Simulasi Variabel Random
Aisyah Kurnia Fitri
2026-03-02
Simulasi Sederhana: Variabel Random Uniform
# Simulasi 1000 variabel random dari distribusi uniform
set.seed(123) # Set seed untuk reproducibility
n <- 1000
uniform_data <- runif(n, min = 0, max = 1)
# Plot histogram
hist(uniform_data, breaks = 30, main = "Histogram Distribusi Uniform", xlab = "Nilai", col = "lightblue")
# Simulasi Distribusi Diskrit: Distribusi Binomial
# Simulasi 1000 variabel random dari distribusi binomial
n_trials <- 10 # Jumlah percobaan
p_success <- 0.5 # Probabilitas sukses
binomial_data <- rbinom(n, size = n_trials, prob = p_success)
# Plot histogram
hist(binomial_data, breaks = 30, main = "Histogram Distribusi Binomial", xlab = "Jumlah Sukses", col = "lightgreen")
# Simulasi Distribusi Kontinu: Distribusi Normal
# Simulasi 1000 variabel random dari distribusi normal
mu <- 0 # Mean
sigma <- 1 # Standar deviasi
normal_data <- rnorm(n, mean = mu, sd = sigma)
# Plot histogram
hist(normal_data, breaks = 30, main = "Histogram Distribusi Normal", xlab = "Nilai", col = "lightpink")
# Distribusi Poisson (Diskrit)
lambda <- 3 # Parameter lambda
poisson_data <- rpois(n, lambda)
hist(poisson_data, breaks = 30, main = "Histogram Distribusi Poisson", xlab = "Jumlah Kejadian", col = "lightyellow")
# Distribusi Eksponensial (Kontinu)
rate <- 1 # Parameter rate
exp_data <- rexp(n, rate)
hist(exp_data, breaks = 30, main = "Histogram Distribusi Eksponensial", xlab = "Nilai", col = "lightcoral")
# Latihan Studi Kasus # Studi Kasus 1: Simulasi Pendapatan Bulanan
# Simulasi pendapatan bulanan
set.seed(123)
n_employees <- 500
mean_income <- 10000000
sd_income <- 500000
income_data <- rnorm(n_employees, mean = mean_income, sd = sd_income)
income_data## [1] 9719762 9884911 10779354 10035254 10064644 10857532 10230458 9367469
## [9] 9656574 9777169 10612041 10179907 10200386 10055341 9722079 10893457
## [17] 10248925 9016691 10350678 9763604 9466088 9891013 9486998 9635554
## [25] 9687480 9156653 10418894 10076687 9430932 10626907 10213232 9852464
## [33] 10447563 10439067 10410791 10344320 10276959 9969044 9847019 9809764
## [41] 9652647 9896041 9367302 11084478 10603981 9438446 9798558 9766672
## [49] 10389983 9958315 10126659 9985727 9978565 10684301 9887115 10758235
## [57] 9225624 10292307 10061927 10107971 10189820 9748838 9833396 9490712
## [65] 9464104 10151764 10224105 10026502 10461134 11025042 9754484 8845416
## [73] 10502869 9645400 9655996 10512786 9857613 9389641 10090652 9930554
## [81] 10002882 10192640 9814670 10322188 9889757 10165891 10548420 10217591
## [89] 9837034 10574404 10496752 10274198 10119366 9686047 10680326 9699870
## [97] 11093666 10766305 9882150 9486790 9644797 10128442 9876654 9826229
## [105] 9524191 9977486 9607548 9166029 9809887 10459498 9712327 10303982
## [113] 9191059 9972219 10259704 10150577 10052838 9679647 9575148 9487936
## [121] 10058823 9526263 9754721 9871954 10921931 9674025 10117693 10038980
## [129] 9519072 9964346 10722275 10225752 10020616 9788752 8973376 10565669
## [137] 9269680 10369974 10954552 9278053 10350892 9868901 9213928 9242666
