612  0.324562309 -0.191784405  1.894952706 -0.703908455
 [331] -0.412512125  0.236798527  0.475824305  0.348334918 -0.872421781  1.218573480
 [337]  0.472774572  0.542584998  0.461478167 -0.715288147  0.288441090 -1.754309954
 [343] -0.978278908  1.171072209  1.296998258 -1.463214643  0.294947500  0.567299114
 [349] -0.176177740  1.189491756 -0.605967127 -1.071661049  0.592684515 -1.230323681
 [355] -0.775553383 -1.388220147  0.372513568 -1.199436499  1.776420970 -0.284854849
 [361]  0.718110027  0.158896492 -0.795627898  1.881453112 -0.055951542  0.213733223
 [367] -1.179415841 -0.171920753 -1.427780294 -0.244620908 -0.188932136 -0.129697665
 [373]  0.982871584  0.347516184  0.390213370 -1.282214239  0.790483098 -1.135584856
 [379] -1.110701421 -0.450206950 -0.331157710  0.826163357 -0.930882289  0.052713332
 [385]  0.089034871 -0.048879911 -1.018844536  0.347939582  0.861013837  0.051349780
 [391]  1.057145684 -1.811672060 -2.544368317  1.125778977  0.740846791  1.629799936
 [397]  0.175348878  1.568233714 -0.281204999  0.736456438 -0.233494351 -0.373552029
 [403]  0.285965710  0.271793411 -0.803293575 -0.244378551 -0.779006161  0.078375656
 [409] -0.162528241 -0.543568523 -0.763488204  0.078275308 -0.622136780 -1.391700818
 [415]  1.639270516 -0.331822455  0.050384910  0.886549848 -0.556419175 -0.232059069
 [421] -1.057052464  0.924619960 -2.059144653  2.120190096 -0.663302990 -0.434849319
 [427]  1.764023548  1.546949050 -1.596315592  0.957383893  1.243177494  1.421615638
 [433] -0.385042754  0.160420083 -1.080056410 -1.620202908 -2.552611364 -0.228154741
 [439] -1.917246535  1.498233241 -0.392778491  0.590452046 -0.862525717 -0.664252870
 [445]  2.997858273  1.074040289  2.405931225 -0.093189153  0.496166834  0.709047537
 [451] -0.356332317  0.247212615  0.133679322  1.439581606 -0.239070964  1.642938736
 [457]  0.686411478 -1.804298587 -0.063280852 -1.678058482  0.104651437 -1.496527848
 [463] -0.291751586 -1.302310080  1.463200523 -0.668628376  1.233070790 -1.379278898
 [469]  0.661514935 -0.259408146 -1.929644392  1.190931080 -0.779495715 -2.009100379
 [475] -0.723066473 -0.219355553  0.940109739  0.892891768 -0.237392958 -0.930790608
 [481] -0.016679954  0.725452008  0.025348265 -1.493420983 -1.643113674 -1.092169622
 [487] -0.277486044  0.785134235 -0.110494217  1.626650527  0.017041790 -0.242041232
 [493]  0.913496731 -0.958114505  1.246781064  0.439968760 -0.476925343  0.946555072
 [499] -0.342216289  0.416530019  2.228252105  0.195726099  0.515314116  0.082909016
 [505]  0.739876465 -0.488751790 -0.166894491  0.162615250  0.916698012  1.644029364
 [511]  0.307517587  0.926003975  0.542097977 -0.427293720 -0.830642354 -0.864333976
 [517]  0.008351432 -0.103470851  1.130191620  0.501159232  0.698939272  0.061010822
 [523] -0.055481115  1.835001580  0.089852944 -0.577581147 -1.224095495 -0.102134997
 [529]  0.894068369 -0.302263608 -0.849063277 -0.605365594  0.291974179 -1.544245613
 [535]  1.430110760  0.159596486 -1.231190733  1.353899030 -2.509275192 -1.907478488
 [541] -0.672799130  1.419917969  0.290108014  1.213003257  1.270471161 -0.425931821
 [547]  0.398306883  0.738075578 -1.573008271  0.751885469  0.580408889  0.812021203
 [553]  0.425688878  0.644905971 -0.086633242 -0.062003203 -0.623104060 -1.214724520
 [559]  1.316804848  0.610495639  0.528256694 -0.815228795 -1.732024704 -0.291452446
 [565] -1.034083649  1.023480723  0.945552445  1.267074398  1.280411691  0.839227036
 [571] -1.074891796  0.362341117  1.351776239 -0.728114053  0.386450329  0.747142478
 [577]  0.994231129 -0.894539351  0.776043362 -1.177158725 -0.377850561 -0.809717138
 [583] -0.998849246 -0.055607586 -0.303300643 -0.760511507 -1.206578274 -0.378466253
 [589] -0.470341941  0.692275515 -0.238252206  1.513052408 -0.585803459  1.107112954
 [595] -0.437381834  1.450019708  1.384955259 -0.606559108 -0.717579757 -0.084140723
 [601]  0.992653573  0.889101840 -1.788966018 -0.597794069  0.187477154  0.208375282
 [607]  1.186287981 -0.498756944 -0.902829974 -0.414685710 -0.437314846  0.276983833
 [613]  1.144990020 -2.094601239 -0.904111156  0.622746027 -0.475505472  1.680346745
 [619] -1.438249905  0.037391752 -1.488935244 -0.416140773 -0.789098224 -0.632369921
 [625]  0.870352619 -0.668103872  1.206644565 -1.706759381  1.393745624  1.510086464
 [631] -0.486441791 -1.931572504 -1.357881197  1.592168843  0.400554281  0.269123679
 [637] -0.380443796 -0.301573153 -0.936048474 -0.231235195 -1.567336382  0.545019097
 [643] -0.271849049  0.729339394  0.720849480 -0.074655228  0.351904291 -0.837866770
 [649] -0.659215717 -0.297031733  0.117989230 -0.016430065 -0.190784751  0.666886898
 [655] -0.771424566  0.925508171 -0.629630505  2.234412092  0.857163018  0.575388981
 [661]  0.057066842  0.296230863  0.034920924 -0.661277018 -0.020074943 -0.633919905
