A rat is put into the following maze: The rat has a probability of 1/4 of starting in any compartment and suppose that the rat chooses a passageway at random when it makes a move from one compartment to another at each time. Let Xn be the compartment occupied by the rat after n moves.   Explain why {Xn} is a MC and find the transition matrix P . Explain why the chain is irreducible, aperiodic and positive What is the limit of Pn? Find the probability that the rat is in compartment 3 after two In the long run, how many times that the rat enters in compartment 4 in 100 mov

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A: Given:-             n = 13            X¯ = ∑xin     = 52.2308s = ∑xi -xi2n-1

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