BTVN
Nguyễn Minh Dạ Mẫn
2023-06-05
#Bài về nhà tuần 1
Buổi 1 Mô phỏng ít nhất 5 biến ngẫu nhiên(có phân phối xác suất khách nhau),mô phỏng, vẽ đồ thị, tính toán các đặc trưng đo lường và giải thích ý nghĩa.
#Phân phối chuẩn
##Mô phỏng
N <- rnorm(1000, mean=1, sd=0.5)
N## [1] 0.314951858 1.014037093 1.127775938 0.292364200 1.427115977
## [6] 1.542706730 1.206054872 0.920928766 1.355377714 0.530398169
## [11] 0.496389391 1.237217945 -0.314049010 0.026799542 1.030139150
## [16] 1.317449973 1.411824070 0.688479718 0.405489120 0.866531583
## [21] 0.443996949 1.168628016 1.251702278 0.742522837 1.397550764
## [26] 0.848803098 0.888118240 1.393769825 1.462683571 1.198490911
## [31] 1.570947440 1.290938400 0.747818847 0.740838007 0.892865822
## [36] 0.274104500 1.380106305 1.160639293 0.352061233 0.729722060
## [41] 1.194639409 1.956831842 0.807634804 0.635564983 0.879839280
## [46] 0.245954268 1.355926678 1.095046353 1.159834797 1.027337622
## [51] 1.028345630 1.524911675 1.114185660 0.800890183 1.259509768
## [56] 0.835820678 0.131138664 0.998987127 1.278756559 0.883257656
## [61] 0.594960076 1.047489257 1.015256210 0.317947314 0.405747987
## [66] 1.051784836 0.618405884 0.805773736 1.325764126 1.329237069
## [71] 1.139526092 1.809149704 1.213617583 1.169325557 1.502416085
## [76] 1.232678948 1.090440104 1.210215555 1.735990295 0.941577738
## [81] 1.039522504 0.484616529 1.286349477 0.938287641 1.653696166
## [86] 0.866315152 1.184297550 0.469219908 1.095393259 0.106767943
## [91] 0.426529593 1.115300063 2.324818274 -0.212153325 0.592524256
## [96] 0.969267138 1.641934053 1.183343984 1.223457839 0.545637283
## [101] 1.482648488 0.854290800 -0.219955827 0.035776556 1.287311758
## [106] 0.166373599 0.425633746 1.000712560 1.082220563 2.091249079
## [111] 0.726249307 1.574184340 1.265120395 1.156304114 1.060659206
## [116] 0.633241462 0.953091880 0.070736384 1.401927530 1.276412604
## [121] 1.113269988 0.447285833 1.158927576 0.643218000 1.081729978
## [126] 1.124810338 0.338398044 0.462849082 0.816568921 1.515414218
## [131] 1.210591062 1.808400335 0.571222408 0.574464253 1.395716202
## [136] 1.118245270 1.185293421 0.400341932 0.280479690 0.234081070
## [141] 0.872047368 1.178486379 0.977135609 1.437190640 0.382561043
## [146] 0.465942327 1.274224242 1.632146184 1.033774019 1.460704230
## [151] 1.280237541 1.051096710 1.423621046 0.826458873 1.094910747
## [156] 0.484202729 0.759091629 0.046995081 1.587218435 0.519111016
## [161] 1.586706446 1.224815570 0.759379952 0.496534769 1.797323554
## [166] 1.026907193 0.854653426 0.710089440 0.566486607 0.659721618
## [171] 1.179361578 0.670222649 0.881021751 1.069104306 0.193748691
## [176] 0.756053662 0.566053359 0.286270094 0.717782081 0.731587042
## [181] 0.150193579 0.106281544 1.094329992 2.305881087 1.388779772
## [186] 0.679344053 1.161521074 0.897264993 1.009833934 1.218427608
## [191] 1.111176607 1.051000030 1.259650841 0.793378010 1.266429877
## [196] 1.938751184 1.401565937 0.836475019 1.713020228 0.891579882
## [201] 0.493338209 1.269054578 0.595680813 0.777877645 1.467641418
## [206] 0.097530683 0.866598300 1.353156120 1.175769121 0.545190548
## [211] 1.494180279 1.075487006 0.794523594 1.338131467 0.519456537
## [216] 1.153188939 0.435090014 0.545495688 1.013239046 1.815252702
## [221] 0.750346025 0.714895055 0.939391567 0.841411669 1.173352308
## [226] 1.286009882 0.219699247 1.338864881 0.787748914 1.247971015
## [231] 2.346084644 1.331843866 1.113926641 1.755955014 1.140530248
## [236] 0.153578074 1.039534553 2.266898081 1.020687985 0.232542056
## [241] 1.164262629 0.931527669 1.716026622 0.916688867 0.805949914
## [246] 1.542198849 1.542108685 0.634990097 0.830675078 1.783551924
## [251] -0.006578474 0.684410445 1.198383550 0.943051903 0.294015430
## [256] 1.129649648 1.256821420 1.138083133 0.938247599 0.454175472
## [261] 1.759836165 0.699085293 1.263295087 0.811934936 0.640120403
## [266] 1.366123390 0.975451289 1.593617169 0.728988934 0.815507752
## [271] 0.580790942 1.870748553 0.368836008 1.895252610 0.436536276
## [276] 0.532000063 0.691788583 1.021561675 1.730333650 0.445976229
## [281] 0.957595814 0.829003732 0.977872565 2.227697797 1.013450214
## [286] 0.459557783 1.189613421 1.527438602 0.894887214 0.919804733
## [291] 0.032490851 0.278577125 0.593739025 1.629474469 1.402803131
## [296] 0.572287754 1.892654073 1.927714115 1.391325936 0.182703514
## [301] 0.828448382 0.642138900 -0.410093450 0.742158726 2.008125617
## [306] 0.867929710 1.084982856 -0.326211069 0.587135414 0.458737856
## [311] 1.122422559 2.727614391 0.904876496 0.415426218 1.321729229
## [316] 1.827618742 1.496482479 1.148533971 0.377802883 -0.114687475
## [321] 0.935188331 0.819594567 0.062385221 1.782254930 0.737129666
## [326] 1.800969846 2.030113137 1.133272182 0.854452716 -0.829393815
## [331] 0.249920655 1.076649622 1.039809974 0.529764265 1.753384192
## [336] 1.309691803 1.712543081 0.575604403 -0.074284377 1.066442695
## [341] 1.309192877 0.510231915 0.102973033 1.752311367 1.264374745
## [346] 1.052155821 1.075180176 0.619649373 0.754953895 1.612699636
## [351] -0.066572881 1.007839224 0.620188688 1.734679348 1.055291949
## [356] 0.959048143 0.946210383 0.348647513 1.435226384 0.986481435
## [361] 1.975675550 0.996270274 0.773180499 0.958934479 0.645003042
## [366] 0.476298522 0.098807139 0.976333403 1.912847703 0.270892016
## [371] -0.111914369 1.146725907 0.765297363 1.662919137 0.594972966
## [376] -0.019255695 0.950103456 0.847845404 0.766669144 1.013317440
## [381] 0.962272422 0.641125116 1.387986956 1.484371352 1.367943476
## [386] 0.775536607 0.727405721 0.450267866 1.732231965 1.166659876
## [391] 0.327585756 1.121553823 1.157657884 1.630243890 1.292521282
## [396] 1.526001035 0.197749526 0.302090011 1.077418902 0.933211723
## [401] 0.197565248 -0.123260825 0.762185027 1.302485445 0.881317098
## [406] 1.445630351 0.892924875 0.748579618 -0.191615914 0.749470097
## [411] 0.699711910 0.539505329 1.528670555 1.094517502 1.029606588
## [416] 0.982093358 1.629641350 1.561067317 -0.174926280 0.896455303
## [421] 0.568726736 1.165084366 1.057435397 1.144495868 0.797847280
## [426] 0.267980719 1.342635459 0.042919704 1.105174541 0.686373112
## [431] 0.640218364 0.869857025 1.282744636 1.114504964 1.081524622
## [436] 0.827258960 1.289536680 1.583621168 0.552418511 1.403535282
## [441] 1.106323170 2.099619425 1.435278688 0.197317231 1.380264695
## [446] 1.021549097 0.549167985 0.889025715 0.838841400 1.771864522
## [451] 0.194138777 2.048225143 -0.085812903 0.872588687 0.717738587
## [456] 0.430685837 0.624051187 1.399410494 0.573739225 1.429901250
## [461] 0.341644260 1.104987031 1.158619406 0.426901858 1.555186849
## [466] 0.854579685 1.184326518 0.473534351 0.464358637 1.364507489
## [471] 1.015653323 1.314468473 0.558514292 0.189513605 1.258798731
## [476] 1.288859254 0.385431093 1.459061925 1.917599662 1.444378567
## [481] 0.698313238 2.274923048 1.261233108 0.692719954 0.949081229
## [486] 1.183207861 1.283570118 1.232940094 1.335185043 1.243727179
## [491] 2.075418385 0.678774957 0.954251193 1.400337549 0.898415671
## [496] -0.537862277 1.195309179 1.021970221 0.912917799 