A rat is put into the following maze: 3 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. (a) Explain why {X₂} is a MC and find the transition matrix P. (b) Explain why the chain is irreducible, aperiodic and positive recurrent. (c) What is the limit of Pn? Explain.

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