 [667]  0.063855145 -0.568784925  1.243743700 -1.494572645 -0.179248837 -0.734905514
 [673]  0.139434584  0.243790992  1.539481257 -0.523059363  1.791530939 -0.744497984
 [679]  1.216504816 -0.994232256 -0.239351177  0.360276545 -0.417458610  0.717064728
 [685]  1.471598695 -0.222341326 -0.476499837 -0.196552154 -1.366932818  1.441309129
 [691]  0.397875080 -1.227182182  1.703247008 -0.721731324  1.639534973  0.384033095
 [697]  0.489544294  0.857072472 -1.232115878 -0.341062053 -0.087668424  0.865532311
 [703]  0.380821452  0.281590068 -0.508771703 -1.263037712 -1.447539621 -0.814161229
 [709]  1.430633047 -2.001361966 -0.713355058 -1.424581659  1.040179564  0.385264737
 [715] -0.875910985 -0.181940950  0.313282911 -1.070751338 -1.429114646  0.555922561
 [721]  0.294210676  0.335826757 -0.957178267  3.002694766  0.249487709 -0.914968840
 [727] -0.392607768 -0.989348759 -0.320113010  0.234150835  0.862454604 -0.652720652
 [733]  1.018869864 -0.193224334  0.805924981 -0.065880086 -4.585813352 -0.027401145
 [739] -1.255346812  0.938568504 -0.477673831  0.018885616 -2.029048410  0.730679597
 [745] -0.334099902 -0.468890967  0.144205982  1.293136165  0.761760954  0.629159683
 [751] -0.049364800 -1.082766149 -0.081426754  0.340275681 -1.482838919 -1.286735871
 [757] -0.224829509 -0.179624787 -2.473045835  0.621259254  0.840302237  0.019560864
 [763] -1.627437076  2.349573391  0.655715073  0.030276431 -0.042139476 -2.335263949
 [769] -0.101982677 -1.281463160  0.684069164  0.900612913  1.765388158  0.580697220
 [775]  0.771116436  0.629016123  1.013607386  0.835897280  0.560555828  0.395127346
 [781] -1.027216514  0.303323166  0.298827099  0.556421184 -0.552431466  0.087174831
 [787]  0.582273011  1.444976782 -1.055313739  0.669498068  0.628132207 -0.310523133
 [793] -1.866244586 -1.062337070  0.152817813  0.466295720  1.202197814  1.221012575
 [799]  2.358441496 -2.087618986 -1.329786072 -0.616475911 -0.044861780  0.116965317
 [805] -0.494580823  1.276463177  0.312118292 -0.063558162 -0.027475491 -1.661660382
 [811] -1.135492660  0.262560822 -1.320153739  1.159975131 -0.436912854 -0.496479846
 [817] -3.093385191  0.972754143 -1.956184689 -0.406461226  1.805476930  1.034285206
 [823]  0.725484320 -0.985396622 -0.058044352  0.137771727  0.606828206  0.713820007
 [829] -2.170622641 -0.919910634  2.264682049 -1.323651690 -1.846588754 -0.593444599
 [835] -1.266035823 -0.230447353 -0.768409376  0.611002514 -0.476761906 -0.174164005
 [841]  0.393530561 -0.274123132  1.193064887 -0.510460228 -0.491518566 -0.001459399
 [847] -0.759206631  0.269696904 -1.530023772 -0.181527322 -0.840994395  2.731030583
 [853]  2.879320077 -0.364052089  0.926557014  0.522149165 -2.030214884 -0.184068142
 [859]  1.512984037  0.975195149 -0.171715912 -0.237632030 -0.353900262 -1.997639476
 [865] -0.227064459 -1.998406563 -0.572694530 -0.777149105 -0.963550689 -0.597459122
 [871]  0.140954418  0.196556378  3.074860763 -0.757403023  0.026326376 -1.292310149
 [877]  1.468470160  0.437059042 -0.446270308 -0.080540502  1.103347710  1.576114500
 [883]  0.076602103  1.191692959 -0.529423012  2.267072218  1.107139275 -1.086597002
 [889] -1.744689062 -0.817604776 -0.003462798 -0.265594790  1.281955927 -0.696266175
 [895] -0.330935655  0.582103241  0.735449455 -0.855896392  1.531279534  0.324762514
 [901]  0.381069575  0.839765203 -0.605795217  1.418478976 -1.563252894  1.227428729
 [907]  0.173145613  0.527254833  0.410682178  0.380302872 -0.588406928 -0.897620198
 [913]  1.064283375  0.620107075  0.643292398 -0.536952977 -0.290551852  0.838556333
 [919]  1.057501579 -0.248157064 -1.347248934 -0.998314287  0.007268626 -0.684158868
 [925] -0.599039525 -1.154373954 -1.183437398  1.869538300 -0.354941992  1.772312867
 [931] -0.102812699 -0.002381763  0.010406382  0.909433789 -0.596527799  0.790769430
 [937]  0.646623286 -0.570091241 -0.002172750 -2.649592358 -2.128487373  1.143587851
 [943] -0.874068300  2.458965375  1.700205663 -0.565804969 -1.317959305 -0.115375263
 [949]  1.637957227  0.321208362  0.758578953 -0.746675081  0.434495080 -1.537640107
 [955] -0.629765997  1.415526793 -0.863784155 -0.134643260 -0.266378440 -0.397167184
 [961] -1.448065933 -1.438325079  0.845355053  0.102390594 -1.372358935 -0.766739341
 [967] -0.801068097  0.789843969 -0.505847528 -0.071229035 -0.747665693  0.311737809
 [973]  0.615935619  1.134707165 -1.573880646 -0.336207303 -0.426903596  0.940660241
 [979] -0.161815515 -0.039211550  0.161729238  0.212957822  1.661129869 -1.620450219
 [985] -0.706927219  1.160682233  0.036148048  0.665653699  1.074055316 -1.010949980
 [991] -0.513393007  0.676751452 -0.490318090  0.070992161  1.812488900  0.623634095
 [997]  0.341276105 -1.075468301  0.304492274 -0.745034894
> length(a)
[1] 1000

