Consider the simple queueing process of Example 5.7. Suppose that you watch the size of the queue. If there are j people in the queue the next time the queue size changes it will either decrease to j - 1 or increase to j + 1. Use the result of Exercise 34 to show that the probability that the queue size decreases to j - 1 is µ/(µ + λ) and the probability that it increases to j + 1 is λ/(µ + λ). When the queue size is 0 it can only increase to 1. Write a program to simulate the queue size. Use this simulation to help formulate a conjecture containing conditions on µ and λ that will ensure that the queue will have times when it is empty.