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2. Markov Chain States Consider a Markov chain on the state space S = {1,2,3,4,...} with the following transition matrix: 1/2 1/2 0 0 0 2/3 0 1/3 0 0 3/4 0 0 1/4 0 P = 4/5 0 0 0 1/5 5/6 0 0 0 0 That is, Pij = i/(i + 1) if j = 1, Pij = 1/(i + 1) if j = i + 1, and Pij = 0 otherwise. (a) Classify all states of the Markov chain (transient, recurrent) (b) Determine if the Markov chain is irreducible.

2. Markov Chain States Consider a Markov chain on the state space S = {1,2,3,4,...} with the following transition matrix: 1/2 1/2 0 0 0 2/3 0 1/3 0 0 3/4 0 0 1/4 0 P = 4/5 0 0 0 1/5 5/6 0 0 0 0 That is, Pij = i/(i + 1) if j = 1, Pij = 1/(i + 1) if j = i + 1, and Pij = 0 otherwise. (a) Classify all states of the Markov chain (transient, recurrent) (b) Determine if the Markov chain is irreducible.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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2. Markov Chain States Consider a Markov chain on the state space S = {1,2,3,4,...} with the following transition matrix: 1/2 1/2 0 0 0 2/3 0 1/3 0 0 3/4 0 0 1/4 0 P = 4/5 0 0 0 1/5 5/6 0 0 0 0 That is, Pij = i/(i + 1) if j = 1, Pij = 1/(i + 1) if j = i + 1, and Pij = 0 otherwise. (a) Classify all states of the Markov chain (transient, recurrent) (b) Determine if the Markov chain is irreducible.
Transcribed Image Text:2. Markov Chain States Consider a Markov chain on the state space S = {1,2,3,4,...} with the following transition matrix: 1/2 1/2 0 0 0 2/3 0 1/3 0 0 3/4 0 0 1/4 0 P = 4/5 0 0 0 1/5 5/6 0 0 0 0 That is, Pij = i/(i + 1) if j = 1, Pij = 1/(i + 1) if j = i + 1, and Pij = 0 otherwise. (a) Classify all states of the Markov chain (transient, recurrent) (b) Determine if the Markov chain is irreducible.
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