49. Consider a Markov chain with states having transition probability matrix Image (a) If the chain is

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49. Consider a Markov chain with states having transition probability matrix Image

(a) If the chain is currently in state 1, find the probability that after two transitions it will be in state 2.

(b) Suppose you receive a reward Image whenever the Markov chain is in state i, Image. Find your long run average reward per unit time.

Let denote the number of transitions, starting in state i, until the Markov chain enters state 3.

(c) Find Image.

(d) Find Image.

(e) Find Image.

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