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Let (Yo, Y₁, Y2,...) be a new discrete-time homogeneous Markov chain on the same state space obtained by modifying this chain as follows. At each time I toss a biased coin which has probability 1/3 of showing Heads. If it shows a Head then I take one step in the chain with transition matrix P; if it shows a Tail I remain in the same state. Let Q be the transition matrix for (Yo, Y₁, Y2, ...). (e) Write down the matrix Q. (f) Does this Markov chain have a limiting distribution? Justify your answer.

Let (Yo, Y₁, Y2,...) be a new discrete-time homogeneous Markov chain on the same state space obtained by modifying this chain as follows. At each time I toss a biased coin which has probability 1/3 of showing Heads. If it shows a Head then I take one step in the chain with transition matrix P; if it shows a Tail I remain in the same state. Let Q be the transition matrix for (Yo, Y₁, Y2, ...). (e) Write down the matrix Q. (f) Does this Markov chain have a limiting distribution? Justify your answer.

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
Problem 1P
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Let (X0, X1, X2, . . .) be the discrete-time, homogeneous Markov chain on state space S = {1, 2, 3, 4, 5, 6} with X0 = 1 and transition matrix

P = 0 0 0 0 0 0 0 0 1/2 1/2 1/2 1/2 1/3 2/3 0 1/3 2/3 0 0 0 3/4 1/4 0 0 0 1/4 3/4 0 0 0 0 000 0 0
Transcribed Image Text:P = 0 0 0 0 0 0 0 0 1/2 1/2 1/2 1/2 1/3 2/3 0 1/3 2/3 0 0 0 3/4 1/4 0 0 0 1/4 3/4 0 0 0 0 000 0 0
Let (Yo, Y₁, Y2,...) be a new discrete-time homogeneous Markov chain on the same state space obtained by modifying this chain as follows. At each time I toss a biased coin which has probability 1/3 of showing Heads. If it shows a Head then I take one step in the chain with transition matrix P; if it shows a Tail I remain in the same state. Let Q be the transition matrix for (Yo, Y₁, Y2,...). (e) Write down the matrix Q. (f) Does this Markov chain have a limiting distribution? Justify your answer.
Transcribed Image Text:Let (Yo, Y₁, Y2,...) be a new discrete-time homogeneous Markov chain on the same state space obtained by modifying this chain as follows. At each time I toss a biased coin which has probability 1/3 of showing Heads. If it shows a Head then I take one step in the chain with transition matrix P; if it shows a Tail I remain in the same state. Let Q be the transition matrix for (Yo, Y₁, Y2,...). (e) Write down the matrix Q. (f) Does this Markov chain have a limiting distribution? Justify your answer.
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