Prak.Komstat_Aluna Nailatul Izzah

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 Datasets mttcars",
       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){
  
  # 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
# P(X >= 2)=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){
  atas <- (factorial(k)/(factorial(k-x)*factorial(x))) *
          (factorial(N-k)/(factorial((N-k)-(n-x))*factorial(n-x)))
  bawah <- factorial(N)/(factorial(N-n)*factorial(n))
  hasil <- atas/bawah
  return(hasil)
}
hyper(2,100,10,5)

## [1] 0.07021881