0.668224859
## [501] 1.710511551 0.327082373 0.940546920 1.807507940 0.896745292
## [506] 1.372199328 0.288244795 0.884354976 1.421238736 1.138597248
## [511] 0.710083443 0.667535447 1.361593004 0.862046776 1.794685042
## [516] 1.751366343 1.695577163 0.811417297 1.163083576 0.702782695
## [521] 1.582233957 1.135858247 0.556459136 1.338552906 -0.096200891
## [526] 1.001964077 0.227037741 0.911171588 1.500836561 0.386090250
## [531] 1.605219356 0.732962664 1.426910529 0.688109544 1.132334991
## [536] 1.797838444 1.350550428 1.002283619 1.795023589 1.377946171
## [541] 1.269097083 1.873751699 0.508590631 1.982709208 0.671744436
## [546] 0.693660813 1.774071856 1.576080643 -0.010599048 0.985627628
## [551] 1.308868290 1.164818917 1.390218817 1.394987450 1.269805087
## [556] 0.104008542 0.864683971 0.885986386 0.785101887 0.719023033
## [561] 0.929701953 0.522262684 1.373583797 0.230741007 1.730478863
## [566] 1.275626829 1.103710620 0.505023768 1.579232400 1.285945539
## [571] 1.305048577 1.144479964 1.553013153 1.029435777 1.250375282
## [576] 1.176064756 0.558656184 1.090668151 0.959669732 2.279899979
## [581] 0.706096415 0.598055896 1.688704128 1.454181236 1.129855702
## [586] 0.935199497 1.381302901 1.167769824 0.588306149 0.561211114
## [591] 0.933387412 1.260835226 0.913785061 1.262775105 0.763865534
## [596] 0.772462436 0.343370173 0.381640939 1.039082545 0.908829147
## [601] 1.465170460 0.678801911 0.462394159 1.114177525 1.336841658
## [606] 0.705637578 0.905288710 1.977315524 0.767609413 1.158514456
## [611] 0.308639478 0.815990692 1.011122109 1.656940469 0.793972913
## [616] 0.768497482 0.913944336 1.854025838 0.973609488 -0.042593988
## [621] 1.058431896 2.064960774 0.849520872 1.731454192 0.944804117
## [626] 1.097095770 0.687264475 1.820996472 1.206978155 0.874047937
## [631] 0.740431904 1.255250725 0.858540056 0.759755962 0.792833364
## [636] 1.037098904 0.876263831 1.809866951 1.205275215 0.364351192
## [641] 0.671066294 0.850547549 1.487933234 1.615652173 0.981078479
## [646] 2.197978758 0.983530144 2.128718785 0.313841980 2.260365699
## [651] 1.553851984 1.236122311 1.865014697 1.441133237 1.382694241
## [656] 1.602764287 1.023474992 1.497071559 1.086696106 0.476016201
## [661] 0.883395562 1.180638849 1.104105975 1.960008351 0.850674509
## [666] 1.101243252 0.088673471 0.698536822 0.086170829 0.222639191
## [671] 1.065835021 0.601610886 1.003229196 1.897394493 1.193623238
## [676] 0.632962761 1.066817179 0.811670799 1.588231181 1.609178327
## [681] 0.573193624 1.051861627 1.544886888 1.447763255 1.349585392
## [686] 0.888918351 0.293432083 1.677531857 0.843993268 0.925536063
## [691] 1.469281615 0.655419278 0.985640602 0.731383494 0.819467430
## [696] 0.727633381 1.327281076 0.277253666 1.222680793 1.513027769
## [701] 0.454132509 0.874014435 1.728615132 0.514366062 0.990788223
## [706] 0.696632356 0.946210464 1.472368639 1.343041299 0.918380432
## [711] 1.103146526 0.882186253 0.408481162 0.748634141 0.633108301
## [716] 0.943691833 1.378084722 0.149760222 0.409328217 0.538387272
## [721] 0.654441423 1.374627741 0.834442569 0.514789434 0.222847951
## [726] 0.524713628 -0.230695825 1.140940322 1.045436908 0.964597047
## [731] 0.367144466 1.117049443 1.190325049 1.416912733 0.684105144
## [736] 0.928610571 1.191255446 1.553304199 1.494500284 1.208064840
## [741] 0.843469278 2.156959066 1.142790841 1.132849761 0.653487536
## [746] 1.714120535 1.176779717 1.006043863 2.292024019 2.239617224
## [751] 0.846008392 1.633708491 0.877661502 0.601878891 1.054834030
## [756] 0.659536349 1.293402780 1.434175999 1.434511673 1.047016223
## [761] 0.312111526 0.512924706 1.468598199 1.669779132 0.703393193
## [766] 0.775400500 0.722579446 1.545330354 1.388768115 1.082190319
## [771] 1.355380566 1.655544023 1.801024370 0.662111034 0.456419697
## [776] 2.029568476 0.660906641 0.783505617 1.091378401 0.956852718
## [781] -0.693614496 1.359056493 0.901022484 0.904469066 0.599362483
## [786] 1.402953489 1.005873469 0.399856050 1.183785221 1.677681104
## [791] 0.638999310 0.023233175 1.437774232 0.785403390 0.897395156
## [796] 0.872997418 0.817512591 0.912883011 0.635183437 0.944096490
## [801] 1.159281942 1.272826383 1.697453218 0.642916198 0.837812918
## [806] 1.103850875 0.334236763 0.090393653 1.886292498 1.776717037
## [811] 0.140980335 1.553035413 1.521718083 0.468423802 0.512797603
## [816] 1.389345508 0.859923175 0.915771681 0.742183741 1.247927024
## [821] 1.715006056 0.866068332 1.041369235 0.210821495 0.872580561
## [826] 0.731822789 1.196035432 0.979493563 1.014788200 1.165526447
## [831] 1.015216429 0.713703687 0.753705795 0.418143186 -0.004022053
## [836] 0.361768835 1.638131715 1.655278359 0.586800441 1.092718186
## [841] 0.645263976 0.635595439 1.346128460 0.896532075 1.749403537
## [846] 1.294764923 1.185428838 1.114306297 1.438067259 1.277015553
## [851] 1.543163906 0.942290670 0.799434667 1.302052905 1.242923940
## [856] 0.792319637 1.401975034 1.816274042 1.005934995 1.311676230
## [861] 0.867245726 0.840207492 0.543999813 0.643100979 -0.028548317
## [866] 1.625992452 1.184337120 1.719164920 1.068454620 0.435085830
## [871] 1.577846012 1.712852006 1.325602857 0.836937735 0.521192244
## [876] 1.093327852 0.910738597 0.614780051 0.151043933 0.327335662
## [881] 1.275189369 1.541335259 1.347631329 0.833733245 1.045110047
## [886] 0.894528523 0.848385608 0.886902378 0.403412354 0.581589921
## [891] 1.269263644 1.389911819 0.673545299 1.566181991 1.671786694
## [896] 0.529681755 0.660799956 1.358452038 0.725985846 1.288988125
## [901] 1.367805039 0.655680695 1.531903978 0.955069080 1.972631050
## [906] 1.437142372 -0.123279319 -0.022365152 1.868581286 0.717901249
## [911] 1.063469499 1.285567234 1.217939803 1.914647915 0.415573811
## [916] 1.297852318 0.648677254 0.991467753 1.107996082 0.738569940
## [921] 1.192729821 0.504469889 1.572622744 0.345238107 1.396997998
## [926] 1.541474890 0.171527138 0.822883064 0.333533911 1.801709148
## [931] 0.578665747 0.618384915 1.543588705 0.687811923 0.687102273
## [936] 1.498156791 1.245736498 1.273494181 0.819738874 1.308957888
## [941] 1.305512008 0.956815049 0.573433868 1.216466909 1.169413611
## [946] 1.068895812 1.027665567 1.287894896 0.609830688 0.783615662
## [951] 2.029745206 0.042459747 0.953284659 1.259075140 0.637953639
## [956] 1.600754099 0.987470935 1.227371670 1.468046601 1.689177618
## [961] 0.873770725 1.112441884 0.748165020 1.723192798 1.437013779
## [966] 0.616314116 0.764184206 0.968360630 0.962599773 1.823234744
## [971] 1.604361928 1.122540767 0.527396969 1.243206055 1.364565675
## [976] 2.610267122 0.433035598 0.818353436 1.163783673 0.481068234
## [981] 1.189386335 1.138852116 -0.457687298 1.329364684 1.876651427
## [986] 0.473647682 0.797327282 0.975871360 1.084843911 0.838395484
## [991] 0.989984114 1.067195011 0.846809637 1.448304900 0.840674769
## [996] 2.094068255 0.907571317 1.895617157 1.340821764 1.035970702##Đồ thị
hist(N, main="PP Chuẩn")
##Các đặc trưng
summary(N)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -0.8294 0.6829 1.0059 1.0035 1.3293 2.7276###Ý nghĩa
####Min: Giá trị nhỏ nhất trong phân phối, có giá trị là -0.3975.
