Show full answers and steps to this exercise using Markov Chain Theorem to solve [6] In Theorem 3, we required that all elements of the transition matrix P be strictlypositive, that is, 0 < pij < 1.a) Show that a Markov chain with transition matrix1 0 0[/0P =1/4 1/2 1/40 1has more than one stationary distributions.b)find the matrix that P" converges to, asn→ ∞, and verify that it is not a matrix with identical rows, i.e. not in theform Theorem 3 predicts.

Theorem 3 is a result that applies to ergodic or irreducible Markov chains, which are stochastic…

Answered: [6] In Theorem 3, we required that all…

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[6] In Theorem 3, we required that all elements of the transition matrix P be strictly positive, that is, 0 < Pij < 1.

A First Course in Probability (10th Edition)

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ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

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Question

Show full answers and steps to this exercise using Markov Chain Theorem to solve

[6] In Theorem 3, we required that all elements of the transition matrix P be strictly
positive, that is, 0 < pij < 1.
a) Show that a Markov chain with transition matrix
1 0 0
[/
0
P =
1/4 1/2 1/4
0 1
has more than one stationary distributions.
b)
find the matrix that P" converges to, as
n→ ∞, and verify that it is not a matrix with identical rows, i.e. not in the
form Theorem 3 predicts.

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