Praktikum Week 3
Desmiwa Azhar_2404010003
2026-02-27
1. Simulasi Distribusi Diskrit dan Kontinu
a. Distribusi Diskrit (Binomial): Simulasi Produksi Barang Cacat
Studi Kasus : Sebuah mesin memproduksi barang dengan probabilitas cacat 20%. Dalam 15 produksi, ingin diketahui jumlah barang cacat.
set.seed(123)
n <- 1000
ukuran_produksi <- 15
peluang_cacat <- 0.2
binom_data <- rbinom(n, size = ukuran_produksi, prob = peluang_cacat)
binom_data## [1] 2 4 3 5 6 1 3 5 3 3 6 3 4 3 1 5 2 1 2 6 5 4 3 7 4 4 3 3 2 1 6 5 4 4 0 3 4
## [38] 2 2 2 1 3 3 2 1 1 2 3 2 5 1 3 4 1 3 2 1 4 5 2 4 1 2 2 4 3 4 4 4 3 4 3 4 0
## [75] 3 2 2 3 2 1 2 4 3 4 1 3 7 5 5 2 1 4 2 4 2 2 4 1 3 3 3 2 3 6 3 5 5 3 3 1 5
## [112] 2 1 6 4 1 3 6 3 3 3 2 2 2 2 7 1 1 1 4 3 5 4 4 3 4 4 4 6 3 2 3 0 2 5 2 2 1
## [149] 2 4 5 3 2 2 1 2 3 2 3 2 3 2 4 2 2 3 4 2 3 2 3 2 5 4 4 3 2 3 5 3 5 2 4 2 3
## [186] 3 2 3 5 5 2 2 7 3 5 3 3 4 1 3 2 6 3 3 3 5 2 2 2 2 3 2 2 4 1 4 2 3 4 5 2 6
## [223] 4 4 1 2 3 3 4 5 3 3 3 1 2 2 2 4 1 4 3 4 2 3 2 4 3 6 6 4 2 2 3 2 3 4 2 3 3
## [260] 5 5 5 4 6 3 3 2 2 0 3 5 0 1 1 4 4 6 3 1 4 4 1 2 2 1 2 1 2 1 4 2 1 1 5 4 4
## [297] 7 1 1 4 4 0 4 4 3 3 1 0 3 3 2 3 4 1 2 4 4 2 2 5 5 2 1 4 1 0 9 0 2 5 3 2 4
## [334] 4 2 3 4 3 3 6 3 1 3 2 3 2 7 2 2 3 1 6 3 1 3 7 4 3 2 4 1 2 5 2 2 4 2 0 3 3
## [371] 3 2 5 3 3 6 4 2 2 6 3 4 2 4 3 5 2 2 1 2 6 2 4 4 1 2 2 1 1 7 7 1 5 3 2 3 4
## [408] 1 2 4 2 4 2 3 2 2 6 2 3 0 3 3 3 2 5 3 2 2 1 5 6 3 2 8 2 3 1 3 1 1 2 3 4 1
## [445] 5 4 4 1 2 4 3 2 2 1 2 5 4 4 1 1 6 3 3 1 3 2 2 4 2 4 1 4 3 4 4 3 3 0 2 4 2
## [482] 4 2 4 5 1 1 4 3 4 6 1 3 4 1 7 2 1 4 4 2 2 2 1 2 2 3 3 6 2 3 1 5 2 4 2 3 4
## [519] 1 4 2 2 2 1 3 4 5 0 7 2 6 4 3 4 1 4 2 4 3 2 4 1 4 2 4 6 1 5 4 2 2 2 3 5 3
## [556] 3 4 3 3 0 1 5 4 2 4 4 2 4 3 5 3 5 3 3 6 4 3 0 3 3 5 4 5 2 5 1 2 4 6 3 3 