PrakKomstat_Pert3

library(ggplot2)
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.s = element_text(hjust=0.5))

## Warning in plot_theme(plot): The `axis_test.s` 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

#distribusi binomial

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=1-cmfbinom(1,12,0.2)
Peluang

## [1] 0.7251221

#poisson

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

#hipergeometrik
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