2.2 Let Xo, X,... be a Markov chain with transition matrix 1 2 3 1/2 1/2...

 

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2.2 Let Xo, X₁,... be a Markov chain with transition matrix 1 2 3 1/2 1/2 0 2 1 0 3 1/3 1/3 1/3) and initial distribution a = (1/2,0, 1/2). Find the following: (a) P(X₂ = 1|X₁ = 3) (b) P(X₁ = 3, X₂ = 1) (c) P(X₁ = 3|X₂ = 1) (d) P(X, = 1|X₁ = 3, X4 = 1, X₂ = 2) 2.2 Let Xo, X₁,... be a Markov chain with transition matrix 1 2 3 1/2 1/2 0 2 1 0 3 1/3 1/3 1/3) and initial distribution a = (1/2,0, 1/2). Find the following: (a) P(X₂ = 1|X₁ = 3) (b) P(X₁ = 3, X₂ = 1) (c) P(X₁ = 3|X₂ = 1) (d) P(X, = 1|X₁ = 3, X4 = 1, X₂ = 2)