Matriks Korelasi & Distribusi Peluang Diskrit

Matriks Korelasi

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")]

# Matriks 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 = "red") +
  geom_text(aes(label = round(value, 2)), color = "black") +
  scale_fill_gradient2(low = "pink", high = "lightgreen", mid = "lightyellow", 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))

Distribusi Bernoulli

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

## [1] 0.5

Distribusi Binomial

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

Distribusi Poisson

cmfpois <- function(x, lambda) {   
if (lambda <= 0) { 
  stop("Lambda Harus Bernilai > 0") 
} 
  if (x < 0) {     
    return(0) 
  }      
  cmf <- 0   
  for (k in 0:x) { 
    cmf <- cmf + (exp(-lambda) * (lambda^k) / factorial(k)) 
  } 
  return(cmf) 
} 
Peluang2 <- cmfpois(10, 2) - cmfpois(0, 2) 
Peluang2

## [1] 0.8646564

Distribusi Geometrik

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

## [1] 0.07203

Distribusi Hipergeometrik

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

```