9. The "random" parts of the algorithm in Self-Test Problem 8 can be w in terms of the generated values of a sequence of independent un

(0, 1) random variables, known as random numbers. With [x] defined a largest integer less than or equal to x, the first step can be written as fol.

Step 1. Generate a uniform (0, 1) random variable U. Let X [m]

and determine the value of n(X).

(a) Explain why the above is equivalent to step 1 of Problem 8.

HINT: What is the probability mass function of X?

(b) Write the remaining steps of the algorithm in a similar style.