A Markov chain Xo, X₁, X₂... on states 0, 1, 2 has the transition probability matrix P (shown on the right) and initial distribution P(X₁ = 0) = 0.3, P(X。 = 1) = 0.4 and P(X₁ = 2) = 0.3. (1) Show that P is regular. (2) Find P(Xo = 2, X₁ = 0, X₂ = 1). (3) Find P(X₂ = 2, X₁ = 1|X₁ = 0). (4) Determine the limiting distribution. 0 0 0.7 P=10 1 2 0.2 0.1 0.6 0.4 20.5 0 0.5

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