# Ex 3
# n dimensão da amostra de X
# p  vector de  probabilidades
rX <- function(n, p)
{
       set.seed(1)
	# gerar uniform(0,1) 
	U <- runif(n)
	# Vector para guardar a geração de X
	X <- rep(0,n)
	# Qual dos U's pertence a [0,p1]
	w1 <- which(U < p[1])
	X[w1] <- 1
	# which U are in the second interval
	w2 <- which( (U >= p[1]) & (U < sum(p[1:2])) )
	X[w2] <- 2
	# which U are in the third interval
	w3 <- which( U >= sum(p[1:2]) )
	X[w3] <- 3
	return(X)
}
X = rX(10000, c(.4, .25, .35))

# Verificação

resul=c(mean(X==1),mean(X==2),mean(X==3))


################################################################
# Bernoulli
#######################################


n <- 10000 ; set.seed(1); p <- 0.4  
u <- runif (n)
x <- as.integer(u <= p) #(u <= 0.4) 
 mean (x); var(x)

#########################################

my.bernoulli <- c()
n <- 10000 
p <- 0.4
set.seed(1)
for(i in 1:n){
  u <- runif(1)
  if(u <= p) my.bernoulli[i] <- 1
  else my.bernoulli[i] <- 0
}


print(c(head(my.bernoulli), tail(my.bernoulli))) 


mean(my.bernoulli)

###########################################################
#
#   Transformação inversa para a geração de Exp(1)
############################################################ 
inverse_exp<-function(u,mu=1){
    return(-log(u)/mu)
}

compare_data<-data.frame(inv_data=inverse_exp(u=runif(1000)),rexp_data=rexp(1000))


library(ggplot2)
library(patchwork)

p1 <- ggplot(data=compare_data) + geom_histogram(aes(x=inv_data),binwidth=0.2)
p2 <- ggplot(data=compare_data) + geom_histogram(aes(x=rexp_data),binwidth=0.2)

p1 + p2