The discrete uniform distribution on { 1, ... , n) corresponds to the probability mass function (a) Determine the mean and variance. (b) Suppose X and Y are independent random variables, each having...

The discrete uniform distribution on { 1, ... , n) corresponds to the probability mass function

(a) Determine the mean and variance.

(b) Suppose X and Y are independent random variables, each having the discrete uniform distribution on 10, . . . , n}. Determine the probability mass function for the sum Z = X + Y.

(c) Under the assumptions of (b), determine the probability mass function for the minimum U = min{X, Y).