Matriks Korelasi dan Distribusi 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.text.x=element_text(hjust=0.5))

#distribusi bernoulli
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
  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

#distribusi 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

#distrbusi geometrik
geo<-function(x,p){p*(1-p)^(x-1)}
geo(5,0.3)

## [1] 0.07203

#distribusi 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