Simulasi Variabel Random
Febriana Dwi Rahayu
2026-03-02
Distribusi Diskrit
set.seed(123)
n_simulasi <- 1000
lambda_kendaraan <- 15
poisson_data <- rpois(n_simulasi, lambda_kendaraan)
hist(poisson_data, breaks = 25, main = "histogram jumlah Kendaraan per 5 menit", xlab = "jumlah Kendaraan",
col = "floralwhite")
mean(poisson_data)## [1] 15.01sum(poisson_data > 20)/n_simulasi## [1] 0.082Distribusi Kontinu
set.seed(123)
n <- 1000
rate <- 1/5
exp_data <- rexp(n, rate)
hist(exp_data, breaks = 30, main = "histogram waktu tunggu pelanggan", xlab = "Waktu (menit)", col = "mistyrose2")
mean(exp_data)## [1] 5.149896sum(exp_data > 10)/n## [1] 0.137Distribusi Kontinu : Distribusi Normal
set.seed(123)
n_botol_uji <- 500
mean_volume <- 500
sd_volume <- 5
volume_data <- rnorm(n_botol_uji, mean = mean_volume, sd = sd_volume)
volume_data## [1] 497.1976 498.8491 507.7935 500.3525 500.6464 508.5753 502.3046 493.6747
## [9] 496.5657 497.7717 506.1204 501.7991 502.0039 500.5534 497.2208 508.9346
## [17] 502.4893 490.1669 503.5068 497.6360 494.6609 498.9101 494.8700 496.3555
## [25] 496.8748 491.5665 504.1889 500.7669 494.3093 506.2691 502.1323 498.5246
## [33] 504.4756 504.3907 504.1079 503.4432 502.7696 499.6904 498.4702 498.0976
## [41] 496.5265 498.9604 493.6730 510.8448 506.0398 494.3845 497.9856 497.6667
## [49] 503.8998 499.5832 501.2666 499.8573 499.7856 506.8430 498.8711 507.5824
## [57] 492.2562 502.9231 500.6193 501.0797 501.8982 497.4884 498.3340 494.9071
## [65] 494.6410 501.5176 502.2410 500.2650 504.6113 510.2504 497.5448 488.4542
## [73] 505.0287 496.4540 496.5600 505.1279 498.5761 493.8964 500.9065 499.3055
## [81] 500.0288 501.9264 498.1467 503.2219 498.8976 501.6589 505.4842 502.1759
## [89] 498.3703 505.7440 504.9675 502.7420 501.1937 496.8605 506.8033 496.9987
## [97] 510.9367 507.6631 498.8215 494.8679 496.4480 501.2844 498.7665 498.2623
## [105] 495.2419 499.7749 496.0755 491.6603 498.0989 504.5950 497.1233 503.0398
## [113] 491.9106 499.7222 502.5970 501.5058 500.5284 496.7965 495.7515 494.8794
## [121] 500.5882 495.2626 497.5472 498.7195 509.2193 496.7403 501.1769 500.3898
## [129] 495.1907 499.6435 507.2228 502.2575 500.2062 497.8875 489.7338 505.6567
## [137] 492.6968 503.6997 509.5455 492.7805 503.5089 498.6890 492.1393 492.4267
## [145] 491.9923 497.3455 492.6912 503.4396 510.5005 493.5648 503.9387 503.8452
## [153] 501.6610 494.9581 499.4027 498.5980 502.8149 498.1378 504.8849 498.1271
## [161] 505.2636 494.7541 493.6992 516.2052 497.9157 501.4911 503.1828 497.5811
## [169] 502.5843 501.8448 498.9231 500.3265 499.8297 510.6423 496.2933 494.5200
## [177] 500.1889 501.5524 502.1826 497.7082 494.6834 506.3159 498.2517 495.6724
## [185] 498.8186 499.0141 505.5496 500.4237 503.7703 497.5035 501.0722 498.3766
## [193] 500.4729 495.5232 493.4460 509.9861 503.0035 493.7436 496.9442 494.0726
## [201] 510.9941 506.5621 498.6743 502.7160 497.9283 497.6188 496.0570 497.0269
## [209] 508.2545 499.7299 500.5962 501.2184 506.1624 497.4197 495.0375 508.3785
## [217] 497.7942 496.3847 493.8186 493.5764 497.1301 503.0899 505.5492 503.5379
## [225] 498.1817 500.2987 496.4770 496.4139 504.4233 494.9220 509.7765 499.5484
## [233] 501.0727 496.3074 497.1281 493.4149 499.0854 502.0949 501.6215 496.0923
