Prak. Komstat. Pert. 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="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
  #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