Q5 Suppose {Xn,n > 0} is a three-state Markov chain (with states 1,2,3) with the transition probability matrix (1/3 1/3 1/3 1/2 1/2 1 . Assume that P(X, = 1) = P(Xo = 2) = 1/2. Q5(i.) Find P(X, = 1, X1 = 2, X, = 3) Q5 (ii.) Find P(X, = i) for i = 1, 2, 3. Q5 (iii.) Find P(T3 = 2), where T3 = inf{n > 0, X, = 3} Hint: Look at all possible ways the Markov chain reaches 'state 3' in 2-steps!!

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