计算样本期望和样本方差：

• 样本期望

  > mean(a)
  [1] 0.03244432
  

• 样本方差

  > var(a)
  [1] 1.090253
  

b)根据由 (a) 生成的随机变量，画所对应得直方图

> hist(a,freq=F)

并与 a) 所得到的期望和方差比较

期望很接近0，直方图的峰值在0的附近，左右近乎对称分布；

方差很接近1，大多数值分布在 $\pm 1$±1之内.

第二题

a) 产生一组长度为 100 的随机向量， 记为$x=(x_1,x_2,...,x_{100})$x=(x1​,x2​,...,x100​),其中$x_i$xi​服从泊松分布P（2）.

 x=rpois(100,2)
> x
  [1] 0 2 0 6 2 2 4 3 2 3 1 2 0 2 2 1 2 0 2 1 0 0 2 2 1 2 4 2 5 5 3 0 2 1 2 2 3 0 0 3
 [41] 0 2 4 2 5 2 3 3 3 1 2 2 1 6 3 2 3 1 5 1 1 1 1 1 3 2 1 2 3 1 2 1 1 2 1 1 5 1 4 1
 [81] 3 4 1 0 1 1 2 3 0 2 1 2 0 1 2 1 3 1 0 2

计算

• 均值

  > mean(x)
  [1] 1.92
  

• 方差

  > var(x)
  [1] 1.973333
  

直方图

> hist(x,freq=F)

b) 重复 2(a)1000次，得到 1000 组长度 为 100 的随机向量，计算每组均值，记为$y_i(i=1,2,...,1000)$yi​(i=1,2,...,1000).

/*脚本*/
y <- list()
for (i in 1:1000) {

x=rpois(100,2)

