alpha=2
lambda=2
n=100000

X=rgamma(n, alpha, lambda) #p,d,g
histogram(X)
mean(X) #alpha/lambda
var(X) #alpha/lambda^2
hist(X, prob=TRUE, ylim=range(0,0.8), breaks=100, col='red')
#hist(X)
#x=c(1:100)
#X1=dgamma(x, 100)
#plot(X1)
curve(dgamma(x,alpha, lambda), 0, 5, add=TRUE)


###
n=100
X=rgamma(n, alpha, lambda) #p,d,g
plot(ecdf(X), col="red")
rug(X)
curve(pgamma(x,alpha,lambda), add=TRUE)


die <- function(n){
  X <- runif(n)*6
  floor(X)+1
  return(floor(X)+1)
}
m=100 #moze byc cos nie tak jak wypadnie tylko 5 wartosci
hist(die(m), prob=TRUE)
x=die(m)
x=factor(x, levels=c(1:6))
T=table(x)
#T=T/m
#T=factor(T, levels=c(1,2,3,4,5,6))
barplot(T)
chisq.test(T, p=c(1/6, 1/6, 1/6, 1/6, 1/6, 1/6)) #samemu napisac chisq test



####

losowanie <- function(m){
  lista=c(1:m)
  for (i in 1:m){
    U=runif(1) 
    X=rbinom(1,9,U) #X|U z Bin(n,U)
    lista[i]=X
  }
  return(lista)
}

T=table((losowanie(10000)))
barplot(T)