#!/usr/bin/env Rscript
#2014. 1.a)
fi <- c(3, 2, 4, 2, 3, 5, 1, 1)
x <- c(0 : 7)

a <- 0
b <- 0
a <- sum(x * fi)
a
for(i in 1 : 8){
    b <- b + (7-(i -1))* fi[i]
}
b
# MLE L(p) = c * p^(suma i * fi[i]) * (1 - p)^(suma((5-i) * fi[i]))
# i sada deriviramo logaritmirani izraz

D(expression(log(p^66 * (1-p)^81)), "p")

f <- function(p){
    (66 * p^65 * (1 - p)^81 - p^66 * (81 * (1 - p)^80))/(p^66 * (1 - p)^81)
}

x0 <- uniroot(f, c(0.1, 0.99)) $ root
x0 # procjenjeni p iznosi 0.4489797