6.1 Suppose that X has a discrete uniform distribution on {1, 2, ..., n}, that is P(X = i) = 1 n

for every i = 1, ..., n.

a) Compute the moment generating function of X.

b) Deduce that EX = n + 1 2

and EX2 = (n + 1)(2n + 1)

6 .