4. For each of the below listed descriptions, provide the transition graph of a Markov Chain that satisfies them. Explain in a few sentences why your example has the properties. If such an example does not exist, explain why: (a) A 2 state Markov Chain without limiting distribution but with at least one stationary distribution. (b) A 2 state Markov Chain with limiting distribution. Determine it. (c) An irreducible 4 state Markov Chain which is not aperiodic. (d) An irreducible 3 state Markov Chain which is aperiodic. (e) An irreducible 4 state Markov Chain which is aperiodic and such that the expected return time to state 1 is infinite (i.e. E[T₁|X0 = 1] = ∞.). (f) A Markov Chain with more than one communication class and a limiting distribution.
4. For each of the below listed descriptions, provide the transition graph of a Markov Chain that satisfies them. Explain in a few sentences why your example has the properties. If such an example does not exist, explain why: (a) A 2 state Markov Chain without limiting distribution but with at least one stationary distribution. (b) A 2 state Markov Chain with limiting distribution. Determine it. (c) An irreducible 4 state Markov Chain which is not aperiodic. (d) An irreducible 3 state Markov Chain which is aperiodic. (e) An irreducible 4 state Markov Chain which is aperiodic and such that the expected return time to state 1 is infinite (i.e. E[T₁|X0 = 1] = ∞.). (f) A Markov Chain with more than one communication class and a limiting distribution.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Please solve completely part a-c
![4.
For each of the below listed descriptions, provide the transition graph of a Markov
Chain that satisfies them. Explain in a few sentences why your example has the properties. If
such an example does not exist, explain why:
(a) A 2 state Markov Chain without limiting distribution but with at least one stationary
distribution.
(b) A 2 state Markov Chain with limiting distribution. Determine it.
(c) An irreducible 4 state Markov Chain which is not aperiodic.
(d) An irreducible 3 state Markov Chain which is aperiodic.
(e) An irreducible 4 state Markov Chain which is aperiodic and such that the expected return
time to state 1 is infinite (i.e. E[T₁|X0 = 1] = ∞.).
(f) A Markov Chain with more than one communication class and a limiting distribution.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffe4f043a-40ec-446c-a7ff-f52648c59722%2Fd65fcf6f-a3f9-404b-a8d3-6deebab5a2af%2Fqk2bzf_processed.png&w=3840&q=75)
Transcribed Image Text:4.
For each of the below listed descriptions, provide the transition graph of a Markov
Chain that satisfies them. Explain in a few sentences why your example has the properties. If
such an example does not exist, explain why:
(a) A 2 state Markov Chain without limiting distribution but with at least one stationary
distribution.
(b) A 2 state Markov Chain with limiting distribution. Determine it.
(c) An irreducible 4 state Markov Chain which is not aperiodic.
(d) An irreducible 3 state Markov Chain which is aperiodic.
(e) An irreducible 4 state Markov Chain which is aperiodic and such that the expected return
time to state 1 is infinite (i.e. E[T₁|X0 = 1] = ∞.).
(f) A Markov Chain with more than one communication class and a limiting distribution.
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