## [145] 9199232 9734547 9269122 10343958 11050054 9356485 10393869 10384521
## [153] 10166101 9495812 9940274 9859802 10281495 9813781 10488487 9812710
## [161] 10526356 9475411 9369922 11620520 9791571 10149114 10318285 9758110
## [169] 10258431 10184482 9892310 10032647 9982966 11064226 9629332 9452002
## [177] 10018894 10155240 10218262 9770817 9468337 10631593 9825175 9567244
## [185] 9881860 9901412 10554960 10042369 10377027 9750354 10107223 9837657
## [193] 10047292 9552318 9344599 10998607 10300354 9374364 9694417 9407260
## [201] 11099405 10656206 9867427 10271597 9792830 9761877 9605699 9702691
## [209] 10825454 9972986 10059623 10121844 10616238 9741968 9503746 10837848
## [217] 9779418 9638467 9381863 9357642 9713013 10308993 10554924 10353794
## [225] 9818171 10029875 9647702 9641391 10442325 9492204 10977647 9954840
## [233] 10107269 9630736 9712806 9341492 9908537 10209491 10162152 9609232
## [241] 9605689 9748901 10748030 9431348 9910474 10951181 9949513 9320080
## [249] 9667615 10242730 9812199 9719062 9828041 10045248 10799254 9955717
## [257] 10540400 10315377 9943180 9233549 9739441 9755065 10023577 10650099
## [265] 11146539 10773791 9933425 9121736 9805610 10044604 10422507 10481264
## [273] 10342155 9302363 10424822 9776721 10087401 10037276 10214083 10012337
## [281] 9166262 10368248 10193013 9867174 10059072 10067019 10110510 10820423
## [289] 9890475 10084033 10584192 10527091 10572632 9711266 11001241 10033350
## [297] 10933426 9324549 10010492 10624957 9642379 9623656 9530731 9473743
## [305] 9781420 10165590 8992895 10105990 10618338 11018787 10650588 10378387
## [313] 9136635 9699247 9823977 10351762 9947164 9370676 10842218 10455696
## [321] 10118715 10609054 9330613 10330410 9738544 10341873 9969589 10316480
## [329] 10667759 10003645 10508779 9405783 9639198 10759609 10188694 8973889
## [337] 9317981 9899609 10432890 9949058 10312094 10479503 10835527 10028008
## [345] 9974009 9123381 10049664 9714075 9512995 9910047 10507472 9003626
## [353] 9786360 10058319 9553396 10166951 10205715 9983482 8767051 11285729
## [361] 9897350 10325597 10136883 10512337 10408830 9895103 10189084 9527296
## [369] 10428462 9769481 11208387 9174476 9768006 10412690 10255066 9705259
## [377] 9501610 10072238 9992846 9104859 10017276 10095115 10087363 9472491
## [385] 10238067 10689285 10228118 9432206 9782177 10173052 9676477 8921177
## [393] 10442125 9585261 9713220 10751950 9612928 10422866 9369659 9822729
## [401] 9963222 9415674 9682626 9985579 10335348 9174727 9825123 10378203
## [409] 9730595 10113646 10246114 10133918 10326629 9938646 9793162 8678426
## [417] 9953529 10215142 10267699 9722361 10889751 10143212 10063158 10636133
## [425] 9640767 9774831 11198726 10005565 10816784 9280747 9904742 10189212
## [433] 10150019 9497182 10009630 9461290 10356352 10542388 8887506 10617847
## [441] 9379478 10227385 10329951 9900055 9677443 10082661 10219409 10441651
## [449] 8973832 9181810 10715201 10523314 10217644 10357589 10458587 8669539
## [457] 10555139 9757506 10115308 9852421 10435982 9825764 10259252 9804658
## [465] 9453606 10605005 10370450 10862131 10032577 10562501 10987710 9859259
## [473] 9338524 9880324 9892979 10075840 10856152 9836928 10186502 9886158
## [481] 10010225 10157029 10664107 10060659 10356421 10389430 10457387 9712803
## [489] 10813441 9809522 9947108 10702025 10647042 9455004 9563464 9320960
## [497] 10090924 10082420 10182057 10276079# 1. Rata-rata pendapatan simulasi
mean_simulated <- mean(income_data)
