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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 Pi(H' < H")? (f) What is the probability that a Markov chain, which

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 Pi(H' < H")? (f) What is the probability that a Markov chain, which

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
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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?
Transcribed Image Text: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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