Question: 4. Consider a Markov process with state space S = {0, 1, 2, 3, . . ..} The onestep transition probabilities are given by 100,0

4. Consider a Markov process with state space S = {0, 1, 2, 3, . . ..} The onestep transition probabilities are given by 100,0 = 9: 100,2 =30: Pig1 = (I; and P,i+1 = 10 for i 2 1- Here0

p and nd the stationary distribution when I; > p. (c) Let Ti, be the waiting time for returning to state a" given that the process starts from state 2'. Find E(T},), i = 0,1,2,.... (Note only consider the case that q > p) (d) Let T01 be the waiting time for visiting state 1 given that the process starts from state 0. Find E(T01) when q > p

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