Answered: Problem 2: (mean return time) Consider… | bartleby

Linear Algebra: A Modern Introduction

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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Problem 2: (mean return time) Consider a Markov chain {X„} on states {0,1,2,3} with a tran-
sition matrix
1
0.1 0.4 0.2 0.3
P=
0.2 0.2 0.5 0.1
0.3 0.3 0.4
1. Compute the limiting distribution (T0, T1, T2, T3) of this Markov Markov Chain;
2. For each state i, compute (directly) m¡¡ - the average number of steps it takes to get back to i
if started in i, and show that the relation m¡¡ = 1/T; is true.

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