Question: 2. Consider the homogeneous discrete time Markov chain whose state transition diagram is given below: 1-2 1-p 2 Z 3 1-a a) Find P, the

2. Consider the homogeneous discrete time Markov chain whose state transition

2. Consider the homogeneous discrete time Markov chain whose state transition diagram is given below: 1-2 1-p 2 Z 3 1-a a) Find P, the probability transition matrix. b) Under what conditions (if any) will the chain be irreducible and aperiodic? c) Solve for the equilibrium probability vector it. d) What is the mean recurrence time for state 2

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