Uniform Distribution and a 20-Sided Die A 20-side (icosahedral) die has each face marked with a different integer from 1 through 20

Uniform Distribution and a 20-Sided Die

A 20-side (icosahedral) die has each face marked with a different integer from 1 through 20. Assuming that each face is equally likely to occur on a single roll, the outcome is a random variable X~DU(20) (DISCRETE UNIFORM DISTRIBUTION).

a) If the die is rolled twice, find the pdf of the smallest value obtained, say Y.
In this problem there are two ways to solve one is the largest way9 counting every pair of the outcome and the other is the smallest, using CDF.
b) If the die is rolled three times, find the probability that the largest value is 3.
answer is 19/8000
c)Find E(x) and Var(x)