y[i] <- matrix(mean(x))
}
/*运行脚本结果*/

[[661]]
[1] 1.98

[[662]]
[1] 2.16

[[663]]
[1] 1.94

[[664]]
[1] 2.19

[[665]]
[1] 2.11

[[666]]
[1] 2.09

[[667]]
[1] 1.87

[[668]]
[1] 1.83

[[669]]
[1] 2

[[670]]
[1] 2.12

[[671]]
[1] 1.89

[[672]]
[1] 2.09

[[673]]
[1] 2.08

[[674]]
[1] 2.11

[[675]]
[1] 2.12

[[676]]
[1] 1.82

[[677]]
[1] 1.62

[[678]]
[1] 2.03

[[679]]
[1] 2.06

[[680]]
[1] 2.17

[[681]]
[1] 1.78

[[682]]
[1] 1.9

[[683]]
[1] 1.97

[[684]]
[1] 2.05

[[685]]
[1] 2.3

[[686]]
[1] 2.14

[[687]]
[1] 2.09

[[688]]
[1] 1.68

[[689]]
[1] 1.91

[[690]]
[1] 1.76

[[691]]
[1] 2.13

[[692]]
[1] 1.7

[[693]]
[1] 1.92

[[694]]
[1] 2.06

[[695]]
[1] 1.77

[[696]]
[1] 2.06

[[697]]
[1] 2.16

[[698]]
[1] 1.94

[[699]]
[1] 2.11

[[700]]
[1] 1.96

[[701]]
[1] 2.2

[[702]]
[1] 1.87

[[703]]
[1] 1.86

[[704]]
[1] 2.03

[[705]]
[1] 2.2

[[706]]
[1] 2.25

[[707]]
[1] 1.92

[[708]]
[1] 1.92

[[709]]
[1] 2

[[710]]
[1] 2.05

[[711]]
[1] 2.12

[[712]]
[1] 1.96

[[713]]
[1] 1.96

[[714]]
[1] 2.13

[[715]]
[1] 2.03

[[716]]
[1] 1.92

[[717]]
[1] 1.87

[[718]]
[1] 2.02

[[719]]
[1] 1.96

[[720]]
[1] 1.74

[[721]]
[1] 2.09

[[722]]
[1] 1.93

[[723]]
[1] 2.17

[[724]]
[1] 2.19

[[725]]
[1] 1.99

[[726]]
[1] 2.05

[[727]]
[1] 1.93

[[728]]
[1] 1.97

[[729]]
[1] 1.88

[[730]]
[1] 1.99

[[731]]
[1] 1.93

[[732]]
[1] 2.29

[[733]]
[1] 2.15

[[734]]
[1] 1.88

[[735]]
[1] 2.03

[[736]]
[1] 2.04

[[737]]
[1] 1.95

[[738]]
[1] 1.96

[[739]]
[1] 2.13

[[740]]
[1] 2.19

[[741]]
[1] 1.96

[[742]]
[1] 1.85

[[743]]
[1] 2

[[744]]
[1] 1.86

[[745]]
[1] 2.01

[[746]]
[1] 1.95

[[747]]
[1] 2.16

[[748]]
[1] 2.02

[[749]]
[1] 1.81

[[750]]
[1] 2.32

[[751]]
[1] 2.02

[[752]]
[1] 1.9

[[753]]
[1] 2.06

[[754]]
[1] 2.05

[[755]]
[1] 2.23

[[756]]
[1] 1.88

[[757]]
[1] 1.89

[[758]]
[1] 1.94

[[759]]
[1] 1.94

[[760]]
[1] 2.14

[[761]]
[1] 2.05

[[762]]
[1] 2.6

[[763]]
[1] 1.88

[[764]]
[1] 2.13

[[765]]
[1] 2.23

[[766]]
[1] 2.04

[[767]]
[1] 2.15

[[768]]
[1] 1.98

[[769]]
[1] 1.78

[[770]]
[1] 2.23

[[771]]
[1] 2.06

[[772]]
[1] 1.96

[[773]]
[1] 2.04

[[774]]
[1] 1.81

[[775]]
[1] 1.95

[[776]]
[1] 2.11

[[777]]
