Exercise 9.11 (CREDITRISK+) Consider n firms and, given X > 0, suppose that each firm defaults independently with probability pX. Let N be the number of defaulted firms, and let be the generating function of N.
(1) Suppose p = 1. Show that, given X, the conditional generating function

(2) Suppose that X follows a Gamma distribution given in Exercise 3.13 Show that

and obtain P{N = n}. Hint: Use the generalized binomial expansion

Transcribed Image Text:

FN(2) = n=0 P{N = n}zn