Find the mean and variance of a Discrete Uniform random vari

Find the mean and variance of a Discrete Uniform random variable on 1,2,...,n.

A hint was given about using facts about sums.

Solution

Suppose X is a discrete Uniform random variable on 1,2,...,n.

Thus the mean is:

(1+n)/2

The variance is:

((n-1+1)^2-1)/12

=(n^2-1)/12