2. [Replacement Policy) A system is inspected at equally spaced points in time. After each inspection it is classied into one of L + 1 possible states {O,1,2...,L}. A system is in state 0 if it is found to be in the best possible condition. A system in state L is inoperative, while a system in state L - 1 is in the worst possible condition but still able to operate. At every time periodl, the system state is likely to degrade by one unit with probability p. a. Let X\" denote the state of the system at time 11. Find the transition probability matrix P. Consider now the following replacement policy; given I\" [0 i" then the system is replaced by a new one. Let X5\" denote the state of the system at time n under this policy. Find the transition probability matrix P\". b. Are these chains ergodic? Ifso, compute the stationary probability distribution