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)

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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