####1st Qu. (First Quartile): Đây là giá trị mà 25% các giá trị trong phân phối nhỏ hơn hoặc bằng nó. Trong trường hợp này, giá trị 1st Qu. là 0.6745.
####Median: Đây là giá trị chia đôi phân phối, có nghĩa là 50% các giá trị nhỏ hơn hoặc bằng nó. Trong trường hợp này, giá trị Median là 1.0201.
####Mean: Đây là giá trị trung bình của phân phối, được tính bằng cách lấy tổng của tất cả các giá trị trong phân phối và chia cho số lượng giá trị. Trong trường hợp này, giá trị Mean là 1.0166.
####3rd Qu. (Third Quartile): Đây là giá trị mà 75% các giá trị trong phân phối nhỏ hơn hoặc bằng nó. Trong trường hợp này, giá trị 3rd Qu. là 1.3412.
####Max: Giá trị lớn nhất trong phân phối, có giá trị là 2.5086.
###Phương sai
var(N)## [1] 0.2553202####Phương sai được tính bằng cách lấy trung bình của bình phương của sự sai khác giữa mỗi giá trị trong mẫu dữ liệu và giá trị trung bình của mẫu. Phương sai cho biết mức độ biến thiên của dữ liệu xung quanh giá trị trung bình. Nếu phương sai gần với 0, tức là các giá trị trong mẫu gần nhau và tập trung xung quanh giá trị trung bình. Ngược lại, nếu phương sai lớn, tức là dữ liệu có mức độ biến thiên lớn, các giá trị có xu hướng xa giá trị trung bình.
####Với giá trị phương sai là 0.2397924, ta có thể hiểu rằng dữ liệu trong mẫu có mức độ biến thiên tương đối, và các giá trị có xu hướng tách rời khá xa giá trị trung bình.
###Độ lệch chuẩn
sd(N)## [1] 0.5052922####Giá trị độ lệch chuẩn là 0.4955273 cho thấy rằng các giá trị trong mẫu dữ liệu có sự phân tán từ giá trị trung bình. Độ lệch chuẩn càng nhỏ, tức là dữ liệu càng gần nhau và tập trung xung quanh giá trị trung bình.
####Với giá trị độ lệch chuẩn này, ta có thể hiểu rằng các giá trị trong phân phối gần với giá trị trung bình. Tuy nhiên, độ lệch chuẩn không cung cấp thông tin về hình dạng cụ thể của phân phối.
####Để đánh giá độ phân tán và tính biến động của dữ liệu, có thể so sánh độ lệch chuẩn này với các mẫu dữ liệu khác hoặc với các giá trị tham chiếu.
#Phân phối poisson
##Mô phỏng
P <- rpois(1000, lambda = 5)
P## [1] 7 8 3 9 5 9 6 10 3 5 6 8 4 4 8 4 3 5 9 5 5 2 6 6
## [25] 7 2 3 4 2 3 7 9 3 4 5 4 5 6 4 8 7 6 7 8 5 4 7 7
## [49] 4 3 4 4 5 5 4 7 5 5 5 6 6 3 4 4 1 9 10 2 5 7 8 4
## [73] 2 5 4 8 5 3 7 3 6 4 3 6 4 4 4 7 4 6 9 6 4 4 5 4
## [97] 4 4 4 5 5 6 4 6 4 4 8 3 5 3 2 6 6 10 4 4 6 6 8 9
## [121] 6 4 6 4 7 5 3 7 3 6 4 6 7 2 9 4 5 6 6 4 1 5 6 3
## [145] 5 5 10 2 6 4 6 10 10 5 4 2 2 10 6 5 5 8 5 5 5 8 5 8
## [169] 5 6 7 5 8 12 2 2 7 4 6 3 5 8 5 5 5 11 6 5 4 5 7 4
## [193] 8 5 4 4 9 5 4 5 4 6 9 7 6 4 4 5 11 3 5 1 2 6 3 7
## [217] 5 4 7 8 7 3 6 6 6 4 1 5 6 3 4 4 2 5 6 6 4 2 5 4
## [241] 4 6 8 6 4 3 6 4 11 2 6 3 4 2 6 7 4 2 10 2 2 4 5 5
## [265] 5 5 1 7 6 8 2 3 5 5 8 5 4 6 4 9 6 5 3 2 5 3 9 6
## [289] 9 5 9 3 4 4 6 6 4 5 5 8 7 6 5 11 7 1 1 4 6 5 2 3
## [313] 2 6 5 6 3 4 3 1 6 5 5 6 6 7 2 1 5 8 1 7 2 8 1 5
## [337] 3 3 8 4 10 5 7 7 6 3 4 3 6 4 6 7 6 5 6 4 5 4 4 4
## [361] 3 5 4 8 7 6 2 2 5 9 8 5 5 3 5 7 8 7 4 6 5 3 7 10
## [385] 5 3 5 2 3 1 8 5 4 7 12 3 6 9 4 3 6 3 7 3 4 3 6 1
## [409] 6 10 5 4 7 4 13 6 8 1 6 5 2 6 7 6 1 4 6 1 3 9 1 3
## [433] 3 8 3 5 4 6 3 7 2 4 4 6 3 6 4 7 0 7 4 4 7 2 4 3
## [457] 4 7 5 5 5 2 6 5 6 5 2 4 2 3 6 3 5 0 3 11 6 4 5 4
## [481] 4 3 6 3 2 7 4 4 4 1 7 3 3 5 9 6 6 4 5 5 3 1 7 4
## [505] 10 5 6 4 7 8 2 4 6 6 7 5 2 2 9 6 4 4 3 7 3 6 4 2
## [529] 7 7 8 1 6 6 6 4 3 6 3 4 6 4 4 7 5 7 12 7 6 4 8 9
## [553] 8 5 10 3 4 8 1 2 4 4 4 7 1 2 7 6 7 4 3 5 8 4 2 2
## [577] 4 6 0 3 5 5 4 3 7 4 5 7 5 7 3 4 8 7 2 7 3 5 8 6
## [601] 11 7 8 8 2 3 4 1 5 3 5 6 4 9 5 3 2 6 5 7 7 4 4 6
## [625] 2 4 3 3 8 3 6 7 9 7 2 6 1 4 7 5 9 6 5 6 4 9 5 3
## [649] 3 4 1 3 3 8 10 2 4 7 4 6 5 2 7 3 3 5 3 3 6 4 3 5
## [673] 4 4 5 8 8 4 3 5 6 8 6 8 3 5 2 2 5 0 7 8 6 9 3 4
## [697] 4 10 6 4 5 2 9 4 2 2 4 5 2 4 7 5 3 3 8 10 3 5 6 4
## [721] 3 6 9 3 4 3 8 3 3 2 6 4 5 3 7 6 9 3 9 6 6 3 4 5
## [745] 4 2 5 4 8 4 6 7 5 10 5 0 4 6 3 3 3 3 9 4 4 5 8 4
## [769] 8 8 5 5 5 4 4 3 7 4 8 4 7 10 4 7 5 6 7 3 8 4 2 10
## [793] 8 6 6 7 7 4 4 3 5 4 3 6 5 2 5 7 6 4 7 4 5 2 4 8
## [817] 4 12 5 2 2 4 5 3 8 3 5 6 4 6 2 3 7 8 3 3 4 4 8 4
## [841] 2 2 5 5 3 6 4 5 4 5 6 5 3 5 4 6 6 5 4 7 7 7 7 8
## [865] 5 11 3 5 3 7 5 9 4 3 3 4 6 5 3 5 1 3 8 2 4 5 3 5
## [889] 5 7 10 6 4 3 3 6 5 8 7 7 6 5 2 5 5 3 3 7 8 8 7 8
## [913] 2 3 9 7 2 8 4 5 7 4 2 4 6 5 6 5 4 6 7 8 4 2 5 7
## [937] 5 3 3 3 6 2 2 4 3 4 1 4 5 9 3 11 3 4 5 3 3 1 8 4
## [961] 6 4 7 5 6 10 2 6 7 5 3 2 9 2 5 6 2 5 6 3 6 6 4 2
## [985] 3 4 6 7 6 5 4 5 6 4 7 4 3 3 6 3##Đồ thị
hist(P, main="PP Poisson")
##Các đặc trưng
summary(P)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.000 3.000 5.000 5.033 6.000 13.000###Phương sai
var(P)## [1] 4.826738###Độ lệch chuẩn
sd(P)## [1] 2.196984#Phân phối exponential
##Mô phỏng
ED <- rexp(1000, rate = 0.1)
ED## [1] 0.006348374 14.941837695 3.762985484 18.750628754 5.908305715
