Given the initial distribution matrix P = [0.2 0.3 0.5] 0.5 0 0.5 1 0 0 and the initial distribution p(0) = [0.5 0.5 0] answer the following questions: (a) Is this Markov Chain (MC) irreducible? (b) Find p(1) and p(2). (c) Calculate P(X₁ = 1; X₂ = 2; X3 = 0). (d) Determine P(X3 = 1|X₁ = 0). (e) Find f2) and f. (f) Determine 22. (g) Find d(2). (h) What is the long-run average number of visits to state 2?

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