A Markov chain {X 0 , X 1 , ...} has state space Z = {0, 1, 2} and transition matrix (1) Determine P ⎝X 2 = 2|X 1 = 0, X0 = 1) and P(X 2 = 2, X 1 = 0|X 0 = 1 ⎠ (2) Determine P⎝X 2 = 2, X 1 = 0|X 0 =...

A Markov chain {X₀, X₁, ...} has state space Z = {0, 1, 2} and transition matrix

(1) Determine P ⎝X₂
= 2|X₁
= 0, X0 = 1) and P(X₂
= 2, X₁
= 0|X₀
= 1 ⎠

(2) Determine P⎝X₂
= 2, X₁
= 0|X₀
= 0) and, for n > 1,

(3) Assuming the initial distribution