Chapter 6, Problem 6.10STPE

The “random” parts of the algorithm in Self-Test Problem 6.9 &1 can be written in terms of the generated values of a sequence of independent uniform (0, 1) random variables, known as random numbers. With [x] defined as the largest integer less than or equal to x, the first step can be written as follows:

Step 1. Generate a uniform (0, 1) random variable U. Let $X=\left[mU\right]+1$ and determine the value of $n\left(X\right)$.

a. Explain why the above is equivalent to step I of Problem 6.8.

Hint: What is the probability mass function of X?

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