1
## [593] 6 1 1 5 3 2 5 0 2 4 2 2 2 4 1 4 2 2 3 1 0 7 3 4 5 4 6 1 5 5 4 2 1 2 2 5 2
## [630] 2 4 5 3 4 1 2 6 4 4 3 3 4 5 2 1 3 4 1 2 3 4 5 3 3 4 5 5 1 3 2 5 4 1 4 2 1
## [667] 5 1 3 2 0 3 1 2 3 3 4 2 3 3 4 4 4 5 6 3 3 2 3 2 1 3 3 1 2 3 1 1 3 2 5 2 0
## [704] 5 2 3 3 2 2 3 3 3 4 4 3 2 0 0 7 1 3 4 4 5 3 4 5 3 4 0 3 5 3 5 2 2 4 7 2 0
## [741] 7 1 1 3 2 3 4 1 4 6 2 2 1 1 3 3 3 5 1 2 3 2 3 3 3 1 1 3 4 4 5 4 4 4 1 2 2
## [778] 3 3 4 2 4 0 4 4 3 2 0 2 5 5 3 2 3 4 3 1 2 2 2 3 2 1 1 2 6 3 3 4 4 1 4 2 5
## [815] 4 1 2 1 3 3 4 2 3 7 4 1 3 1 2 4 0 4 3 4 4 3 4 4 2 1 6 4 3 1 3 2 5 0 2 1 2
## [852] 4 7 4 3 3 6 1 1 5 3 1 3 3 3 2 1 1 3 3 1 2 4 3 5 4 0 4 5 3 1 5 4 1 4 6 3 2
## [889] 2 2 3 4 4 3 4 4 0 2 1 4 5 3 5 3 4 3 4 5 4 1 0 1 5 3 2 6 3 3 2 2 4 1 2 5 4
## [926] 4 2 3 1 4 5 2 4 3 6 1 3 5 5 0 6 3 2 3 1 1 3 2 3 2 3 1 6 1 2 6 3 1 3 3 3 3
## [963] 3 1 5 3 3 1 4 3 4 1 4 2 2 3 6 0 2 3 3 4 5 3 5 4 1 1 2 3 1 2 3 3 3 4 3 2 4
## [1000] 1# Histogram
hist(binom_data, breaks = 30,
main = "Histogram Distribusi Binomial",
xlab = "Jumlah Barang Cacat",
col = "lightgreen")
# Rata-rata simulasi
mean_binom <- mean(binom_data)
cat("Rata-rata jumlah cacat:", mean_binom, "\n")## Rata-rata jumlah cacat: 2.977# Probabilitas cacat lebih dari 5
prob_more_5 <- sum(binom_data > 5) / n
cat("Probabilitas cacat > 5:", prob_more_5, "\n")## Probabilitas cacat > 5: 0.062Simulasi ini memodelkan jumlah barang cacat menggunakan distribusi binomial. Rata-rata simulasi mendekati nilai teoritis (n × p = 15 × 0.2 = 3) dan Probabilitas dihitung berdasarkan proporsi data simulasi yang melebihi 5.
b. Distribusi Kontinu (Normal): Simulasi berat paket
Studi kasus : Sebuah perusahaan ekspedisi akan mengirim beberapa paket. Paket yang dikirim memiliki rata-rata 2 kg dengan standar deviasi 0.3 kg.
