Consider the compound rv S with primary distribution N and secondary distribution M. The primary distribution N is a zero-truncated negative binomial rv with β = 1 and r = 3. In other words, N is an (a, b, 1) member with a = β /(β+1) = 1/2 and b = (r−1)β/(β+1) = 1. The pmf of M is given by f0 = 0.1, f1 = 0.65 and f2 = 0.25. Compute the pmf of S, i.e., gk = P (S = k) for k = 0, 1, 2, 3.
Solution:
