13. The Discrete Rejection Method: Suppose we want to simulate X having probability mass function P[X = i] = P^9 i = 1 , . . . , ç and suppose we can easily simulate from the probability mass function QI9 ÓúÙú = 1>

Qi > 0. Let C be such that Pt < CQt, / = 1 , . . . , n. Show that the following algorithm generates the desired random variable.

Step 1: Generate Y having mass function Q and U an independent, random number.

Step 2: If U < PY/CQY, set X = Y. Otherwise return to Step 1.