Question: Can u help me solve this question? 2. (35 points, 7 each) Let X = {Xn : n : 0, 1,2, . . .} be

Can u help me solve this question?

2. (35 points, 7 each) Let X = {Xn : n : 0, 1,2, . . .} be a discrete time Markov chain on state space S = {1, 2, 3,4} with transition matrix 11 953i 0~0 p24 41 (3%??? 1010 (a) Find P{X2 = 4IX0 = 2}. (b) Find ]P'{X2 = 2,X4 = 4, X5 =1|X0 = 2}. (c) What is the period of each state? (d) Let 71' = (, %, g, i). Is 7r the unique stationary distribution of X ? Explain your answer. (6) Let P" be the nth power of P. Does lirnn_>00 P1734 : i hold? Explain your

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