1. Modelkan pendapatan bulanan dari 1000 pegawai yang berdistribusi
normal dengan rata-rata pendapatan Rp10.000.000,- dan standar deviasi
Rp200.000,-.
set.seed(123)
n <- 1000
mu <- 10000000
siqma <- 200000
normal_data <-rnorm(n, mean = mu, sd = siqma)
normal_data
## [1] 9887905 9953965 10311742 10014102 10025858 10343013 10092183 9746988
## [9] 9862629 9910868 10244816 10071963 10080154 10022137 9888832 10357383
## [17] 10099570 9606677 10140271 9905442 9786435 9956405 9794799 9854222
## [25] 9874992 9662661 10167557 10030675 9772373 10250763 10085293 9940986
## [33] 10179025 10175627 10164316 10137728 10110784 9987618 9938807 9923906
## [41] 9861059 9958417 9746921 10433791 10241592 9775378 9919423 9906669
## [49] 10155993 9983326 10050664 9994291 9991426 10273720 9954846 10303294
## [57] 9690249 10116923 10024771 10043188 10075928 9899535 9933359 9796285
## [65] 9785642 10060706 10089642 10010601 10184453 10410017 9901794 9538166
## [73] 10201148 9858160 9862398 10205114 9943045 9755856 10036261 9972222
## [81] 10001153 10077056 9925868 10128875 9955903 10066356 10219368 10087036
## [89] 9934814 10229762 10198701 10109679 10047746 9874419 10272130 9879948
## [97] 10437467 10306522 9952860 9794716 9857919 10051377 9950662 9930491
## [105] 9809676 9990994 9843019 9666412 9923955 10183799 9884931 10121593
## [113] 9676423 9988888 10103881 10060231 10021135 9871859 9830059 9795174
## [121] 10023529 9810505 9901889 9948782 10368772 9869610 10047077 10015592
## [129] 9807629 9985738 10288910 10090301 10008247 9915501 9589351 10226267
## [137] 9707872 10147990 10381821 9711221 10140357 9947561 9685571 9697066
## [145] 9679693 9893819 9707649 10137583 10420022 9742594 10157548 10153808
## [153] 10066441 9798325 9976109 9943921 10112598 9925512 10195395 9925084
## [161] 10210542 9790165 9747969 10648208 9916628 10059646 10127314 9903244
## [169] 10103372 10073793 9956924 10013059 9993187 10425690 9851733 9780801
## [177] 10007558 10062096 10087305 9908327 9787335 10252637 9930070 9826897
## [185] 9952744 9960565 10221984 10016947 10150811 9900142 10042889 9935063
## [193] 10018917 9820927 9737840 10399443 10120142 9749746 9877767 9762904
## [201] 10439762 10262483 9946971 10108639 9917132 9904751 9842279 9881077
## [209] 10330181 9989194 10023849 10048737 10246495 9896787 9801499 10335139
## [217] 9911767 9855387 9752745 9743057 9885205 10123597 10221970 10141518
## [225] 9927269 10011950 9859081 9856556 10176930 9796881 10391059 9981936
## [233] 10042908 9852294 9885122 9736597 9963415 10083796 10064861 9843693
## [241] 9842276 9899560 10299212 9772539 9964190 10380472 9979805 9728032
## [249] 9867046 10097092 9924879 9887625 9931217 10018099 10319702 9982287
## [257] 10216160 10126151 9977272 9693420 9895777 9902026 10009431 10260040
## [265] 10458616 10309516 9973370 9648695 9922244 10017841 10169003 10192506
## [273] 10136862 9720945 10169929 9910689 10034961 10014910 10085633 10004935
## [281] 9666505 10147299 10077205 9946870 10023629 10026808 10044204 10328169
## [289] 9956190 10033613 10233677 10210836 10229053 9884506 10400497 10013340
## [297] 10373370 9729819 10004197 10249983 9856952 9849462 9812292 9789497
## [305] 9912568 10066236 9597158 10042396 10247335 10407515 10260235 10151355
## [313] 9654654 9879699 9929591 10140705 9978866 9748270 10336887 10182278
## [321] 10047486 10243622 9732245 10132164 9895418 10136749 9987836 10126592
## [329] 10267104 10001458 10203512 9762313 9855679 10303844 10075478 9589555
## [337] 9727193 9959844 10173156 9979623 10124837 