[1] 1.9

[[778]]
[1] 1.81

[[779]]
[1] 1.98

[[780]]
[1] 1.93

[[781]]
[1] 2.05

[[782]]
[1] 2.16

[[783]]
[1] 2.18

[[784]]
[1] 2.15

[[785]]
[1] 2.01

[[786]]
[1] 2.08

[[787]]
[1] 2.13

[[788]]
[1] 2.1

[[789]]
[1] 1.86

[[790]]
[1] 1.88

[[791]]
[1] 2.21

[[792]]
[1] 1.99

[[793]]
[1] 2.16

[[794]]
[1] 2.17

[[795]]
[1] 1.98

[[796]]
[1] 2.08

[[797]]
[1] 1.76

[[798]]
[1] 2.17

[[799]]
[1] 1.89

[[800]]
[1] 1.97

[[801]]
[1] 1.84

[[802]]
[1] 2.04

[[803]]
[1] 1.82

[[804]]
[1] 1.79

[[805]]
[1] 1.98

[[806]]
[1] 1.87

[[807]]
[1] 1.98

[[808]]
[1] 1.86

[[809]]
[1] 1.88

[[810]]
[1] 1.97

[[811]]
[1] 1.93

[[812]]
[1] 2.03

[[813]]
[1] 1.97

[[814]]
[1] 2.07

[[815]]
[1] 1.92

[[816]]
[1] 1.92

[[817]]
[1] 2.16

[[818]]
[1] 2.05

[[819]]
[1] 1.79

[[820]]
[1] 2.04

[[821]]
[1] 1.92

[[822]]
[1] 1.84

[[823]]
[1] 1.93

[[824]]
[1] 1.78

[[825]]
[1] 1.97

[[826]]
[1] 1.92

[[827]]
[1] 1.89

[[828]]
[1] 2.02

[[829]]
[1] 1.85

[[830]]
[1] 1.9

[[831]]
[1] 1.95

[[832]]
[1] 1.95

[[833]]
[1] 2.06

[[834]]
[1] 1.95

[[835]]
[1] 2.12

[[836]]
[1] 2.09

[[837]]
[1] 2.18

[[838]]
[1] 2.16

[[839]]
[1] 2.14

[[840]]
[1] 2.03

[[841]]
[1] 1.9

[[842]]
[1] 2.34

[[843]]
[1] 2

[[844]]
[1] 1.84

[[845]]
[1] 1.89

[[846]]
[1] 1.96

[[847]]
[1] 1.9

[[848]]
[1] 1.92

[[849]]
[1] 1.86

[[850]]
[1] 1.87

[[851]]
[1] 1.94

[[852]]
[1] 1.94

[[853]]
[1] 1.84

[[854]]
[1] 1.94

[[855]]
[1] 2.04

[[856]]
[1] 2.26

[[857]]
[1] 2.04

[[858]]
[1] 1.93

[[859]]
[1] 2.02

[[860]]
[1] 2.19

[[861]]
[1] 2.19

[[862]]
[1] 2.21

[[863]]
[1] 2.03

[[864]]
[1] 1.83

[[865]]
[1] 1.98

[[866]]
[1] 1.9

[[867]]
[1] 1.87

[[868]]
[1] 2.01

[[869]]
[1] 1.77

[[870]]
[1] 2.02

[[871]]
[1] 2.05

[[872]]
[1] 1.8

[[873]]
[1] 1.95

[[874]]
[1] 2.32

[[875]]
[1] 1.94

[[876]]
[1] 1.93

[[877]]
[1] 2.08

[[878]]
[1] 2.05

[[879]]
[1] 1.93

[[880]]
[1] 1.95

[[881]]
[1] 1.97

[[882]]
[1] 1.83

[[883]]
[1] 1.89

[[884]]
[1] 2

[[885]]
[1] 1.77

[[886]]
[1] 2.14

[[887]]
[1] 2.06

[[888]]
[1] 1.82

[[889]]
[1] 2.33

[[890]]
[1] 1.93

[[891]]
[1] 1.95

[[892]]
[1] 2.09

[[893]]
[1] 2.09

[[894]]
[1] 1.63

[[895]]
[1] 1.81

[[896]]
