Let (Xn)nzo be a Markov chain with state space S = {1, 2, 3, 4, 5} and transition matrix P given by P = Compute PX(X₁ = 5). 0 3 λ = 0 IN OF IN 140 ● 00100 4 0 01120 TITOLI 120 Compute the following probabilities: (a) P(X₂ = 1|Xo = 4) (b) P(X12 = 1, X13 = 2|X10 = 4, X7 = 3) (c) Suppose that the Markov chain (Xn)nzo starts with initial distribution 0 0 1:1). 1 1 1 0, 3 4' 6

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