10191801 10334211 10011203
## [345] 9989604 9649353 10019866 9885630 9805198 9964019 10202989 9601450
## [353] 9914544 10023327 9821358 10066781 10082286 9993393 9506820 10514292
## [361] 9958940 10130239 10054753 10204935 10163532 9958041 10075634 9810918
## [369] 10171385 9907792 10483355 9669790 9907203 10165076 10102027 9882104
## [377] 9800644 10028895 9997139 9641944 10006910 10038046 10034945 9788997
## [385] 10095227 10275714 10091247 9772882 9912871 10069221 9870591 9568471
## [393] 10176850 9834104 9885288 10300780 9845171 10169146 9747863 9929092
## [401] 9985289 9766270 9873050 9994232 10134139 9669891 9930049 10151281
## [409] 9892238 10045458 10098446 10053567 10130652 9975458 9917265 9471370
## [417] 9981412 10086057 10107080 9888944 10355901 10057285 10025263 10254453
## [425] 9856307 9909932 10479490 10002226 10326714 9712299 9961897 10075685
## [433] 10060008 9798873 10003852 9784516 10142541 10216955 9555002 10247139
## [441] 9751791 10090954 10131981 9960022 9870977 10033064 10087764 10176661
## [449] 9589533 9672724 10286080 10209326 10087058 10143036 10183435 9467815
## [457] 10222055 9903002 10046123 9940968 10174393 9930306 10103701 9921863
## [465] 9781443 10242002 10148180 10344852 10013031 10225001 10395084 9943704
## [473] 9735410 9952130 9957192 10030336 10342461 9934771 10074601 9954463
## [481] 10004090 10062812 10265643 10024264 10142568 10155772 10182955 9885121
## [489] 10325376 9923809 9978843 10280810 10258817 9782002 9825386 9728384
## [497] 10036369 10032968 10072823 10110432 9879621 9801260 10205357 10150212
## [505] 9698167 9980971 9820810 9585850 10030024 9984158 9980526 10043231
## [513] 10176493 10041120 9876713 9853040 9973639 10062003 9792064 9963138
## [521] 10193453 9978344 9860316 9944811 10222930 10110009 10247335 10027820
## [529] 10082055 9888309 10121074 9898733 9715887 10025599 10389170 10160183
## [537] 10233051 10071771 9878289 9959552 9945350 9906260 10140833 9760527
## [545] 10173273 10172830 9760276 10127898 10486045 9888557 10168981 9843560
## [553] 10222142 10049965 10330383 9708206 9989740 9894615 9960547 9874084
## [561] 9833231 10115744 9782484 10296806 9762759 10020216 10106598 10117347
## [569] 9939651 10015900 10192253 9708707 9843652 10064080 9911044 10274001
## [577] 10134651 10014433 9698449 10005220 9936717 9979531 9763688 10099732
## [585] 9792209 9954756 10076285 9843297 10116598 9736698 9438045 10092994
## [593] 10168108 9942831 10100825 9768817 9974570 9611696 10236236 10371982
## [601] 10214802 9994531 9993334 9696786 10158077 9957853 9868651 9717595
## [609] 9940048 9830188 9920594 9756480 10337518 9996799 10214989 9479660
## [617] 9909360 9864904 9755415 10309322 9716944 10063678 10169287 10035638
## [625] 9824949 10188233 10034118 9787300 9722390 10417343 9864299 9628886
## [633] 10106652 10062046 9729233 9611409 9976739 10227879 10127225 9901413
## [641] 9833162 10054213 10031471 10125942 9920840 10179871 9833838 9933891
## [649] 10148163 10197994 9612299 10021438 10121756 9709835 10096125 9834365
## [657] 10204051 10107696 10153810 10024144 10172730 10276103 10393250 9994321
## [665] 9550190 10006305 10041112 9968931 10113658 10202136 9896404 9941181
## [673] 10079568 9889955 10018253 9607658 9776020 9734449 9829275 9861339
## [681] 10076461 10196423 9854523 9800632 9791662 9917082 9952194 10096724
## [689] 9935735 9584302 9981713 10237437 10238320 9842207 9690445 10491612
## [697] 9967516 9980510 10084115 9677192 9854356 9691912 9861381 10023770
## [705] 9727058 10117997 10057869 9819157 