###################
### CETVRTI CAS ###
###################

# 1.
#a
sum(dbinom(7:10,10,1/2))
1-pbinom(6,10,1/2)
#b
1-pbinom(q = 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)
sum(dgeom(seq(from = 1, to = 10000, by = 2), prob = 0.7))

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

#4.
mean(rgeom(n = 10000, prob = 0.3)+1)
mean(rgeom(n = 10000, prob = 0.3))

#5.
s <- function(n){
  x <- sample(1:n, size = 2, replace = F)
  return(max(x))
}
mean(replicate(n = 1000, s(50)))

#6.
#a 
1-pbinom(5,100,0.02)
#b
mean(rbinom(1000,100,0.02))