cat("Rata-rata pendapatan simulasi:", mean_simulated, "\n")## Rata-rata pendapatan simulasi: 10017295# 2. Probabilitas pendapatan di atas Rp 12.000.000
prob_above_12m <- sum(income_data > 12000000) / n_employees
cat("Probabilitas pendapatan di atas Rp 12.000.000:", prob_above_12m, "\n")## Probabilitas pendapatan di atas Rp 12.000.000: 0summary(income_data)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 8669539 9712684 10010359 10017295 10342606 11620520Studi Kasus 2: Simulasi Jumlah Pelanggan
# Simulasi jumlah pelanggan
set.seed(123)
n_days <- 30
lambda_customers <- 50
customers_data <- rpois(n_days, lambda_customers)
customers_data## [1] 46 58 38 50 62 53 41 37 58 52 52 50 46 59 55 49 44 42 47 44 57 48 41 41 47
## [26] 47 49 56 48 52# 1. Rata-rata jumlah pelanggan simulasi
mean_customers <- mean(customers_data)
cat("Rata-rata jumlah pelanggan simulasi:", mean_customers, "\n")## Rata-rata jumlah pelanggan simulasi: 48.96667# 2. Probabilitas jumlah pelanggan lebih dari 60
prob_above_60 <- sum(customers_data > 60) / n_days
cat("Probabilitas jumlah pelanggan lebih dari 60:", prob_above_60, "\n")## Probabilitas jumlah pelanggan lebih dari 60: 0.03333333Tugas Praktikum 3
1. Buat simulasi untuk distribusi diskrit dan distribusi kontinu.
Diskrit - Geometrik
# Simulasi distribusi geometrik
set.seed(123)
n <- 1000
p <- 0.3 # probabilitas sukses
geo_data <- rgeom(n, prob = p)
# Histogram
hist(geo_data,
breaks = 30,
main = "Histogram Distribusi Geometrik",
xlab = "Jumlah Percobaan hingga Sukses",
col = "lightblue")
# Kontinu - Gamma
# Simulasi distribusi gamma
set.seed(123)
shape <- 2
rate <- 0.5
gamma_data <- rgamma(n, shape = shape, rate = rate)
# Histogram
hist(gamma_data,
breaks = 30,
main = "Histogram Distribusi Gamma",
xlab = "Waktu Tunggu",
col = "lightgreen")
2. Buat studi kasus sendiri yang melibatkan simulasi variabel random dari distribusi yang telah dipelajari.
Studi Kasus: Simulasi Waktu Tunggu Mahasiswa di Kantin
# Simulasi Data
set.seed(123)
n_students <- 200
rate_wait <- 1/5 # rata-rata 5 menit
waiting_time <- rexp(n_students, rate = rate_wait)
# Tampilkan ringkasan
summary(waiting_time)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.02184 1.58985 3.85975 5.03617 7.12369 36.05504# Rata-rata waktu tunggu
mean_wait <- mean(waiting_time)
cat("Rata-rata waktu tunggu:", mean_wait, "menit\n")## Rata-rata waktu tunggu: 5.036166 menit# Probabilitas menunggu lebih dari 10 menit
prob_wait_10 <- sum(waiting_time > 10) / n_students
cat("Probabilitas menunggu > 10 menit:", prob_wait_10, "\n")## Probabilitas menunggu > 10 menit: 0.1# Visualisasi
hist(waiting_time,
breaks = 30,
main = "Histogram Waktu Tunggu Mahasiswa",
xlab = "Menit",
col = "lightcoral")