[1] 1.98

[[897]]
[1] 1.91

[[898]]
[1] 2.01

[[899]]
[1] 2.09

[[900]]
[1] 2.22

[[901]]
[1] 1.82

[[902]]
[1] 2.06

[[903]]
[1] 1.92

[[904]]
[1] 2.13

[[905]]
[1] 1.93

[[906]]
[1] 1.84

[[907]]
[1] 1.68

[[908]]
[1] 1.94

[[909]]
[1] 2.07

[[910]]
[1] 2

[[911]]
[1] 2.07

[[912]]
[1] 1.94

[[913]]
[1] 1.97

[[914]]
[1] 2.09

[[915]]
[1] 2.08

[[916]]
[1] 2.11

[[917]]
[1] 2.02

[[918]]
[1] 2.26

[[919]]
[1] 2.18

[[920]]
[1] 1.96

[[921]]
[1] 2

[[922]]
[1] 2.15

[[923]]
[1] 2.13

[[924]]
[1] 2.15

[[925]]
[1] 2.03

[[926]]
[1] 1.84

[[927]]
[1] 1.88

[[928]]
[1] 2

[[929]]
[1] 1.94

[[930]]
[1] 1.92

[[931]]
[1] 1.81

[[932]]
[1] 1.95

[[933]]
[1] 1.64

[[934]]
[1] 1.86

[[935]]
[1] 1.63

[[936]]
[1] 2.07

[[937]]
[1] 1.78

[[938]]
[1] 1.93

[[939]]
[1] 2.04

[[940]]
[1] 1.71

[[941]]
[1] 2.11

[[942]]
[1] 1.72

[[943]]
[1] 1.86

[[944]]
[1] 1.79

[[945]]
[1] 2

[[946]]
[1] 2.11

[[947]]
[1] 2.26

[[948]]
[1] 2.12

[[949]]
[1] 2.08

[[950]]
[1] 2.02

[[951]]
[1] 2.29

[[952]]
[1] 2.02

[[953]]
[1] 2.14

[[954]]
[1] 1.93

[[955]]
[1] 2.24

[[956]]
[1] 1.96

[[957]]
[1] 2.11

[[958]]
[1] 2.24

[[959]]
[1] 1.78

[[960]]
[1] 1.86

[[961]]
[1] 2.1

[[962]]
[1] 2.21

[[963]]
[1] 2.17

[[964]]
[1] 2.14

[[965]]
[1] 1.91

[[966]]
[1] 1.86

[[967]]
[1] 1.97

[[968]]
[1] 2.16

[[969]]
[1] 2.09

[[970]]
[1] 1.71

[[971]]
[1] 1.84

[[972]]
[1] 1.97

[[973]]
[1] 1.97

[[974]]
[1] 2.22

[[975]]
[1] 1.84

[[976]]
[1] 1.75

[[977]]
[1] 2.21

[[978]]
[1] 2

[[979]]
[1] 1.97

[[980]]
[1] 1.84

[[981]]
[1] 1.92

[[982]]
[1] 2.22

[[983]]
[1] 1.97

[[984]]
[1] 2

[[985]]
[1] 1.93

[[986]]
[1] 2.21

[[987]]
[1] 2.23

[[988]]
[1] 2.32

[[989]]
[1] 1.97

[[990]]
[1] 1.99

[[991]]
[1] 1.8

[[992]]
[1] 2.16

[[993]]
[1] 1.86

[[994]]
[1] 2.06

[[995]]
[1] 1.93

[[996]]
[1] 1.84

[[997]]
[1] 1.93

[[998]]
[1] 1.97

[[999]]
[1] 2.08

[[1000]]
[1] 1.76

c) 标准化$y_i(i=1,2,...,1000)$yi​(i=1,2,...,1000),求均值方差。

for (i in 1:1000) {

y[i] <- (mean(rpois(100,2)))

}
sy <- list()
for (i in 1:1000) {

sy[i] = ((y[[i]]-2)/sqrt(2/100))

}

均值

mean(sy)
0.0136

方差

var(sy)
0.9801

c) 直方图

hist(sy)

相较于(a)中的更加集中在0的附近