Prak.Komstat.3

library(ggplot2)
library(reshape2)
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="skyblue", mid="pink",
                       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)
}
#Peliang paling sedikit 2 orang sembugh=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