################
### PETI CAS ###
################

# Ravnomerna raspodela U(1,3)
1-punif(q = 1.5, min = 1, max = 3)
punif(q = 2, min = 1, max = 3)-punif(q = 1, min = 1, max = 3)

#1. 
1-punif(q = 2, min = 1.5, max = 4)
punif(q = 3, min = 1.5, max = 4)

# Eksponencijalna raspodela E(3)
1-pexp(q = 1, rate = 3)
pexp(q = 3, rate = 3)-pexp(q = 1, rate = 3)
1-pexp(q = -1, rate = 3)
pexp(q = 1, rate = 3)
qexp(p = 0.8, rate = 3)
pexp(q =0.536, rate = 3)
qexp(p = 0.9, rate = 3)

#2.
x <- rexp(10000, rate = 2)
hist(x)
z <- 1-exp(-2*x)
hist(z)
sum(z > 1/2)/length(z)

#3.
x <- rexp(10000, rate = 1/2)
y <- exp(-2*x)
mean(y)
var(y)

# Normalna raspodela N(5,9)
pnorm(q = 2, mean = 5, sd = 3) - pnorm(q = 1, mean = 5, sd = 3)
qnorm(p = 0.9, mean = 5, sd = 3)
qnorm(p = 0.95, mean = 0, sd = 1)*3+5

#5.
1-pbinom(q = 59, size = 100, p = 1/2)
1-pnorm(q = 60, mean = 50, sd = 5)

#7. 
1-pweibull(q = 600, shape = 3, scale = 200)
pweibull(q = 500, shape = 3, scale = 200)
qweibull(p = 0.9, shape = 3, scale = 200)

#8.
1-pgamma(q = 120, shape = 120, rate = 1.2)