# Zadacha 1
# Во текот на 30 дена броени се примените и испратените пораки во еден ден кон еден
# број. Резултатите се запишани во следните два вектори
library(stats4)
X <<- c(5,4,7,8,4,0,3,7,4,5,11,4,7,10,5,4,8,6,6,9,9,4,5,7,3,1,4,5,6,9)
Y <<- c(3,2,2,3,2,1,2,2,1,3,2,0,1,1,3,0,2,0,1,2,5,4,3,2,2,3,1,2,1,3,1)
par(mfrow = c(1,2))
hist(X, nclass = (max(X) - min(X)), freq = F)
lines(density(X), lwd = 3)
hist(Y, nclass = (max(Y) - min(Y)), freq = F)
lines(density(Y), lwd = 3)
paste("Prosek na prateni poraki : ", mean(X))
paste("Prosek na primeni poraki : ", mean(Y))
paste("Da pretpostavime deka X i Y ~ Po, taka shto lambda_x = 6, lambda_y = 2")
paste("Spored MLE se dobiva :")
poisson.lik.X <- function(lambda_x = 2) {
  n <- length(X)
  logl <- sum(X) * log(lambda_x) - n * lambda_x
  return(-logl)
}
poisson.lik.Y <- function(lambda_y = 2) {
  n <- length(Y)
  logl <- sum(Y) * log(lambda_y) - n * lambda_y
  return(-logl)
}
mle(poisson.lik.X)
mle(poisson.lik.Y)

# ----------------------------------------------------------------------------
# MLE eksponencijalna... (pr. 4)
lambda = 2
X <<- rexp(3000, lambda)
log.L <- function(lam = 2) {
  n <- length(X)
  - n * log(lam) + lam * sum(X)
}
(fit <- mle(log.L))

# --------------------------------------------------