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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,...

# 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,...

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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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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