## [6] 0.509384135 3.834157316 23.652021402 0.226759848 5.214941809
## [11] 23.724440279 14.649321476 0.528293131 8.713093446 2.409536750
## [16] 14.017131564 6.399275870 4.332545595 6.712877178 17.080019861
## [21] 17.420875243 11.638279238 10.053441645 8.780842311 22.204986630
## [26] 27.426536473 6.249318039 8.657046947 3.801003005 13.957206233
## [31] 3.228097595 4.623637516 12.196317715 15.582333441 13.291394878
## [36] 11.230116682 16.988890274 2.852819855 22.762600471 4.404867934
## [41] 4.185795290 3.804961294 1.017575396 0.345199653 0.544452377
## [46] 13.516789339 18.021906613 0.075745308 8.685992668 5.664273435
## [51] 1.809869788 4.770635115 5.301750237 3.177794863 0.839637170
## [56] 1.751667093 43.254486339 11.188686043 14.203150875 4.355276409
## [61] 13.395286901 3.560032733 0.689044897 2.259711700 10.455130469
## [66] 0.669348916 16.567629966 11.608185963 3.275891918 16.700755469
## [71] 6.123522730 3.016798007 7.584172329 2.766757252 2.144660620
## [76] 10.746215907 30.159432660 12.134539270 4.600420734 2.788327285
## [81] 19.025100972 18.238349873 3.656055029 3.272191910 5.358228050
## [86] 6.471968917 29.653255565 16.044793650 3.374117641 0.147260185
## [91] 2.447948097 8.781614944 1.245634756 19.300730321 2.793584266
## [96] 15.043175220 20.852111518 5.448281414 7.364798924 0.780799920
## [101] 4.778376129 19.734890684 19.882361627 18.374741002 25.053996461
## [106] 8.319759750 0.809340029 0.777513933 4.861192470 11.759012539
## [111] 0.185192930 1.053212387 2.803098350 0.847574286 5.757833254
## [116] 6.976392628 1.114582566 8.805153323 4.245391460 29.132512686
## [121] 3.981017731 8.269344251 1.017926405 2.427229821 7.340751964
## [126] 2.482550566 4.121082374 2.318123825 7.217539855 6.450632331
## [131] 11.494393283 14.959756330 4.175647525 12.784911952 0.853080854
## [136] 19.087097458 0.654347174 3.276611054 11.904306757 0.655690584
## [141] 14.780847504 19.993242099 0.845023370 21.733404266 15.845108316
## [146] 17.446228433 4.882657700 3.335466979 16.919361762 9.882527068
## [151] 8.675127765 2.153196019 5.001741410 13.800386441 10.655418513
## [156] 0.792844980 5.252149082 6.517456132 8.926486675 0.321633815
## [161] 1.730361823 5.336928722 0.087161488 1.351615530 1.331555629
## [166] 0.189730185 2.345611975 22.299965635 37.983808124 9.374167756
## [171] 8.186079897 18.699558730 15.890500824 1.497840207 14.250526546
## [176] 10.629511149 0.810966049 3.043029248 24.169180224 9.215559604
## [181] 12.307883622 3.989998321 3.140366818 2.991016144 4.536822280
## [186] 11.211100835 4.707150403 0.557814045 5.871985154 6.218935912
## [191] 1.663697907 12.064247271 5.180902244 0.817182958 7.887169318
## [196] 6.175912339 0.897560450 11.629860168 0.409517284 20.020188185
## [201] 4.559933888 11.348463371 6.469946550 12.385915331 4.051302127
## [206] 35.172189826 1.850433117 33.240895046 0.057268078 18.728228285
## [211] 23.188208784 34.198224881 2.784848656 0.982668558 8.180423732
## [216] 19.550031236 5.519270211 8.026472264 7.238509468 2.885212349
## [221] 0.251877209 1.940465351 6.384341358 9.509082734 17.593201044
## [226] 0.388032473 4.697954860 3.395987454 10.574435768 10.717866765
## [231] 6.658080192 0.215605416 5.600996111 5.426694802 6.343098159
## [236] 7.818910844 13.327501732 20.604623648 0.861711353 22.665032774
## [241] 6.121530873 32.580406143 2.969102594 43.390982244 1.474568681
## [246] 8.123442903 15.916452947 13.708270331 7.267599916 20.317392740
## [251] 0.454132766 0.060448241 2.696615518 12.242036871 8.403283422
## [256] 9.456692301 17.133637647 0.272052228 13.096663327 11.766790635
## [261] 6.693084957 1.375971923 15.782506450 7.461771017 11.298291124
## [266] 4.546225359 7.333810105 23.755042650 6.330576707 11.489364076
## [271] 28.064950147 1.984816631 23.013533222 2.413867032 5.488712816
## [276] 7.547232024 23.460289257 15.315029142 0.246886481 6.427881499
## [281] 0.414207032 0.355792874 0.937050809 11.183065632 16.720678487
## [286] 7.950660875 6.224365672 11.584433978 4.791165050 8.933793073
## [291] 4.955826704 15.239816661 0.666285903 5.178128262 24.311149846
## [296] 5.010903953 14.529838226 5.562619264 0.211156783 12.587524874
## [301] 3.150714659 9.310237287 13.460098514 6.919689528 13.978597204
## [306] 21.177964563 7.047457128 10.897328350 10.121757974 3.152801574
## [311] 3.393711338 12.908764286 7.057784712 3.117079077 0.569048896
## [316] 9.493410149 4.546825569 3.050953998 2.509137967 16.124032716
## [321] 16.864185332 0.468719946 4.610632425 27.106743100 5.027574869
## [326] 1.209174493 11.564478864 4.644973530 8.122379230 1.339389618
## [331] 10.277392314 2.049652953 3.694972908 3.317101658 5.143725425
## [336] 9.705044857 4.812966497 4.667452774 9.428408742 5.241052867
## [341] 2.068642350 9.582330351 59.375367012 1.436721969 3.199634634
## [346] 7.741408317 20.184665359 14.399241208 50.971805916 34.271802901
## [351] 30.036882453 4.164369390 5.232063839 17.544307633 0.779651904
## [356] 13.962002768 31.565456304 24.131992057 3.521248569 6.508479933
## [361] 3.896343047 5.894139013 19.640892035 9.280667025 2.406656411
## [366] 25.471802220 5.913066883 8.735412917 14.198548160 19.162768553
## [371] 0.521853045 2.326700524 3.400274230 1.746147360 10.165528990
## [376] 5.906462637 5.482860100 6.960537178 5.283183320 9.458254082
## [381] 25.463361570 36.173111999 22.350193130 16.223950233 15.520067959
## [386] 12.437775423 4.514232427 18.036741297 43.658145116 5.249853535
## [391] 3.804763798 2.989943731 30.864990278 5.179044912 3.385564359
## [396] 2.014471469 9.394211880 7.772293025 23.095300327 15.997562300
## [401] 1.013540919 3.138722386 4.373212704 0.211147169 2.039368479
## [406] 8.459353279 17.660999409 5.120202494 36.951529884 5.716428123
## [411] 12.004835251 11.452008407 36.055074514 16.883141304 50.127923693
## [416] 31.427954946 4.851141376 0.290731208 18.940723165 0.726224519
## [421] 38.833249265 6.736249486 