Let X1 denote the initial state at time 1 of the Markov

Chapter 3, Problem 10

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Let X1 denote the initial state at time 1 of the Markov chain for which the transition matrix is as specified in Exercise 5, and suppose that the initial probabilities are as follows: Pr(X1 = 1) = 1/8, Pr(X1 = 2) = 1/4, Pr(X1 = 3) = 3/8, Pr(X1 = 4) = 1/4. Determine the probabilities that the chain will be in states 1, 2, 3, and 4 at time n for each of the following values of n: (a) n = 2; (b) n = 3; (c) n = 4.

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