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### CETVRI CAS ###
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# 1. 
#a)
sum(dbinom(7:10, size = 10, prob = 1/2))
# ili
1-pbinom(6, size = 10, prob = 1/2)
#b)
1-(2, size = 10, prob = 1/2)

# 2.
#a)
1-pgeom(4,prob = 0.7)
#b)
pgeom(6,prob = 0.7) - pgeom(1,prob = 0.7)
#v)
sum(dgeom(seq(from = 1, to = 1000, by = 2), prob = 0.7))

#3.
1-ppois(1, lambda = 2)

#4.
mean(rgeom(10^5, 0.3)+1)
mean(rgeom(10^5, 0.3))

#5.
s <- function(n){
  x <- sample(1:n, size = 2, replace = F)
  return(max(x))
}
mean(replicate(10^4, s(10)))

#6. 
#a)
1-pbinom(5, 100, 0.02)
#b)
mean(rbinom(10^4, 100, 0.02))

#7.
# DOMACI