## [241] 496.0569 497.4890 507.4803 494.3135 499.1047 509.5118 499.4951 493.2008
## [249] 496.6762 502.4273 498.1220 497.1906 498.2804 500.4525 507.9925 499.5572
## [257] 505.4040 503.1538 499.4318 492.3355 497.3944 497.5506 500.2358 506.5010
## [265] 511.4654 507.7379 499.3342 491.2174 498.0561 500.4460 504.2251 504.8126
## [273] 503.4215 493.0236 504.2482 497.7672 500.8740 500.3728 502.1408 500.1234
## [281] 491.6626 503.6825 501.9301 498.6717 500.5907 500.6702 501.1051 508.2042
## [289] 498.9047 500.8403 505.8419 505.2709 505.7263 497.1127 510.0124 500.3335
## [297] 509.3343 493.2455 500.1049 506.2496 496.4238 496.2366 495.3073 494.7374
## [305] 497.8142 501.6559 489.9289 501.0599 506.1834 510.1879 506.5059 503.7839
## [313] 491.3663 496.9925 498.2398 503.5176 499.4716 493.7068 508.4222 504.5570
## [321] 501.1872 506.0905 493.3061 503.3041 497.3854 503.4187 499.6959 503.1648
## [329] 506.6776 500.0365 505.0878 494.0578 496.3920 507.5961 501.8869 489.7389
## [337] 493.1798 498.9961 504.3289 499.4906 503.1209 504.7950 508.3553 500.2801
## [345] 499.7401 491.2338 500.4966 497.1407 495.1300 499.1005 505.0747 490.0363
## [353] 497.8636 500.5832 495.5340 501.6695 502.0571 499.8348 487.6705 512.8573
## [361] 498.9735 503.2560 501.3688 505.1234 504.0883 498.9510 501.8908 495.2730
## [369] 504.2846 497.6948 512.0839 491.7448 497.6801 504.1269 502.5507 497.0526
## [377] 495.0161 500.7224 499.9285 491.0486 500.1728 500.9512 500.8736 494.7249
## [385] 502.3807 506.8929 502.2812 494.3221 497.8218 501.7305 496.7648 489.2118
## [393] 504.4213 495.8526 497.1322 507.5195 496.1293 504.2287 493.6966 498.2273
## [401] 499.6322 494.1567 496.8263 499.8558 503.3535 491.7473 498.2512 503.7820
## [409] 497.3060 501.1365 502.4611 501.3392 503.2663 499.3865 497.9316 486.7843
## [417] 499.5353 502.1514 502.6770 497.2236 508.8975 501.4321 500.6316 506.3613
## [425] 496.4077 497.7483 511.9873 500.0556 508.1678 492.8075 499.0474 501.8921
## [433] 501.5002 494.9718 500.0963 494.6129 503.5635 505.4239 488.8751 506.1785
## [441] 493.7948 502.2738 503.2995 499.0006 496.7744 500.8266 502.1941 504.4165
## [449] 489.7383 491.8181 507.1520 505.2331 502.1764 503.5759 504.5859 486.6954
## [457] 505.5514 497.5751 501.1531 498.5242 504.3598 498.2576 502.5925 498.0466
## [465] 494.5361 506.0501 503.7045 508.6213 500.3258 505.6250 509.8771 498.5926
## [473] 493.3852 498.8032 498.9298 500.7584 508.5615 498.3693 501.8650 498.8616
## [481] 500.1023 501.5703 506.6411 500.6066 503.5642 503.8943 504.5739 497.1280
## [489] 508.1344 498.0952 499.4711 507.0203 506.4704 494.5500 495.6346 493.2096
## [497] 500.9092 500.8242 501.8206 502.7608hist(volume_data, breaks = 30, main = "histogram volume isi botol", xlab = "volume (ml)", col = "darkgrey")
mean(volume_data)## [1] 500.173sum(volume_data < 490)/n_botol_uji## [1] 0.02Simulasi ini memodelkan volume isi botol minuman menggunakan distribusi mormal dengan rata-rata 500 ml dan standar deviasi 5 ml. Rata-rata hasil simulasi sebesar 500.173 ml, yang sangat mendekati nilai mean teoritis, sehingga menunjukkan bahwa data mengikuti asumsi distribusi yang digunakan. Probabilitas volume kurang dari 490 ml sebesar 0,02 atau 2%, yang berarti hanya sebagian kecil botol yang berada di bawah batas tersebut.
