Komstat per 3

library(ggplot2)

## Warning: package 'ggplot2' was built under R version 4.5.3

library(reshape2)

## Warning: package 'reshape2' was built under R version 4.5.3

data <- datasets::mtcars
data_mtcars <- data[, c("mpg", "disp", "hp", "wt", "qsec")]

# Matrix korelasi
cor_mtcars <- cor(data_mtcars)
cor_mtcars

##             mpg       disp         hp         wt       qsec
## mpg   1.0000000 -0.8475514 -0.7761684 -0.8676594  0.4186840
## disp -0.8475514  1.0000000  0.7909486  0.8879799 -0.4336979
## hp   -0.7761684  0.7909486  1.0000000  0.6587479 -0.7082234
## wt   -0.8676594  0.8879799  0.6587479  1.0000000 -0.1747159
## qsec  0.4186840 -0.4336979 -0.7082234 -0.1747159  1.0000000

# Heatmap
data_cor <- melt(cor_mtcars)
ggplot(data_cor, aes(Var1, Var2, fill = value)) +
  geom_tile(color = "black") +
  geom_text(aes(label = round(value, 2)), color = "black") +
  scale_fill_gradient2(
    low = "red",
    high = "green",
    mid = "yellow",
    midpoint = 0,
    limit = c(-1, 1),
    name = "Korelasi"
  ) +
  theme_minimal() +
  labs(
    title = "Heatmap Dataset mtcars",
    x = "Variabel 1",
    y = "Variabel 2"
  ) +
  theme(
    plot.title = element_text(hjust = 0.5),
    axis.text.x = element_text(hjust = 0.5)
  )

bern<-function(x,p){p^x*(1-p)^(1-x)}
bern(1,3/6)

## [1] 0.5

cmfbinom <- function(k, n, p) {
  # Validasi input
  if (k < 0 || n < 0 || p < 0 || p > 1) {
    stop("input tidak valid")
  }
  
  # Inisialisasi CMF
  cmf <- 0
  # Menghitung CMF
  for (x in 0:k) {
    prob <- choose(n, x) * (p^x) * ((1 - p)^(n - x))
    cmf <- cmf + prob
  }
  return(cmf)
}

# Peluang paling sedikit 2 orang sembuh = 1 - P(X <= 1)
Peluang <- 1 - cmfbinom(1, 12, 0.2)
Peluang

## [1] 0.7251221

# Poisson CMF
cmfpois <- function(x, lambda) {
  # Validasi input
  if (lambda <= 0) {
    stop("Lambda Harus Bernilai > 0")
  }
  if (x < 0) {
    return(0)
  }
  
  cmf <- 0
  for (k in 0:x) {
    prob <- (exp(-lambda) * (lambda^k)) / factorial(k)
    cmf <- cmf + prob
  }
  return(cmf)
}

# Hitung peluang
peluang2 <- cmfpois(10, 2) - cmfpois(0, 2)
peluang2

## [1] 0.8646564

#Geometr
geo<-function(x,p){p*(1-p)^(x-1)}
geo(5,0.3)

## [1] 0.07203

hyper <- function(x, N, n, k) ((((factorial(k)) / (factorial(k - x) * factorial(x))) * (factorial(N - k) / (factorial((N - k) - (n - x)) * factorial(n - x)))) / (factorial(N) / (factorial(N - n) * factorial(n))))
hyper(2, 100, 10, 5)

## [1] 0.07021881