Pemodelan Statistika dan Simulasi_Tugas Praktikum 3

set.seed(123)
n <- 1000

#Distribusi Diskrit (Binomial)

size <- 20
p <- 0.3
binomial_data <- rbinom(n, size = size, prob = p)

hist(binomial_data, breaks = 30, main = "Histogram Distribusi Binomial", xlab = "Jumlah Sukses", col = "yellow")

#Distribusi Kontinu (Eksponensial)

rate <- 0.5  # Parameter rate
exp_data <- rexp(n, rate)
hist(exp_data, breaks = 30, main = "Histogram Distribusi Eksponensial", xlab = "Nilai", col = "grey")

#Simulasi

n_students <- 200
mean_score <- 80
sd_score <- 10
scores <- rnorm(n_students, mean = mean_score, sd = sd_score)

hist(scores,
     breaks = 20,
     main = "Simulasi Nilai Ujian Mahasiswa",
     xlab = "Nilai",
     col = "pink")

# Rata-rata nilai
mean(scores)

## [1] 80.10804

# Probabilitas lulus (misal lulus jika nilai >= 70)
prob_pass <- mean(scores >= 70)
prob_pass

## [1] 0.815

# Ringkasan statistik
summary(scores)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   56.48   72.46   79.14   80.11   87.40  106.66