Prak Komstat Pert. 3

library(ggplot2)
library(reshape2)
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.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] 114154887