Consider the simple queueing process of Example. Suppose that you watch the size of the queue. If there are [math]j[/math] people in the queue the next time the queue size changes it will either decrease to [math]j - 1[/math] or increase to [math]j + 1[/math]. Use the result of Exercise to show that the probability that the queue size decreases to [math]j - 1[/math] is [math]\mu/(\mu +\lambda)[/math] and the probability that it increases to [math]j + 1[/math] is [math]\lambda/(\mu + \lambda)[/math]. 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 [math]\mu[/math] and [math]\lambda[/math] that will ensure that the queue will have times when it is empty.