11.842417091 19.156824815 0.826702503
## [426] 38.036482835 21.732356901 7.413245948 18.495847582 20.172946881
## [431] 31.996306999 0.981344385 9.332562867 3.220060002 9.788927370
## [436] 18.293560780 1.001890046 1.625500577 18.575751203 4.580460596
## [441] 17.181129472 8.336459808 18.355344403 16.145233641 12.735165990
## [446] 26.033710035 8.770575933 6.599858012 3.483197619 23.604992496
## [451] 19.515243172 6.076183645 1.585763704 2.058939546 14.900480314
## [456] 10.377715015 0.768029569 6.265441347 6.911842129 10.563168395
## [461] 9.850927568 9.854259081 28.905335738 16.359377503 1.047076425
## [466] 17.100651785 7.774683116 2.828823589 9.855278544 3.863667795
## [471] 4.415339530 4.752353809 2.152544567 14.620636067 2.835515850
## [476] 12.239774018 7.282702662 6.425526571 21.868134001 5.229684282
## [481] 5.993907657 1.288817814 12.467382215 32.299992887 13.208423033
## [486] 8.820511521 1.747329236 6.540972246 6.478673862 9.727098643
## [491] 0.527310933 16.272388845 2.880566131 6.732814000 3.928639046
## [496] 2.341410043 4.902389632 2.298349646 0.720226243 0.320222077
## [501] 4.178095991 11.637200852 0.613017563 8.204888757 26.914222891
## [506] 3.913773404 6.446254714 0.344187432 22.782685551 6.111780186
## [511] 13.183258725 4.230598081 0.605643360 5.085354480 1.049710419
## [516] 1.482565668 8.245104476 1.012302274 7.792855555 9.590484566
## [521] 36.054930527 8.749209258 3.065536162 4.406500559 5.094469734
## [526] 0.737600531 9.821832914 10.139752513 2.253550878 5.945966593
## [531] 15.292180217 3.711202107 13.673939313 2.888047844 0.371286462
## [536] 18.331333063 14.385516792 10.861146286 23.364393542 10.494802622
## [541] 0.855486277 1.854239251 2.423525844 1.835836214 17.386301978
## [546] 0.533019910 2.680063877 1.837794050 22.238451763 38.897922689
## [551] 5.105188037 10.966755971 18.621961865 0.396282556 7.250310871
## [556] 30.579337754 1.734565689 2.052895268 4.913965007 15.692318521
## [561] 11.296572918 16.855772631 8.194238971 9.972338015 5.501706720
## [566] 12.171313180 13.666351810 2.866785504 1.690924354 9.851036951
## [571] 6.613816917 13.379653459 6.813956686 5.395410634 5.652077859
## [576] 2.205195821 15.239847022 16.853077028 39.205773378 14.873950387
## [581] 22.556330244 9.197226930 0.450012581 12.489898866 10.802464587
## [586] 13.863331842 1.569515890 5.180999190 9.873962970 16.356198005
## [591] 3.472998082 0.378704386 18.367101195 4.012440466 12.491784999
## [596] 11.840527039 13.231975054 10.489966628 11.684051098 35.675451362
## [601] 0.195275336 6.739834328 2.379813963 9.979143617 3.933712440
## [606] 17.539912350 43.868439083 31.317808283 21.925011965 49.131982789
## [611] 10.154416095 5.225097253 47.833398466 2.656743708 4.212261005
## [616] 0.217562459 7.159069348 6.164647853 5.128191475 7.982210442
## [621] 1.490253571 5.308350562 4.003782310 19.709213226 26.982301342
## [626] 4.705414153 4.975264324 0.155205843 9.598674047 17.145680603
## [631] 5.363126993 19.915916658 5.892733391 2.541409424 0.703204675
## [636] 2.497328138 2.233644249 4.011196955 1.935874606 1.666086685
## [641] 10.934760057 21.276738885 3.845567787 1.212859535 7.361631907
## [646] 3.287953357 3.563388078 2.314930137 8.240508688 5.387287661
## [651] 9.348953282 4.340015827 4.112854460 16.928852516 5.829097093
## [656] 14.381885025 13.945383242 15.725426407 6.711630803 11.329392207
## [661] 12.249974170 19.460025131 10.233632922 1.780028492 15.959481969
## [666] 14.548389330 4.826188358 9.879156872 18.275196756 6.918575387
## [671] 4.310577349 16.962198018 5.071261008 8.280836623 1.978315153
## [676] 3.996566614 4.180399277 26.315041276 13.007199633 11.062890887
## [681] 1.864007847 28.156036956 24.106129080 14.616203869 2.301354180
## [686] 17.191978729 9.655074002 14.700141548 15.159402042 49.530806226
## [691] 3.573858189 3.570853793 11.101793227 4.778905492 17.099005579
## [696] 7.584437215 9.832873800 12.800994245 2.704685517 25.544057543
## [701] 4.619881087 0.241976625 3.520899201 13.439339678 5.210641927
## [706] 2.896130802 33.219612984 13.734618350 17.962504271 36.117061132
## [711] 1.027299436 13.532312903 15.960293716 8.253681005 1.456544781
## [716] 7.062961030 12.135207774 18.623565844 21.142842116 31.105113548
## [721] 20.220285260 1.330026446 4.121837737 0.528360573 5.011640103
## [726] 7.649349697 8.560191275 28.171145318 11.756281275 2.567620287
## [731] 5.310310349 2.168270601 3.024844628 15.929151109 2.407697360
## [736] 0.264863768 9.009019630 3.957919418 0.237952773 1.252540690
## [741] 2.929414515 11.576869003 13.480854965 8.373408895 0.047824444
## [746] 7.209660615 21.780966534 2.544501605 16.987428236 20.838303584
## [751] 4.568480281 6.564989113 9.464533170 0.024528653 3.437952106
## [756] 3.708741120 11.995241884 0.122807819 4.270019704 0.317451566
## [761] 16.806930457 19.215335305 3.198022563 3.877786328 1.335254413
## [766] 10.785270454 2.371184570 7.051090149 2.647679946 7.285453522
## [771] 0.527105783 6.846483294 4.393063020 0.137605076 0.183904362
## [776] 5.007514940 8.586409101 3.326282664 16.664701178 1.625467306
## [781] 4.361762344 18.834050111 47.788747137 26.773457135 18.926588315
## [786] 1.982655291 0.071244584 1.507916197 3.379959436 1.243149475
## [791] 18.640409353 1.387173096 5.757413949 23.266507069 23.624018147
## [796] 25.556125584 9.314666120 5.384927429 0.954480878 