Distribusi Diskrit : Distribusi Poisson
set.seed(123)
n_simulasi <- 1000
lambda_pasien <- 6
pasien_data <- rpois(n_simulasi, lambda_pasien)
pasien_data## [1] 5 8 5 9 10 2 6 9 6 6 10 6 7 6 3 9 4 2 5 10 9 7 7 13
## [25] 7 7 6 6 5 3 11 9 7 8 2 6 8 4 5 4 3 5 5 5 4 3 4 6
## [49] 4 9 2 5 8 3 6 4 3 8 9 5 7 3 5 4 8 6 8 8 8 5 8 7
## [73] 7 0 6 4 5 7 5 3 4 7 5 8 3 5 12 9 9 4 3 7 5 7 5 4
## [97] 8 3 6 6 6 5 6 10 6 9 9 7 5 3 10 5 2 10 7 3 6 10 6 5
## [121] 7 5 5 4 5 12 4 3 3 7 7 9 7 7 6 7 8 8 11 5 5 5 1 4
## [145] 8 4 4 3 4 7 9 6 5 4 3 5 6 4 5 4 6 5 7 5 5 6 7 4
## [169] 5 4 7 4 9 8 7 7 5 6 9 6 8 5 7 4 6 6 4 6 9 9 4 5
## [193] 12 7 10 6 5 7 4 6 4 11 6 6 5 9 5 5 4 4 6 4 4 7 2 7
## [217] 5 5 8 10 4 11 7 7 2 5 6 6 7 9 7 5 6 2 4 5 4 8 4 8
## [241] 6 7 4 7 5 7 5 11 11 7 4 4 6 4 6 8 4 5 6 9 10 9 7 10
## [265] 6 6 5 5 2 6 9 1 3 4 8 7 11 6 3 7 8 3 5 4 2 5 3 4
## [289] 2 7 5 3 3 9 8 8 12 3 3 8 8 1 8 7 7 6 4 1 6 6 5 6
## [313] 7 2 5 8 8 4 5 9 9 5 3 7 3 2 15 2 5 9 7 5 7 8 5 6
## [337] 7 7 7 11 5 3 6 4 6 5 12 5 4 7 3 11 6 4 7 12 7 5 5 8
## [361] 3 4 9 5 5 8 4 2 5 6 5 5 9 6 6 11 8 4 5 11 6 8 5 8
## [385] 6 9 4 4 3 4 11 5 7 8 3 4 4 3 3 13 12 3 9 6 5 6 7 3
## [409] 5 7 5 8 4 6 4 4 10 5 6 2 6 7 6 5 9 7 5 5 4 9 10 6
## [433] 5 14 4 7 3 6 3 4 4 6 7 4 9 7 8 3 5 7 6 5 4 2 4 9
## [457] 8 8 4 3 11 5 6 4 6 4 4 7 4 8 3 8 5 8 7 5 7 0 4 7
## [481] 4 8 5 7 10 3 3 7 5 8 11 3 6 7 3 13 4 2 7 8 5 5 5 3
## [505] 5 4 6 6 10 5 6 3 9 5 7 4 6 8 3 8 5 5 5 2 6 7 9 2
## [529] 12 5 10 7 6 8 2 7 5 8 6 4 8 3 8 4 8 11 3 9 8 5 5 4
## [553] 6 9 6 6 7 6 6 1 2 10 8 4 7 7 5 8 6 9 6 9 6 5 10 7
## [577] 5 2 6 6 9 8 9 5 9 4 4 7 11 6 6 2 11 3 3 9 6 5 9 2
## [601] 4 7 4 5 4 8 3 8 5 5 7 