10045265 10149616 10212219 9957430
## [713] 9981273 9982657 10288292 10225014 10166880 9942532 10074648 10080658
## [721] 9791665 9654339 10128366 9694138 10000337 10050050 10112773 10037885
## [729] 9853429 10197273 10347727 10176236 9611270 10279915 9988789 10104983
## [737] 10124407 9980663 9984947 10203831 10142320 10198052 10476585 10132883
## [745] 10041476 9557873 10538343 9903465 10474947 10074929 10307686 9978058
## [753] 10102294 10042792 9962776 9975921 10202567 9959708 9592464 9960822
## [761] 10107958 10123291 10123314 9661580 10073748 10193572 10255316 9955008
## [769] 9935621 10297568 9666414 9912634 10091492 9676445 10055926 10375573
## [777] 9999188 9944309 10094982 9944186 10162680 10180887 10000538 9764662
## [785] 9736356 9881401 10159476 9608359 9622735 9869244 10078879 9817287
## [793] 10177350 10066674 9965872 10163766 10077673 9910813 10046223 10129503
## [801] 10071257 9868398 10171040 10230587 10055255 10028821 9984875 10432283
## [809] 10055263 9968341 9498416 9686944 9984465 10041259 10055374 10164301
## [817] 9961170 10242918 9815697 9758311 9754203 10148459 9983416 10157964
## [825] 9946459 9881622 9926329 9629477 9766077 9711593 10210864 9880534
## [833] 10157892 10303298 9961645 10056776 9649786 9836266 10011243 10059817
## [841] 9848120 10536972 9908322 10012849 10129958 9994796 9871287 10209061
## [849] 10323109 9994061 10112453 9980518 10203291 9768767 10464172 9879294
## [857] 9708230 9929816 10029342 10324724 10182242 10028492 9722103 9826792
## [865] 9967343 10510605 9627954 10226211 9894553 10333198 9772160 10028725
## [873] 9780090 10180703 10296756 10390144 10159520 10368653 10249285 9973625
## [881] 10095407 9805601 9962960 10244193 10108257 10091471 9792374 9879097
## [889] 9847079 10079059 9801898 10112408 9776717 10365706 10092118 9859799
## [897] 10048209 9929509 10074230 10048707 9797177 9841737 10059919 10327810
## [905] 10216923 9875087 10165185 9990286 10060263 10052072 10515090 9762942
## [913] 10020184 9644005 10117967 10219322 10289132 9614971 10082554 10318674
## [921] 9917197 9957570 9992693 10073004 10133032 10263564 9980902 10039256
## [929] 10497600 10086220 10037751 9731551 10000571 9955735 9997791 9884916
## [937] 9862637 9855845 9957099 10273627 10209817 9928005 9662817 9831083
## [945] 9908448 10020728 9867479 10401336 9945546 9757211 9971748 9798924
## [953] 10031231 10046727 10071118 9675628 10044142 10062090 9715778 10191073
## [961] 10156834 10459924 10031341 10009347 10019317 10013953 9630305 9665775
## [969] 9984492 9883787 10010947 9577758 9700260 9779703 10197212 9780302
## [977] 9840097 10015975 9935451 10029283 10461012 9775079 9938906 9896648
## [985] 10302479 9846103 9983583 10157427 9788282 10331035 10135152 9785159
## [993] 10090916 9957339 10062646 9982005 10214103 9729780 9895477 9950162
hist(normal_data, breaks = 30, main = "Histogram Distribusi Normal (Pendapatan Bulanan)", xlab = "Nilai", col = "blue")
2. Modelkan jumlah pelanggan yang datang setiap hari ke suatu
restoran yang mengikui pola distribusi poisson dengan laju kedatangan
pelanggan 35 pelanggan perhari.
set.seed(123)
n <- 30
lambda <- 35
poisson_data <- rpois(n, lambda)
poisson_data
## [1] 31 42 25 35 45 37 27 24 42 37 37 35 31 42 39 34 30 28 33 28 31 34 28 28 33
## [26] 27 40 40 39 39
hist(poisson_data, breaks = 30, main = "Histogram Distribusi Poisson (Kedatangan Pelanggan)", xlab = "Jumlah Pelanggan", col = "red")
3. Buatlah dua kasus Anda sendiri dengan melibatkan distribusi
variabel random dari teori yang telah dipelajari.
