EXERCISE 3.1. Let be an irreducible transition matrix on X, and let be a probability distribution on X. Show that the transition matrix P(x,y) V(x,y) x(y) (y.x) x(x)V(x,y) 1- ^ if y + x, if y = z (=)V(=,x) Σ Ψ(1,2) x(x)V (1,2) 2:27x defines a reversible Markov chain with stationary distribution. ^
EXERCISE 3.1. Let be an irreducible transition matrix on X, and let be a probability distribution on X. Show that the transition matrix P(x,y) V(x,y) x(y) (y.x) x(x)V(x,y) 1- ^ if y + x, if y = z (=)V(=,x) Σ Ψ(1,2) x(x)V (1,2) 2:27x defines a reversible Markov chain with stationary distribution. ^
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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Transcribed Image Text:EXERCISE 3.1. Let V be an irreducible transition matrix on X, and let a be a
probability distribution on X. Show that the transition matrix
V(1, y)
T(y)V (y.1)
T(2)V(1,y)
if y + x,
P(r, y) =
1- E ♥(r, z)
if y = r
(z*z)4(r)
defines a reversible Markov chain with stationary distribution n.
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