set.seed(123)
n <- 1000
mean_berat <- 2
sd_berat <- 0.3
normal_data <- rnorm(n, mean = mean_berat, sd = sd_berat)
normal_data## [1] 1.831857 1.930947 2.467612 2.021153 2.038786 2.514519 2.138275 1.620482
## [9] 1.793944 1.866301 2.367225 2.107944 2.120231 2.033205 1.833248 2.536074
## [17] 2.149355 1.410015 2.210407 1.858163 1.679653 1.934608 1.692199 1.781333
## [25] 1.812488 1.493992 2.251336 2.046012 1.658559 2.376144 2.127939 1.911479
## [33] 2.268538 2.263440 2.246474 2.206592 2.166175 1.981426 1.908211 1.885859
## [41] 1.791588 1.937625 1.620381 2.650687 2.362389 1.663067 1.879135 1.860003
## [49] 2.233990 1.974989 2.075996 1.991436 1.987139 2.410581 1.932269 2.454941
## [57] 1.535374 2.175384 2.037156 2.064782 2.113892 1.849303 1.900038 1.694427
## [65] 1.678463 2.091059 2.134463 2.015901 2.276680 2.615025 1.852691 1.307249
## [73] 2.301722 1.787240 1.793597 2.307671 1.914568 1.633785 2.054391 1.958333
## [81] 2.001729 2.115584 1.888802 2.193313 1.933854 2.099535 2.329052 2.130554
## [89] 1.902221 2.344642 2.298051 2.164519 2.071620 1.811628 2.408196 1.819922
## [97] 2.656200 2.459783 1.929290 1.692074 1.786878 2.077065 1.925992 1.895737
## [105] 1.714514 1.986492 1.764529 1.499617 1.885932 2.275699 1.827396 2.182389
## [113] 1.514635 1.983331 2.155822 2.090346 2.031703 1.807788 1.745089 1.692761
## [121] 2.035294 1.715758 1.852833 1.923172 2.553159 1.804415 2.070616 2.023388
## [129] 1.711443 1.978608 2.433365 2.135451 2.012370 1.873251 1.384026 2.339401
## [137] 1.561808 2.221984 2.572731 1.566832 2.210535 1.921341 1.528357 1.545600
## [145] 1.519539 1.840728 1.561473 2.206375 2.630033 1.613891 2.236322 2.230713
## [153] 2.099661 1.697487 1.964164 1.915881 2.168897 1.888268 2.293092 1.887626
## [161] 2.315813 1.685247 1.621953 2.972312 1.874943 2.089468 2.190971 1.854866
## [169] 2.155059 2.110689 1.935386 2.019588 1.989780 2.638536 1.777599 1.671201
## [177] 2.011337 2.093144 2.130957 1.862490 1.681002 2.378956 1.895105 1.740346
## [185] 1.929116 1.940847 2.332976 2.025421 2.226216 1.850212 2.064334 1.902594
## [193] 2.028375 1.731391 1.606760 2.599164 2.180213 1.624619 1.816650 1.644356
## [201] 2.659643 2.393724 1.920456 2.162958 1.875698 1.857126 1.763419 1.821615
## [209] 2.495272 1.983792 2.035774 2.073106 2.369743 1.845181 1.702248 2.502709
## [217] 1.867651 1.783080 1.629118 1.614585 1.827808 2.185396 2.332954 2.212277
## [225] 1.890903 2.017925 1.788621 1.784835 2.265395 1.695322 2.586588 1.972904
## [233] 2.064362 1.778442 1.827683 1.604895 1.945122 2.125695 2.097291 1.765539
## [241] 1.763413 1.849340 2.448818 1.658809 1.946285 2.570709 1.969708 1.592048
## [249] 1.800569 2.145638 1.887319 1.831437 1.896825 2.027149 2.479553 1.973430
## [257] 2.324240 2.189226 1.965908 1.540129 1.843665 1.853039 2.014146 2.390060
## [265] 2.687924 2.464274 1.960055 1.473042 1.883366 2.026762 2.253504 2.288758
## [273] 2.205293 1.581418 2.254893 1.866033 2.052441 2.022365 2.128450 2.007402
## [281] 1.499757 2.220949 2.115808 1.920305 