3.3. Suppose that f,, ,, ... are independent and identically distributed with Pr(6R = ± 11 = ;. Let N be independent of 6, ,2, ... and follow the geometric probability mass function p,,(k) = all - a)' for k = 0, 1, ... , where 0 < a < 1. Form the random sum Z = , + +

(a) Determine the mean and variance of Z.

(b) Evaluate the higher moments m, = E[Z'] and m,, = E[Z°].

Hint: Express Z' in terms of the ;'s where C; = 1 and E[6; ;] = 0.