Komstat Pertemuan 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")] 

# 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 = "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){
if (k < 0 || n < 0  || p < 0 || p > 1) {
  stop("Input Tidak Valid")
}

#Inisialisasi CMF
cmf <- 0

#Menhitung CMF
for(x in 0:k) {
  prob <- choose(n, x) * (p^x) * ((1-p)^(n-x))
  cmf <- cmf + prob
}
return(cmf)
}

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