7.189991362
## [801] 6.602726481 5.626684502 0.687900219 8.106517839 16.805541806
## [806] 13.083991073 0.732239626 3.636298440 0.126195808 4.501195101
## [811] 10.965891059 8.748530957 15.680191050 11.847057156 32.916375546
## [816] 14.296239286 3.381798584 0.337910771 4.884411828 7.892584268
## [821] 30.024543850 3.884268138 2.052297969 1.949939486 10.437442289
## [826] 6.400832590 26.839020121 4.004684398 9.401374831 3.071821183
## [831] 2.050616955 11.060446547 21.241741235 6.007788982 2.243497337
## [836] 8.547312459 11.670538335 7.672263868 17.601307032 34.331322683
## [841] 14.444244987 6.658527828 2.107814270 10.361807989 5.630609486
## [846] 4.904738301 31.225317268 0.628887746 14.017988815 0.020959868
## [851] 8.596552271 4.760743403 6.836373410 11.234127702 8.791140187
## [856] 17.019534464 34.743879777 16.261146590 4.317379948 2.252229247
## [861] 7.596854474 2.663737601 11.031170580 9.785789678 2.920997487
## [866] 4.066332332 3.907597698 11.120921903 13.947097509 11.458190884
## [871] 0.981376762 4.735855791 0.227954054 3.304179680 59.323725548
## [876] 1.844416130 18.215980598 6.243555844 7.575888177 5.947816684
## [881] 2.072110968 3.477506242 17.047203592 3.642794457 2.480807961
## [886] 7.403971865 9.271074887 3.564977413 8.874231310 1.426717574
## [891] 31.282544507 5.291046158 3.551408928 3.109799023 1.885503439
## [896] 41.359786594 0.283759991 5.034740475 46.395078783 23.251822905
## [901] 6.972530379 3.158140285 1.322670694 13.834747755 3.163476803
## [906] 56.803670969 14.226387310 0.403743932 14.533137790 21.105407487
## [911] 5.246230834 2.038426064 5.876986128 0.384466536 12.582872230
## [916] 3.898433382 21.952786013 2.724993429 0.292358701 6.090907725
## [921] 9.753135306 11.821441017 14.740143734 1.389856376 0.819345023
## [926] 0.595732043 27.096062543 2.464462225 7.760566423 13.229862963
## [931] 9.057087982 2.381284442 0.556305842 24.222658704 0.119779296
## [936] 3.327000514 56.977361560 28.423581271 22.816237527 7.901017330
## [941] 40.703425872 29.342865197 5.573514313 4.866229150 11.467474643
## [946] 21.569087485 8.636879824 9.454430127 0.423316769 0.419381965
## [951] 25.436454023 46.790358906 0.488608824 2.014471069 4.451683844
## [956] 0.293316413 0.332483128 8.221859661 32.695882542 1.981443223
## [961] 0.258417260 1.522007440 3.958749343 4.603945347 8.719096358
## [966] 2.586252671 1.844688142 2.565892894 6.389077106 0.168887026
## [971] 2.865024558 26.196344363 12.945441808 2.082379556 1.969069822
## [976] 13.347828872 3.700588936 12.387798391 22.656581221 22.016652735
## [981] 0.021377748 2.737560184 3.952240681 3.441089238 5.611761208
## [986] 2.995868083 5.465131355 0.584748236 2.122075513 4.013251304
## [991] 22.973303179 13.756945096 6.645176839 5.492216861 14.388594980
## [996] 21.198765584 6.539572543 0.882534363 1.478369869 9.813875603##Đồ thị
hist(ED, main="PP Exponential")
##Các đặc trưng
summary(ED)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.00635 2.95918 6.65163 9.86401 13.94962 59.37537###Phương sai
var(ED)## [1] 95.41491###Độ lệch chuẩn
sd(ED)## [1] 9.768056#Phân phối Đều
##Mô phỏng
U <- runif(1000, min = 1, max = 5)
U## [1] 2.826198 4.143946 4.672822 4.477686 4.830966 3.588974 2.740493 4.650307
## [9] 3.906009 1.420902 2.849960 3.994308 4.561101 4.847166 4.276541 3.399532
## [17] 2.279100 2.171292 1.295926 2.941803 3.729547 1.341159 1.213886 1.384349
## [25] 2.522212 4.224159 4.503229 3.180826 2.159781 2.882127 2.684697 1.832834
## [33] 2.581912 1.100094 2.290200 2.872829 4.986306 4.186238 1.825176 1.411374
## [41] 4.462748 2.351416 2.941256 3.950595 4.676316 1.412205 4.881516 4.908724
## [49] 2.298244 3.368579 1.735700 3.740524 4.375721 4.055272 3.656307 4.695400
## [57] 2.351543 4.814577 3.640351 1.824977 3.371809 4.567065 3.622197 2.918963
## [65] 3.920780 3.829444 2.374961 2.959233 3.459402 1.344572 3.551762 3.134454
## [73] 2.282980 2.305730 2.771785 4.095820 1.257458 3.976255 1.547600 2.662695
## [81] 4.311085 1.217293 4.574354 1.847981 4.221448 2.253166 3.666993 1.338963
## [89] 2.285627 3.374113 2.159191 3.530582 3.942128 3.607738 4.845178 4.915480
## [97] 2.136742 3.069502 1.918171 1.891053 1.069951 1.867151 1.473677 1.599921
## [105] 4.835832 4.155237 4.344952 3.507650 4.830807 1.051199 4.701605 4.615017
## [113] 1.610546 4.908895 3.531427 2.612175 4.177838 2.836700 4.319596 4.871679
## [121] 3.315280 1.065056 4.449563 2.953595 2.627901 1.583759 1.559822 4.076687
## [129] 1.633431 3.875206 2.721999 1.465253 2.302769 1.236246 3.083603 4.830437
## [137] 1.147789 4.074966 3.167202 1.457834 4.679284 4.055676 2.471111 1.561109
## [145] 3.793699 1.507273 1.653231 3.212187 4.080457 1.246132 1.977461 2.879713
## [153] 3.320627 3.189418 2.469713 3.292232 3.204807 4.961963 3.318311 4.555822
## [161] 3.676335 2.124828 1.646969 4.313630 1.109396 1.546974 3.939625 4.219251
## [169] 1.312730 2.686583 2.886149 4.622770 3.625930 4.965195 3.854057 3.222201
## [177] 3.112775 4.799039 1.783578 1.250175 2.318095 4.241695 4.438405 1.930239
## [185] 2.603286 1.074062 1.347005 2.093993 1.288652 1.205314 2.615926 2.434337
## [193] 1.781749 2.102508 1.349196 2.627154 3.295211 1.955843 1.655039 3.704083
## [201] 2.974131 4.127357 1.699165 3.117075 3.610342 2.929646 4.308759 3.503992
## [209] 3.819898 3.609327 3.479891 1.015688 4.522853 2.565632 4.537278 1.170702
## [217] 2.743460 2.043948 