1. (a) Analyse the state space S = {1,2,3,4} for each of the three Markov chains given by the following transition matrices. That is, write down the commu- nication classes and their periods, label each class as essential or not, and as transient or positive recurrent or null recurrent. i. 7/8 1/2 3/8 0 1/8 1/2 5/8 1 ii. 1/4 1/4 1/4 1/4 1/4 0 3/4 1 1/6 0 5/6 iii. 1/3 1/3 1/3 3/4 1/4 1/2 1/2 1/3 1/3 1/3
1. (a) Analyse the state space S = {1,2,3,4} for each of the three Markov chains given by the following transition matrices. That is, write down the commu- nication classes and their periods, label each class as essential or not, and as transient or positive recurrent or null recurrent. i. 7/8 1/2 3/8 0 1/8 1/2 5/8 1 ii. 1/4 1/4 1/4 1/4 1/4 0 3/4 1 1/6 0 5/6 iii. 1/3 1/3 1/3 3/4 1/4 1/2 1/2 1/3 1/3 1/3
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.7: Applications
Problem 16EQ
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