1. Consider a Markov chain Xmatrix=(Xn)n≥0 with state space S[0.2 0.4 0 0.40.3 0 0.700.5 0 0.5 00 0.1 0.90(a) Which states are transient and which are recurrent?(b) Is this markov chain irreducible or reducible?={1, 2, 3, 4} and transition

The image shows a problem statement and a transition matrix for a Markov chain with state space {1,…

Answered: 1. Consider a Markov chain X matrix =…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter2: Matrices

Section2.5: Markov Chain

Problem 47E: Explain how you can determine the steady state matrix X of an absorbing Markov chain by inspection.

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Explain how you can determine the steady state matrix X of an absorbing Markov chain by inspection.
Suppose that a Markov chain has transition probability matrix 1 2 1 P (1/2 1/2 2 1/4 3/4 (a) What is the long-run proportion of time that the chain is in state i, i = 1,2 ? 5. What should r2 be if it is desired to have the long-run average (b) Suppose that ri reward per unit time equal to 9?
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.
2.- Let X₁, 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. Your answer should refer to the relevant Theorems in the notes. (b) Find the limiting distribution for this Markov chain. (100) (c) Without doing any more calculations, what can you say about p₁,1 (100) ? and P2,1
2. Let X₁, X₁,... be the Markov chain on state space {1,2,3,4} with transition matrix 0 1/2 1/2 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. Your answer should refer to the relevant Theorems
9. Let i be a transient state of a continuous-time Markov chain X with X (0) : = i. Show that the total time spent in state i has an exponential distribution.
ered A Markov chain with state space S = {1,2} is described by the transition matrix 1-a P = where 0< a < 1 and 0< B < 1. 1-3 What is P(X1 = 2|X2 = 2, Xo = 1)? %3D Select one 1- a 2- (a +B) O A a (1-3) (1 – a)² + (1 – B)² a (1- B) (1 – a) B+ a (1 – B) ов a (1-3) a (1-a)+ B (1 - B) OD
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 2/3 1/6 1/6, 0 (b) Find the limiting distribution for this Markov chain. (100) (100) ? Without doing any more calculations, what can you say about P₁,1 and P2,1

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1. Consider a Markov chain X matrix = (Xn)n≥0 with state space S [0.2 0.4 0 0.4 0.3 0 0.7 0 0.5 0 0.5 0 0 0.1 0.9 0 (a) Which states are transient and which are recurrent? (b) Is this markov chain irreducible or reducible? = {1, 2, 3, 4} and transition