.Consider a machine that can be either up (working) or down (not working). If it is up on day n, it is up on day n + 1 with probability pu, independent of the past. If it is down on day n, it is down on day n + 1 with probability pd, also independent of the past. Suppose a workshop has two identical machines similar to the one described in the lecture example. The two machines behave independently of each other. Let Xn be the number of machines that work on day n. Define the state variable(s), and determine the transition probability matrix.