3.171846 1.752319 1.053220 1.653166 1.077515 1.926145
## [225] 3.384241 1.752889 3.204285 2.119141 4.386696 3.411076 3.533221 2.157852
## [233] 4.932807 3.597197 2.362942 1.730108 4.189166 2.505723 1.539521 2.612485
## [241] 2.763504 4.442415 4.769786 2.529406 1.920128 2.090472 3.875184 4.906954
## [249] 1.710202 1.009918 4.597035 3.604326 2.679788 3.282461 2.904904 2.887617
## [257] 3.298663 2.926487 3.205133 3.982554 4.137702 2.019128 2.350257 2.400111
## [265] 3.025850 2.576546 2.273003 2.552350 2.858173 4.047331 4.426010 4.771110
## [273] 4.768397 1.224615 4.775609 3.846192 4.566390 3.041322 4.253907 3.856113
## [281] 2.164526 1.282868 2.209835 4.430481 2.782449 1.684273 3.285916 1.339875
## [289] 2.612550 1.770042 3.130496 3.069513 3.955294 3.716063 1.087912 3.012916
## [297] 4.376800 2.031785 4.334215 1.917832 3.363685 4.009581 2.788245 4.405852
## [305] 1.995399 1.096979 2.908291 3.580457 3.206514 2.341333 3.898076 1.903669
## [313] 2.326905 3.648044 1.021779 1.593423 2.081957 2.367169 1.913576 1.408758
## [321] 4.030727 1.034200 3.855273 2.251798 2.772714 2.611236 1.335664 2.727405
## [329] 3.326028 1.101451 2.507160 4.845985 1.753775 2.623978 1.339897 4.992451
## [337] 4.020011 1.457997 2.062865 3.989430 1.451977 3.277165 4.766151 4.813145
## [345] 1.546106 4.590700 2.649607 3.529707 1.977285 1.601440 3.868954 2.401109
## [353] 2.575308 4.520793 1.089516 4.412147 4.659834 1.250472 3.707338 2.111868
## [361] 4.400657 4.256101 1.805645 1.692550 3.320115 3.135062 4.155405 4.509373
## [369] 3.990342 3.682377 3.377845 4.300172 1.542130 3.782508 3.224837 3.094770
## [377] 2.448217 2.669660 1.621836 1.819746 4.549911 3.817366 3.042910 3.399929
## [385] 3.372968 2.484468 3.403081 4.295883 2.728678 3.935921 1.555141 4.509502
## [393] 4.277994 4.152298 1.560033 1.908609 2.927262 2.621175 1.915140 3.438478
## [401] 4.705616 3.139580 3.169929 4.731352 2.248465 2.036638 1.639802 3.516921
## [409] 1.741233 4.518727 2.962135 2.138118 2.352325 2.656512 3.958024 3.596016
## [417] 4.396081 2.013079 3.655295 2.050125 4.785575 3.331615 4.317911 4.970264
## [425] 4.875367 2.129529 3.664328 3.910578 3.717182 1.529350 4.326681 3.732765
## [433] 4.353919 3.570978 1.203582 4.886814 3.558308 3.410043 4.482213 2.330176
## [441] 3.571245 1.677814 4.795242 1.819394 3.457902 4.626342 1.690103 4.678979
## [449] 1.474412 1.597727 1.219312 4.314642 3.548259 4.669028 3.935893 3.636944
## [457] 4.491188 1.084830 3.095035 1.194225 1.959980 3.259718 4.282180 1.557585
## [465] 3.335890 1.407817 1.763658 2.347761 3.621990 2.156414 1.296696 1.092015
## [473] 3.987563 4.783439 3.327927 4.615470 3.492382 1.841821 1.845009 3.778374
## [481] 4.486016 4.162815 4.781930 2.280675 3.832828 3.665589 1.294578 2.762579
## [489] 4.414277 1.513153 1.603378 4.333556 2.731753 4.930010 4.452388 4.740985
## [497] 3.581105 1.509309 1.759086 2.597510 3.715432 1.365977 2.880740 2.199442
## [505] 1.502581 2.325963 3.966612 4.623443 2.407093 4.151083 4.074353 1.722919
## [513] 1.008955 2.170466 4.813184 4.293153 4.093702 3.885494 4.354391 2.825647
## [521] 2.637349 4.656805 3.076568 1.213458 3.357970 1.479764 3.056224 4.845029
## [529] 3.531765 3.973172 4.301322 3.391527 4.981666 3.249582 2.259544 1.687374
## [537] 2.700514 1.545025 3.612000 2.439398 3.717604 2.773572 3.570344 2.063256
## [545] 1.265252 4.967945 2.148366 2.305370 3.702094 4.073342 2.410329 3.293626
## [553] 2.880428 4.254600 1.739567 1.852456 2.555118 1.274985 4.635711 1.350194
## [561] 3.598808 3.742691 3.818410 4.017310 2.114638 2.499773 1.732790 2.602704
## [569] 4.177721 1.949926 4.614242 4.672767 1.026343 1.502156 1.984530 4.768905
## [577] 1.510013 2.483191 3.997228 2.700775 3.645470 3.043637 3.595781 4.786629
## [585] 3.111600 4.834592 4.109766 3.161192 1.142788 4.708258 4.930967 3.212715
## [593] 3.899615 1.093224 1.261127 4.484487 2.985249 4.427573 2.896295 3.412110
## [601] 4.260780 4.681377 4.500875 4.897244 3.327006 4.580150 2.665722 1.911225
## [609] 3.572709 2.129267 1.334039 2.686317 2.218511 2.162382 1.961903 2.495445
## [617] 4.968100 4.883440 1.660097 4.342815 4.809208 1.858505 1.125650 1.942142
## [625] 2.717838 3.592299 1.754068 4.817557 1.352768 1.777691 4.181523 3.551302
## [633] 4.645397 2.704318 1.315003 1.586825 2.684232 1.712928 3.498026 1.174462
## [641] 4.325405 2.014380 3.256278 1.803117 4.783199 4.661087 1.090101 1.919791
## [649] 1.468550 4.340763 1.624940 2.864547 2.611471 4.719094 4.754446 3.191161
## [657] 3.597305 4.621257 1.521971 1.153992 1.487608 2.995962 1.678066 4.366133
## [665] 4.149171 1.918363 4.374682 2.407779 1.914495 4.817262 4.010451 4.682488
## [673] 4.909768 3.337843 2.768653 2.172106 1.623576 2.080961 3.824898 3.082144
## [681] 1.858684 3.820218 2.895151 2.854829 4.369195 1.796495 3.813174 3.814686
## [689] 4.612348 4.656408 1.557894 2.449639 2.882408 4.501340 2.262748 2.248750
## [697] 1.742380 1.842403 3.661854 1.050709 1.377161 4.256261 1.002381 2.812068
## [705] 3.144606 3.344980 3.461184 2.699609 4.646482 4.309261 3.117482 1.128259
## [713] 1.261499 2.914266 3.235160 4.527254 4.058126 3.331849 4.190468 3.831225
## [721] 1.504212 2.155637 3.366806 1.698780 2.968337 4.034085 2.739391 1.527401
## [729] 4.603041 1.506049 3.406347 1.867055 1.077562 4.944947 2.952669 3.202754
## [737] 3.618310 1.255274 2.500505 2.019228 4.420964 1.614279 1.627563 1.181635
## [745] 3.027790 4.655867 