3 2 13 6 8 9 8 11 2 9 9 8 5
## [625] 2 5 4 9 5 5 8 8 6 7 3 4 10 8 8 5 6 8 9 5 3 7 8 3
## [649] 5 7 8 10 6 6 7 9 9 2 6 5 8 8 3 7 4 3 10 4 7 4 2 6
## [673] 3 4 5 6 8 4 6 6 7 7 8 9 10 6 6 4 6 4 2 7 6 3 4 6
## [697] 4 3 5 5 8 4 2 9 5 7 6 5 4 5 7 6 7 7 6 5 1 1 13 3
## [721] 5 7 7 9 7 8 9 7 8 2 5 9 7 10 4 5 8 12 5 0 13 3 2 6
## [745] 5 6 8 3 7 10 4 4 4 3 6 6 6 9 2 4 6 4 6 6 6 3 3 5
## [769] 7 7 9 8 7 8 3 4 5 5 7 8 4 8 1 7 8 6 4 2 4 9 10 6
## [793] 4 6 8 5 3 4 5 4 6 5 3 2 4 11 6 6 8 7 2 7 5 9 8 3
## [817] 5 3 6 6 7 5 6 12 7 3 6 2 5 7 1 8 6 7 7 6 7 7 5 3
## [841] 11 7 7 3 6 4 9 1 4 3 5 7 13 7 6 5 10 3 3 9 5 2 7 6
## [865] 7 4 4 3 6 6 3 4 8 6 9 7 1 7 9 7 3 10 7 3 8 10 5 5
## [889] 4 4 6 8 7 6 8 8 2 5 2 8 10 6 9 6 7 6 8 9 8 3 1 2
## [913] 9 6 5 11 6 6 5 5 8 2 5 9 7 7 5 6 3 8 9 4 8 6 11 4
## [937] 6 9 9 2 11 6 5 5 3 4 5 5 5 5 6 4 10 2 5 11 7 2 5 5
## [961] 6 6 7 3 9 6 6 3 8 6 8 2 8 4 4 7 10 1 5 5 6 7 10 7
## [985] 9 8 3 4 4 5 3 4 6 5 6 8 7 5 7 3hist(pasien_data, breaks = 15, main = "histogram jumlah pasien DBD per minggu", xlab = "jumlah pasien", col = "bisque1")
mean(pasien_data)## [1] 5.967sum(pasien_data > 10)/n_simulasi## [1] 0.043Simulasi ini memodelkan jumlah pasien DBD yang datang ke puskesmas setiap minggu menggunakan distribusi Poisson dengan parameter λ = 6. Rata-rata hasil simulasi sebesar 5,967, yang sangat mendekati nilai lambda (6), sehingga model yang digunakan sudah sesuai dengan asumsi rata-rata kejadian. Probabilitas jumlah pasien lebih dari 10 sebesar 0,043 atau 4,3%. Hal ini menunjukkan bahwa kejadian lonjakan kasus tergolong jarang terjadi, namun tetap memiliki kemungkinan muncul dalam beberapa minggu tertentu.