A. Seorang guru ingin mensimulasikan hasil ujian 100 siswa, di mana
setiap siswa menjawab 50 soal pilihan ganda. Probabilitas seorang siswa
menjawab benar sebuah soal adalah 0.6 (60%).
set.seed(123)
n <- 100
size <- 50
prob <- 0.6
binomial_data <- rbinom(n, size, prob)
binomial_data
## [1] 32 27 31 26 25 36 30 26 30 30 24 30 28 29 34 26 32 36 32 24 26 28 29 21 29
## [26] 28 30 29 32 34 24 25 28 27 37 30 28 33 32 33 34 31 31 31 34 34 33 30 32 26
## [51] 36 31 27 34 30 33 34 28 26 31 29 35 31 32 27 30 27 27 27 31 28 29 28 41 30
## [76] 33 31 29 31 34 32 29 31 27 34 31 22 26 26 33 34 29 31 29 32 33 27 35 30 30
hist(binomial_data, breaks = 30, main = "Histogram Distribusi Binomial (Hasil Ujian)", xlab = "Jumlah Jawaban Benar", col = "purple")
B.Sebuah call center menerima panggilan pelanggan setiap beberapa
menit. Rata-rata, ada satu panggilan setiap 3 menit. Simulasikan waktu
antar panggilan untuk 200 panggilan.
set.seed(123)
n <- 200
rate <- 1/3
exponential_data <- rexp(n, rate)
exponential_data
## [1] 2.53037178 1.72983081 3.98716460 0.09473208 0.16863293 0.94950365
## [7] 0.94268188 0.43580041 8.17870939 0.08746034 3.01449017 1.44064418
## [13] 0.84304088 1.13135349 0.56485212 2.54935839 4.68961062 1.43628125
## [19] 1.77280451 12.12303513 2.52944919 2.89761363 4.45582738 4.04413346
## [25] 3.50558695 4.81755703 4.49022861 4.71195764 0.09530323 1.79354907
## [31] 6.50351924 1.51984719 0.77867345 7.79067635 3.68707720 2.37204528
## [37] 1.88784023 3.76392301 1.76605393 3.38787010 1.26109441 21.63302273
## [43] 2.53716590 0.67662602 3.30101645 6.74491708 4.09120290 1.72917500
## [49] 8.17582755 3.93648913 0.27177405 0.91861155 3.20163921 0.94054877
## [55] 2.92392045 5.66346995 1.69376581 7.73088399 3.14308724 3.07332403
## [61] 3.08360885 0.85400538 4.68915567 0.12626488 0.29589267 0.29570794
## [67] 0.84115548 0.88736088 2.91728895 2.77208167 4.92721358 4.85973830
## [73] 7.60843662 4.56464887 1.14004261 0.71553890 1.39946227 0.12681435
## [79] 0.95903070 1.93083276 1.71768931 0.64816651 13.49602019 5.57127166
## [85] 2.05637591 4.31835788 5.19346195 3.73434990 4.38990168 4.61218194
## [91] 0.01379738 3.32629640 0.89991095 3.57600902 3.34478611 0.20212767
## [97] 1.44200616 4.71136302 0.77983832 5.57076686 1.38965886 0.70810724
## [103] 3.54629826 0.17901412 1.20971532 2.82881952 1.24974193 2.25965521
## [109] 0.56605916 2.63056161 0.57011346 2.93723462 0.97012748 3.96143266
## [115] 0.95538195 4.81520189 0.43720235 5.40938796 0.09017836 3.91032165
## [121] 0.59937673 5.25436873 5.29100500 2.52913073 1.04625833 9.89347440
## [127] 1.20511852 3.30210520 3.98676952 1.92570794 0.58750115 1.37036657
## [133] 1.11825049 10.39078467 3.82208316 3.24445545 0.89087748 0.25248220
## [139] 8.86020275 5.90475676 1.99156538 4.82817643 1.82051125 0.28095694
## [145] 0.97390585 5.27964694 0.79833216 2.82187850 1.34732608 3.86671944
## [151] 0.53486719 4.71517826 0.18642239 1.71175003 5.19234254 3.93223171
## [157] 3.88461890 1.40193213 0.09866937 0.45911413 3.11541601 3.24733712
## [163] 11.24187341 0.01687827 0.01310211 5.09995248 1.62200445 1.41110583
## [169] 0.15467825 1.55155902 4.44942903 3.83845668 4.27940452 6.35488302
## [175] 4.27248112 2.65234293 8.07296058 6.68972129 1.56841338 0.20595169
## [181] 1.70745160 13.09773281 1.67439530 1.37634391 0.78079112 2.09652523
## [187] 2.88956517 2.19443866 3.33683871 1.81687364 2.01425302 4.89497649
## [193] 0.30577839 1.22395237 8.22104566 8.55563237 0.07252012 1.42678442
## [199] 2.00432586 2.85069091
hist(exponential_data, breaks = 30, main = "Histogram Distribusi Eksponensial (Waktu Antar Panggilan)", xlab = "Waktu Antar Panggilan (Menit)", col = "red")