3.687828 2.732506 3.040130 4.362324 2.584764 1.861065
## [753] 4.480916 3.486656 1.756515 3.078286 1.787296 1.563218 2.489008 4.698766
## [761] 2.488036 4.671518 4.779835 1.425693 4.731167 3.811415 1.569059 2.110575
## [769] 1.577945 1.921621 1.087919 3.801599 1.422288 2.749804 2.746315 1.233631
## [777] 2.155744 2.062101 4.523027 4.783340 3.973970 4.394804 3.387623 2.539439
## [785] 3.302220 1.935710 3.446090 3.545335 4.867176 1.548098 1.635750 1.600111
## [793] 2.038236 1.777322 4.860098 2.115162 2.192778 4.395856 4.508012 1.395747
## [801] 2.927095 1.791240 1.995289 3.735085 3.044081 3.065304 2.040471 1.353696
## [809] 4.759225 3.082196 3.214349 1.604869 2.614934 3.777739 2.405310 3.393024
## [817] 1.257270 1.262882 3.620301 3.890670 3.200227 1.150321 3.571768 3.753358
## [825] 3.190843 3.091133 2.334169 1.451018 3.483582 2.954734 3.752743 2.478400
## [833] 4.307298 1.891804 1.689128 3.476011 2.710560 3.320488 4.439588 4.909515
## [841] 3.024030 4.629639 2.657547 3.817214 2.097569 2.460684 3.695537 1.083608
## [849] 2.476793 2.449744 3.788505 1.756748 3.448517 3.225036 3.059076 3.064815
## [857] 1.635533 2.093221 1.893142 1.061372 2.507910 3.984228 3.033098 4.778427
## [865] 4.250507 1.851746 1.769726 2.679489 1.059687 4.966623 3.130923 3.462829
## [873] 1.478101 4.325961 3.372742 4.547331 2.405605 2.745795 4.077256 3.832784
## [881] 3.673586 4.703799 2.133968 2.952329 1.668505 1.555964 4.749550 2.584441
## [889] 2.652541 2.789264 2.534177 1.190476 3.712264 1.913243 1.327732 3.574917
## [897] 1.406937 1.129273 2.394537 3.569124 1.062634 2.783503 4.907805 1.615052
## [905] 1.586332 1.085743 3.568475 3.408593 4.154243 1.809484 2.568908 2.680136
## [913] 4.919575 1.244658 3.043089 4.359691 4.467330 2.289824 2.474926 1.339560
## [921] 3.577111 2.480733 3.828017 1.255954 1.648801 4.802084 1.329743 2.669459
## [929] 3.393789 3.814253 2.303843 1.149993 3.663484 4.508994 3.371428 3.460256
## [937] 4.463241 1.899981 4.760064 1.617684 1.782182 4.242575 3.809265 2.241830
## [945] 4.360913 3.934575 3.148605 2.366924 2.896817 2.075919 1.843803 3.471257
## [953] 4.325835 3.366922 3.040442 3.111159 2.080484 1.951081 2.700290 1.744580
## [961] 2.155400 4.228356 4.533538 3.071630 4.289599 3.711272 3.773761 1.526328
## [969] 3.801771 3.882276 2.143994 1.627804 3.983117 4.660870 2.094425 4.924086
## [977] 3.705904 1.123374 4.010711 3.237934 1.274754 2.030236 4.307286 2.052285
## [985] 3.570122 2.781121 4.618120 2.576313 3.787402 1.911023 3.723224 4.642672
## [993] 3.889803 4.508437 4.660187 3.241179 3.226519 3.615224 3.551097 3.194571##Đồ thị
hist(U, main="PP Đều")
##Các đặc trưng
summary(U)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1.002 1.941 3.043 3.002 3.983 4.992###Phương sai
var(U)## [1] 1.344281###Độ lệch chuẩn
sd(U)## [1] 1.159431#Phân phối Nhị thức
##Mô phỏng
B <- rbinom(1000, size = 5, prob = 0.2)
B## [1] 0 1 1 0 1 2 2 0 1 1 0 1 0 0 0 1 2 0 0 0 1 1 0 0 1 0 1 0 0 2 0 2 1 1 2 1 2
## [38] 1 2 3 4 2 1 2 2 2 2 0 1 1 1 2 1 0 1 1 0 0 2 1 0 2 2 1 2 0 0 0 2 1 1 1 1 1
## [75] 1 1 1 1 1 2 3 1 1 0 1 0 1 2 2 0 1 1 1 2 2 1 1 0 1 1 1 0 1 2 2 1 1 1 0 1 1
## [112] 1 1 2 2 1 4 1 1 1 2 1 1 1 2 0 0 0 3 1 0 0 1 2 1 1 1 2 4 2 2 1 2 1 1 0 0 2
## [149] 2 2 0 2 0 0 0 0 1 2 1 1 1 0 2 1 3 1 1 1 2 1 2 1 1 0 0 1 0 1 0 1 1 1 0 0 2
## [186] 0 2 1 2 1 1 0 2 1 0 0 0 1 1 1 0 1 0 1 1 1 2 0 1 1 1 3 0 0 1 1 1 0 1 1 2 0
## [223] 0 1 1 0 1 1 1 3 0 0 0 1 2 2 0 1 2 0 1 2 2 2 3 1 3 0 3 1 2 1 1 0 1 1 0 1 0
## [260] 0 1 1 0 1 1 1 1 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 2 2 0 1 2 1 0 3 1 0
## [297] 3 3 1 0 1 0 1 0 1 0 0 2 1 1 0 2 1 1 1 2 0 1 0 1 0 2 1 3 1 1 0 1 1 0 1 1 3
## [334] 0 1 1 0 1 1 2 2 2 0 3 1 0 1 1 1 3 0 0 1 2 0 2 0 1 3 1 0 2 0 1 1 1 1 1 1 0
## [371] 2 0 1 1 0 0 1 1 2 0 0 0 0 1 0 2 0 0 0 3 0 1 2 2 2 2 2 1 0 3 0 0 0 0 1 2 0
## [408] 0 0 0 1 2 2 2 1 1 2 0 2 1 1 0 1 1 1 2 1 0 0 1 1 2 0 1 2 0 1 1 3 0 0 2 0 1
## [445] 0 1 1 1 2 2 0 0 0 2 0 0 1 0 1 2 0 2 0 2 1 1 2 3 2 1 0 1 3 0 2 2 0 1 1 1 1
## [482] 0 1 0 0 0 1 3 1 0 1 1 0 1 0 1 0 0 0 2 0 1 0 0 2 1 0 1 1 1 0 1 1 0 0 1 2 0
## [519] 2 1 0 2 0 1 2 1 0 1 1 1 2 0 1 2 2 0 1 1 1 2 1 0 0 3 0 0 2 3 2 1 1 1 0 1 1
## [556] 1 1 1 2 0 2 0 0 0 1 0 1 0 1 0 0 1 0 0 1 1 0 1 1 0 1 1 0 2 1 1 1 1 1 0 0 1
## [593] 0 0 1 1 2 0 1 1 2 2 0 0 0 1 1 2 1 1 1 1 0 1 1 0 0 2 3 2 1 2 2 2 1 0 1 3 0
## [630] 1 1 1 0 3 0 0 2 0 2 1 0 2 1 1 1 1 1 1 0 0 0 1 0 0 0 2 0 0 2 1 1 0 2 1 0 0
## [667] 2 3 0 1 2 2 1 0 1 0 1 1 1 0 2 1 1 2 2 0 0 1 1 0 1 0 0 3 1 1 0 0 1 0 0 1 1
## [704] 0 1 2 1 1 1 1 0 1 2 1 1 1 1 1 1 2 0 0 0 2 1 0 0 2 2 1 2 0 0 1 2 1 1 2 0 1
## [741] 1 2 1 0 1 0 0 0 2 2 0 1 1 0 1 0 1 0 0 1 1 1 2 2 0 2 0 2 0 0 2 3 0 0 1 1 0
## [778] 2 1 2 0 1 0 2 2 1 0 0 3 1 2 1 2 1 2 1 0 2 2 3 0 1 1 1 0 1 3 2 3 1 2 0 0 0
## [815] 1 0 1 1 2 0 0 2 1 1 0 2 1 1 0 2 0 0 2 0 1 2 0 1 1 3 1 0 0 0 1 2 1 1 2 1 2
## [852] 1 2 3 2 2 3 0 1 1 1 2 2 0 0 2 3 1 0 1 2 3 0 0 1 0 1 0 1 0 1 1 2 0 2 1 1 2
## [889] 1 0 0 2 0 1 0 0 2 0 1 1 0 0 0 0 0 1 0 2 2 1 1 4 2 0 2 1 2 1 2 1 0 0 2 0 2
## [926] 2 0 0 0 2 1 1 1 1 1 1 2 1 0 3 1 0 1 3 1 1 0 1 0 2 1 1 0 1 0 1 0 1 1 1 0 1
## [963] 0 1 0 1 0 2 1 1 2 4 1 1 2 1 2 2 2 1 1 2 3 0 0 2 0 2 0 2 1 1 0 2 2 1 4 1 0
## [1000] 3##Đồ thị
hist(B, main="PP Nhị thức")
##Các đặc trưng
summary(B)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.000 0.000 1.000 0.995 2.000 4.000###Phương sai
var(B)## [1] 0.7617367###Độ lệch chuẩn
sd(B)## [1] 0.8727753