Zulfadli Ahwal Ramadhan - 2507016076 - Materi 3 Praktikum

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 = "green")+
  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

#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 paling sedikit 2 orang sembuh = 1 - P(x <= 1)
peluang = 1 - cmfbinom(1, 12, 0.2)
peluang

## [1] 0.7251221

#poison
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

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

## [1] 0.07203

#hypergeometrik
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