Question: 7. (Problem 3.2.1 in Pinsky and Karlin) Consider the Markov chain whose transition probability matrix is given by 0.3 0.4 0.2 0.1 0.1 0.3 0.4

7. (Problem 3.2.1 in Pinsky and Karlin) Consider the Markov chain whose transition probability matrix is given by 0.3 0.4 0.2 0.1 0.1 0.3 0.4 0.2 P = 0.4 0.2 0.1 0.3 0.2 0.1 0.3 0.4 Suppose that the mitial distribution is pi = 0.25 for i = 0, 1, 2,3. Use proof by induction to show that Pr(Xn = k) = 0.25, k = 0, 1, 2,3, for all n. Comment

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