1. A Markov chain with state space S = {1, 2, 3} has transition matrixP-0 1 000 10(a) Draw a directed graph for the Markov chain.(b) Identify all communication classes and classify them as aperiodic or periodic (givethe period), and as transient or recurrent.=9(c) Find the probability of the first return to state i at the nth step, P(T; = n) f(n)for all i 1, 2, 3 and all n ≥ 1.=(d) Use part (c) to calculate the mean recurrent time, µ = E[T], for each statei = 1, 2, 3.

Given a Markov chain with state space has transition matrix:

Answered: 1. A Markov chain with state space S =…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter2: Matrices

Section2.5: Markov Chain

Problem 49E: Consider the Markov chain whose matrix of transition probabilities P is given in Example 7b. Show...

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Consider the Markov chain whose matrix of transition probabilities P is given in Example 7b. Show that the steady state matrix X depends on the initial state matrix X0 by finding X for each X0. X0=[0.250.250.250.25] b X0=[0.250.250.400.10] Example 7 Finding Steady State Matrices of Absorbing Markov Chains Find the steady state matrix X of each absorbing Markov chain with matrix of transition probabilities P. b.P=[0.500.200.210.300.100.400.200.11]
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Give me right solution according to the question
2. Let Xo, X₁,... be the Markov chain on state space {1,2,3,4} with transition matrix (1/2 1/2 0 0 1/7 0 3/7 3/7 1/3 1/3 1/3 0 0 2/3 1/6 1/6/ (a) Explain how you can tell this Markov chain has a limiting distribution and how you could compute it.

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