Consider a machine that works as follows. If it is up at the beginning of a day, it stays up at the beginning of the next day with probability p and fails with probability 1 p. It takes exactly 2 days for the repairs, at the end of which the machine is as good as new. Let Xn be the state of the machine at the beginning of day n, where the state is 0 if the machine has just failed, 1 if 1 day’s worth of repair work is done on it, and 2 if it is up. Show that {Xn; n>=0} is a DTMC, and display its transition probability matrix.