Consider a machine that works as follows. If it is up at beginning of a day, it stays up at beginning of next day with probability p and fails with probability 1 p. It takes exactly 2 days for repairs, at the end of which the machine is as good as new. Let Xn be the state of the machine at 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.