# 5. The transition matrix for a three-state Markov chain with S = {1,2,3} is P = 0 0 0 0 1 0.5 0.5 0 (a) Show that the chain is irreducible. (b) Show that the chain is periodic and find the period d. Find Pnd, n = 1,2,...

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#5. The transition matrix for a three-state Markov chain with S = {1,2,3} is
P =
0 0
0 0 1
0.5 0.5 0
(a) Show that the chain is irreducible.
(b) Show that the chain is periodic and find the period d. Find Pnd, n = 1,2,....
(c) Use the identity
M = E + P(M - diag(M))
to find the mean recurrent times. Show that they agree with the formula given in
the Basic Limit Theorem for periodic Markov Chains.
Transcribed Image Text:#5. The transition matrix for a three-state Markov chain with S = {1,2,3} is P = 0 0 0 0 1 0.5 0.5 0 (a) Show that the chain is irreducible. (b) Show that the chain is periodic and find the period d. Find Pnd, n = 1,2,.... (c) Use the identity M = E + P(M - diag(M)) to find the mean recurrent times. Show that they agree with the formula given in the Basic Limit Theorem for periodic Markov Chains.
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