MATRIKS KORELASI DAN DISTRIBUSI PELUANG DISKRIT

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.test.x=element_text(hjust=0.5))

## Warning in plot_theme(plot): The `axis.test.x` theme element is not defined in
## the element hierarchy.

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