i need this question done in 10 minutes 1. (a) Consider a discrete-time Markov chain X = {X₂ : n = N} with a transition matrix02/3 1/3M =1/3 0 2/31/4 3/4 0(1)i. Draw the transition diagram of X.ii. Is the Markov chain irreducible and positive recurrent? Justify your arguments.iii. Determine the stationary distribution л of X from the equation лM = π.(b) Let X = {X: t≥ 0} be a time-homogeneous Markov process with state-space $ = {1, 2, 3}.The average time X spends in each state 1, 2 and 3 is given respectively by 1/6, 1/2 and1/3 unit of time. The probability P(XT j|X₁ = i) of making an immediate jump fromstate i to state j, with (i, j) = S, is given by the matrix M (1) in the question 1(a) above.Note that T refers to the jump time of the Markov process.=i. Find the corresponding intensity matrix Q of the Markov process.ii. Find the average time it takes the process to move from states 1 and 2 to state 3.

Step 1:(a) ii. Irreducibility and Positive RecurrenceIrreducibility: The Markov chain is irreducible…

Answered: 1. (a) Consider a discrete-time Markov…

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.
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