2.035443 2.040212 2.066306 2.492254
## [289] 1.934285 2.050420 2.350515 2.316254 2.343579 1.826760 2.600745 2.020010
## [297] 2.560056 1.594729 2.006295 2.374974 1.785427 1.774193 1.718438 1.684246
## [305] 1.868852 2.099354 1.395737 2.063594 2.371003 2.611272 2.390353 2.227032
## [313] 1.481981 1.819548 1.894386 2.211057 1.968299 1.622405 2.505331 2.273417
## [321] 2.071229 2.365433 1.598368 2.198246 1.843126 2.205124 1.981753 2.189888
## [329] 2.400655 2.002187 2.305268 1.643470 1.783519 2.455765 2.113216 1.384333
## [337] 1.590789 1.939766 2.259734 1.969435 2.187256 2.287702 2.501316 2.016805
## [345] 1.984405 1.474029 2.029798 1.828445 1.707797 1.946028 2.304483 1.402175
## [353] 1.871816 2.034991 1.732038 2.100171 2.123429 1.990089 1.260231 2.771437
## [361] 1.938410 2.195358 2.082130 2.307402 2.245298 1.937062 2.113450 1.716377
## [369] 2.257077 1.861688 2.725032 1.504685 1.860804 2.247614 2.153040 1.823156
## [377] 1.700966 2.043343 1.995708 1.462916 2.010365 2.057069 2.052418 1.683495
## [385] 2.142840 2.413571 2.136871 1.659323 1.869306 2.103831 1.805886 1.352706
## [393] 2.265275 1.751157 1.827932 2.451170 1.767757 2.253719 1.621795 1.893637
## [401] 1.977933 1.649405 1.809576 1.991348 2.201209 1.504836 1.895074 2.226922
## [409] 1.838357 2.068188 2.147669 2.080351 2.195977 1.963187 1.875897 1.207055
## [417] 1.972118 2.129085 2.160620 1.833416 2.533851 2.085927 2.037895 2.381680
## [425] 1.784460 1.864898 2.719236 2.003339 2.490071 1.568448 1.942845 2.113527
## [433] 2.090012 1.698309 2.005778 1.676774 2.213811 2.325433 1.332504 2.370708
## [441] 1.627687 2.136431 2.197971 1.940033 1.806466 2.049596 2.131646 2.264991
## [449] 1.384299 1.509086 2.429121 2.313989 2.130587 2.214554 2.275152 1.201723
## [457] 2.333083 1.854504 2.069185 1.911453 2.261589 1.895458 2.155551 1.882795
## [465] 1.672164 2.363003 2.222270 2.517279 2.019546 2.337501 2.592626 1.915555
## [473] 1.603115 1.928195 1.935788 2.045504 2.513691 1.902157 2.111901 1.931695
## [481] 2.006135 2.094217 2.398464 2.036396 2.213853 2.233658 2.274432 1.827682
## [489] 2.488064 1.885713 1.968265 2.421215 2.388225 1.673002 1.738079 1.592576
## [497] 2.054554 2.049452 2.109234 2.165647 1.819432 1.701890 2.308036 2.225318
## [505] 1.547250 1.971456 1.731216 1.378775 2.045036 1.976236 1.970789 2.064846
## [513] 2.264740 2.061679 1.815069 1.779560 1.960459 2.093005 1.688096 1.944707
## [521] 2.290180 1.967516 1.790474 1.917216 2.334395 2.165013 2.371003 2.041729
## [529] 2.123083 1.832463 2.181611 1.848100 1.573830 2.038398 2.583755 2.240274
## [537] 2.349576 2.107657 1.817433 1.939328 1.918026 1.859390 2.211250 1.640791
## [545] 2.259910 2.259246 1.640413 2.191848 2.729068 1.832835 2.253471 1.765339
## [553] 2.333213 2.074947 2.495575 1.562309 1.984611 1.841922 1.940821 1.811126
## [561] 1.749847 2.173617 1.673726 2.445209 1.644138 2.030324 2.159897 2.176021
## [569] 1.909476 2.023851 2.288379 1.563060 1.765478 2.096121 1.866565 2.411001
## [577] 2.201976 2.021650 