Question: Let X, be a markov chain with state space S={1, 2, 3, 4, 5) with the tarnsition matrix 0 1/2 1/2 0 0 0

Let X, be a markov chain with state space S = {1, 2, 3, 4, 5) with the tarnsition matrix 0 1/2 1/2 0 0 0 0 0

Let X, be a markov chain with state space S={1, 2, 3, 4, 5) with the tarnsition matrix 0 1/2 1/2 0 0 0 0 0 1/5 4/5 0 0 0 2/5 3/5 1 0 0 0 0 1/2 0 0 0 1/2 P = (a) Determine which states are recurrent or transient and whether the chain irre- ducible and aperiodic. Briefly justify. (b) Suppose the chain starts in state 1. What is the expected number of steps until the chain is in state 4? (c) Suppose again the chain starts in state 1. What is the probability that the chain will eneter state 5 before it enters state 3?

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a To determine which states are recurrent or transient and whether the chain is irreducible and aperiodic we need to analyze the transition matrix P A state i is recurrent if its possible to return to ... View full answer

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