data("trees")
View(trees)

N = length(trees$Girth)
n = 10

# psu bp obima 10
indeks = sample(1:N, n, replace = F)
uzorak = trees$Volume[indeks]
uzorak

xn = mean(uzorak)
xn
mean(trees$Volume)

xn_iter = c()
for(i in 1:1000) {
  indeks = sample(1:N, n, replace = F)
  uzorak = trees$Volume[indeks]
  
  xn_iter[i] = mean(uzorak)
}
mean(xn_iter)
hist(xn_iter)

# uzorak sp sa v-cama proporcionalnim obimu stabla (Girth)
pi = trees$Girth/sum(trees$Girth)
pi
sum(pi)

indeks = sample(1:N, n, replace = T, prob = pi)
uzorak = trees$Volume[indeks]
uzorak

x_hh = sum(uzorak/pi[indeks])/(N*n)
x_hh
mean(trees$Volume)