14. The Discrete Hazard Rate Method: Let X denote a nonnegative integer valued random variable. The function

, is called the discrete hazard rate function.

(a) Show that .

(b) Show that we can simulate X by generating random numbers stopping at

(c) Apply this method to simulating a geometric random variable. Explain, intuitively, why it works.

(d) Suppose that Image for all n. Consider the following algorithm for simulating X and explain why it works:
Simulate Image where is geometric with mean Image and is a random number. Set and let