Transition probabilities
Consider a (discrete-time) Markov chain {Xn} on the state space S = {1,2,3,4} with transition probabilities given by
( pij ) =
1/2 1/4 1/4 0
1/3 0 2/3 0
1/2 1/2 0 0
Suppose P(X0 = 4) = 1. Compute P(X2 = 3).
Explain your reasoning.
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