Consider a Markov chain with state space 0,1,2, and transition probabilities Pi,i1 1, i 1,2,3, P0,i Pi, i 0,1,2,3, where Pi 0 for all i andi0 Pi 1 (a) Is the chain irreducible (b) What is the period of state 0 (c) What is the period of state i, for all values of i (d) Under what condition is the chain positive recurrent (e) If the chain is positive recurrent, what is the mean number of steps required for it to return to state i if it starts from i

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Question: Consider a Markov chain with state space 0,1,2, and transition probabilities Pi,i1 = 1, i = 1,2,3,; P0,i = Pi, i = 0,1,2,3, where Pi

Consider a Markov chain with state space 0,1,2, and transition probabilities Pi,i1 = 1, i = 1,2,3,; P0,i = Pi, i = 0,1,2,3, where Pi > 0 for all i andi0 Pi = 1.

(a) Is the chain irreducible?

(b) What is the period of state 0?

(d) Under what condition is the chain positive recurrent?

(e) If the chain is positive recurrent, what is the mean number of steps required for it to return to state i if it starts from i?

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