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 12EQ: 12. Robots have been programmed to traverse the maze shown in Figure 3.28 and at each junction...

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