3.16. Consider the generalized geometric distribution defined by

(a) Evaluate po in terms of b and p.

(b) What does the generalized geometric distribution reduce to when b=p?When b=pl(1 -p)?

(c) Show that N = X + Z has the generalized geometric distribution when X is a Bernoulli random variable for which Pr{X = 11 =

a, 0

Pk = b(1 - p)* for k = 1, 2,..., and Po = 1 - Pk, where 0 < p < 1 and p b p/(1 - p). -1-