PRAK 3 KOMSTAT

#Nomor2
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 = 0.05))

bern<-function(x,p){p^x*(1-p)^(1-x)}
bern(1,3/6)

## [1] 0.5

cmfbinom<-function(k,n,p) {
  #Variabel input
  if (k < 0||n<0||p<0||p>1){
    stop("input tidak valid")
}
  #Inisalisasi 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