For this problem consider the following transition matrix for a Markov chain on the states 1, 2, and 3: 1 P = (p(i, j))isij<3 = 1 п/20 п/20 1—п/10 where n is the fourth digit of your Emplid. [For instance, if the fourth digit of your Emplid is 6, then the matrix you would use for this problem is 1 P = 1 3/10 3/10 2/5 (a) Write what P is based on your Emplid. (b) Explain clearly why P is a stochastic matrix. (c) Determine the period of each of the three states. (d) Determine if the Markov chain is irreducible. (e) Does the Markov chain have an invariant probability distribution? Explain your answer. If the Markov chain has an invariant distribution, sav what it is.

For this problem consider the following transition matrix for a Markov chain on the states 1, 2, and 3: 1 P = (p(i, j))isij<3 = 1 п/20 п/20 1—п/10 where n is the fourth digit of your Emplid. [For instance, if the fourth digit of your Emplid is 6, then the matrix you would use for this problem is 1 P = 1 3/10 3/10 2/5 (a) Write what P is based on your Emplid. (b) Explain clearly why P is a stochastic matrix. (c) Determine the period of each of the three states. (d) Determine if the Markov chain is irreducible. (e) Does the Markov chain have an invariant probability distribution? Explain your answer. If the Markov chain has an invariant distribution, sav what it is.

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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Question

100%

fourth digit is 2

\ 3/10 3/10 2/5,
1. For this problem consider the following transition matrix for a Markov chain on the states 1,
2, and 3:
1
P = (p(i,j))i<ij<3
1
\n/20 п/20 1-п/10
where n is the fourth digit of your Emplid. [For instance, if the fourth digit of your Emplid
is 6, then the matrix you would use for this problem is
1
P =
1
3/10 3/10 2/5
(a) Write what P is based on your Emplid.
(b) Explain clearly why P is a stochastic matrix.
(c) Determine the period of each of the three states.
(d) Determine if the Markov chain is irreducible.
(e) Does the Markov chain have an invariant probability distribution? Explain your answer.
If the Markov chain has an invariant distribution, say what it is.

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