prak3komstat

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)

#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 = "tomato", high = "skyblue", mid = "orchid", 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

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

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