1.547673 2.007830 1.905075 1.969296 1.645532 2.149597
## [585] 1.688313 1.932133 2.114428 1.764945 2.174897 1.605047 1.157068 2.139490
## [593] 2.252162 1.914246 2.151238 1.653225 1.961855 1.417544 2.354354 2.557973
## [601] 2.322204 1.991796 1.990001 1.545180 2.237116 1.936780 1.802977 1.576392
## [609] 1.910071 1.745282 1.880891 1.634720 2.506277 1.995199 2.322484 1.219490
## [617] 1.864041 1.797355 1.633122 2.463983 1.575415 2.095517 2.253931 2.053457
## [625] 1.737423 2.282350 2.051176 1.680951 1.583585 2.626015 1.796449 1.443329
## [633] 2.159978 2.093069 1.593850 1.417113 1.965109 2.341819 2.190837 1.852119
## [641] 1.749744 2.081320 2.047206 2.188914 1.881261 2.269806 1.750757 1.900837
## [649] 2.222244 2.296991 1.418449 2.032157 2.182634 1.564753 2.144188 1.751548
## [657] 2.306076 2.161545 2.230716 2.036216 2.259095 2.414154 2.589874 1.991481
## [665] 1.325285 2.009458 2.061668 1.953396 2.170487 2.303203 1.844605 1.911771
## [673] 2.119353 1.834933 2.027380 1.411488 1.664030 1.601673 1.743913 1.792009
## [681] 2.114692 2.294634 1.781785 1.700948 1.687493 1.875623 1.928291 2.145085
## [689] 1.903603 1.376453 1.972570 2.356156 2.357480 1.763311 1.535667 2.737418
## [697] 1.951273 1.970765 2.126172 1.515788 1.781534 1.537867 1.792072 2.035655
## [705] 1.590587 2.176995 2.086803 1.728735 2.067897 2.224424 2.318329 1.936146
## [713] 1.971909 1.973986 2.432439 2.337522 2.250320 1.913798 2.111972 2.120987
## [721] 1.687498 1.481509 2.192549 1.541207 2.000505 2.075074 2.169160 2.056828
## [729] 1.780144 2.295910 2.521590 2.264354 1.416905 2.419873 1.983183 2.157474
## [737] 2.186610 1.970994 1.977421 2.305747 2.213481 2.297079 2.714878 2.199325
## [745] 2.062214 1.336810 2.807514 1.855197 2.712420 2.112393 2.461529 1.967087
## [753] 2.153441 2.064187 1.944164 1.963882 2.303850 1.939563 1.388695 1.941233
## [761] 2.161937 2.184937 2.184970 1.492370 2.110623 2.290358 2.382974 1.932512
## [769] 1.903432 2.446351 1.499622 1.868951 2.137239 1.514668 2.083888 2.563359
## [777] 1.998782 1.916464 2.142474 1.916278 2.244020 2.271331 2.000807 1.646992
## [785] 1.604534 1.822101 2.239214 1.412538 1.434102 1.803866 2.118318 1.725930
## [793] 2.266025 2.100011 1.948808 2.245648 2.116510 1.866219 2.069334 2.194254
## [801] 2.106885 1.802597 2.256561 2.345881 2.082882 2.043231 1.977312 2.648425
## [809] 2.082895 1.952512 1.247625 1.530415 1.976698 2.061888 2.083062 2.246452
## [817] 1.941754 2.364377 1.723545 1.637467 1.631304 2.222689 1.975124 2.236945
## [825] 1.919688 1.822432 1.889494 1.444215 1.649115 1.567390 2.316297 1.820801
## [833] 2.236838 2.454947 1.942468 2.085164 1.474680 1.754399 2.016864 2.089726
## [841] 1.772181 2.805458 1.862483 2.019273 2.194938 1.992194 1.806930 2.313592
## [849] 2.484664 1.991092 2.168680 1.970776 2.304937 1.653150 2.696258 1.818941
## [857] 1.562345 1.894725 2.044013 2.487086 2.273363 2.042738 1.583155 1.740189
## [865] 1.951015 2.765908 1.441932 2.339316 1.841830 2.499797 1.658240 2.043087
## [873] 1.670135 