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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 14EQ

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Suppose that a Markov chain (X,)n>o has a
stochastic matrix given by:
1/2
1/2
1/4
3/4
1/3
1/3
1/3
P =
1/6 2/3
1/6
2/3
1/3
1/6
5/6
1/2
0 0 0
1/2
(c) What is P4(H' < H')?
(d) What is P2(H' < H')?
(e) Suppose now that the Markov chain is initialised
from 1, which is a uniform distribution over all states
1 to 7. What is Pa(H' < H')?
(f) What is the probability that a Markov chain, which
started in state 2, visits state 1 exactly once before
hitting state 7?

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