Question: Find its invariant distribution. Deduce that all states are positive recurrent and that, if the chain is aperiodic, then pi, j (n) 1/N as n

Find its invariant distribution. Deduce that all states are positive recurrent and that, if the chain is aperiodic, then pi, j (n)→ 1/N as n → ∞.

2. Let X be a discrete-time Markov chain with state space S = {1, 2} and transition matrix P =



1 − α α

β 1 − β



.

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