For the Markov chain (Xn)n20 with state space S = {1, 2, 3}, transition probability matrix P, and initial state vector p(0) given by 14 5 P = 151723 31 1 7 6 13 25 STER 12 31 5 7 5 13 " 11 p(0) = [23 10 23 = 2 23 " compute the following: (a) the path probability P(Xo = 1, X₁ = 1, X2 = 2, X3 = 3) = (b) three-step transition probability P(X3 = 2 | Xo = 3) = (c) the state vector p(2)

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A: It is an important part of statistics. It is widely used.

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