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Question no. 24 A Markov chain with state space {-2,-1,0, 1,2} has the following one- step transition probabilities: Pi,t+1 =3/4 for i = -2,-1,0, 1 Pi,i-1 1/4 for i =-1,0, 1,2 p-2,2 = 1/4% =1-p2,-2 %3D !! %3D (a) Determine the classes of the Markov chain. For each class, establish whether it is recurrent or transient and whether it is periodic or aperiodic. (b) Do the limiting probabilities exist? If they do, compute them. (c) Is the chain time-reversible (see p. 147)? Justify.

Question no. 24 A Markov chain with state space {-2,-1,0, 1,2} has the following one- step transition probabilities: Pi,t+1 =3/4 for i = -2,-1,0, 1 Pi,i-1 1/4 for i =-1,0, 1,2 p-2,2 = 1/4% =1-p2,-2 %3D !! %3D (a) Determine the classes of the Markov chain. For each class, establish whether it is recurrent or transient and whether it is periodic or aperiodic. (b) Do the limiting probabilities exist? If they do, compute them. (c) Is the chain time-reversible (see p. 147)? Justify.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Question no. 24 A Markov chain with state space {-2,-1,0, 1,2} has the following one- step transition probabilities: Pi,t+1 =3/4 for i = -2,-1,0, 1 Pi,i-1 = 1/4 for i =-1,0,1, 2 p-2,2 = 1/4% =1- p2,-2 %3D (a) Determine the classes of the Markov chain. For each class, establish whether it is recurrent or transient and whether it is periodic or aperiodic. (b) Do the limiting probabilities exist? If they do, compute them. (c) Is the chain time-reversible (see p. 147)? Justify.
Transcribed Image Text:Question no. 24 A Markov chain with state space {-2,-1,0, 1,2} has the following one- step transition probabilities: Pi,t+1 =3/4 for i = -2,-1,0, 1 Pi,i-1 = 1/4 for i =-1,0,1, 2 p-2,2 = 1/4% =1- p2,-2 %3D (a) Determine the classes of the Markov chain. For each class, establish whether it is recurrent or transient and whether it is periodic or aperiodic. (b) Do the limiting probabilities exist? If they do, compute them. (c) Is the chain time-reversible (see p. 147)? Justify.
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