2.271055 2.445134 2.585216 2.239280 2.552980 2.373927 1.960438
## [881] 2.143111 1.708402 1.944439 2.366289 2.162385 2.137207 1.688561 1.818646
## [889] 1.770618 2.118589 1.702848 2.168612 1.665075 2.548559 2.138177 1.789699
## [897] 2.072314 1.894264 2.111344 2.073060 1.695766 1.762606 2.089878 2.491716
## [905] 2.325385 1.812630 2.247777 1.985429 2.090394 2.078108 2.772635 1.644413
## [913] 2.030276 1.466007 2.176951 2.328983 2.433699 1.422456 2.123831 2.478011
## [921] 1.875795 1.936355 1.989039 2.109506 2.199548 2.395346 1.971354 2.058883
## [929] 2.746399 2.129330 2.056626 1.597327 2.000857 1.933602 1.996686 1.827375
## [937] 1.793955 1.783768 1.935649 2.410440 2.314726 1.892007 1.494225 1.746625
## [945] 1.862672 2.031091 1.801218 2.602004 1.918320 1.635817 1.957621 1.698387
## [953] 2.046847 2.070090 2.106676 1.513443 2.066213 2.093135 1.573667 2.286610
## [961] 2.235251 2.689886 2.047011 2.014020 2.028976 2.020930 1.445458 1.498662
## [969] 1.976738 1.825680 2.016421 1.366637 1.550391 1.669555 2.295817 1.670453
## [977] 1.760146 2.023962 1.903176 2.043925 2.691519 1.662619 1.908359 1.844972
## [985] 2.453719 1.769155 1.975374 2.236140 1.682423 2.496553 2.202729 1.677738
## [993] 2.136373 1.936008 2.093969 1.973007 2.321155 1.594670 1.843215 1.925243# Histogram
hist(normal_data, breaks = 30,
main = "Histogram Distribusi Normal",
xlab = "Berat Paket (kg)",
col = "lightpink"
)
# Rata-rata simulasi
mean_normal <- mean(normal_data)
cat("Rata-rata berat paket:", mean_normal, "\n")## Rata-rata berat paket: 2.004838# Probabilitas berat lebih dari 2.5 kg
prob_above_2_5 <- sum(normal_data > 2.5) / n
cat("Probabilitas berat > 2.5 kg:", prob_above_2_5, "\n")## Probabilitas berat > 2.5 kg: 0.052Simulasi ini menggunakan distribusi normal. Rata-rata simulasi mendekati mean teoritis (2 kg). Probabilitas dihitung dari proporsi data yang lebih dari 2.5 kg. Histogram berbentuk lonceng menandakan bahwa berdistribusi normal.
2. Simulasi Jumlah Pesanan Online per Hari
Sebuah toko online menerima rata-rata 80 pesanan per hari. Diasumsikan mengikuti distribusi Poisson.
# Simulasi jumlah pesanan online
set.seed(123)
n_days <- 30
lambda_pesanan <- 80
orders_data <- rpois(n_days, lambda_pesanan)
orders_data## [1] 74 90 64 81 95 84 68 64 90 83 83 80 75 91 87 79 72 70 77 73 89 78 69 69 77
## [26] 77 78 87 78 82# Histogram
hist(orders_data, breaks = 15,
main = "Histogram Jumlah Pesanan Online",
xlab = "Jumlah Pesanan",
col = "lightblue")
# Rata-rata simulasi
mean_orders <- mean(orders_data)
cat("Rata-rata pesanan per hari:", mean_orders, "\n")## Rata-rata pesanan per hari: 78.8# Probabilitas pesanan lebih dari 95
prob_above_95 <- sum(orders_data > 95) / n_days
cat("Probabilitas pesanan > 95:", prob_above_95, "\n")## Probabilitas pesanan > 95: 0Simulasi ini memodelkan jumlah pesanan harian menggunakan distribusi Poisson dengan diperoleh bahwa Rata-rata simulasi mendekati λ (80) dan Probabilitas dihitung berdasarkan proporsi hari dengan pesanan lebih dari 95.