5. Consider a Markov chain (Xn) with the state space S = {0, 1, 2,...} of non-negative integers and the one-step transition probabilities given by p(i, i + 1) =p and p(i, 0) = 1-p for i > 0, where p= (0, 1). (a) Identify the closed irreducible sets. (b) Is the Markov chain aperiodic? (c) Is there a stationary distribution? Is it unique? Compute the stationary distribution if it exists. (d) Find the transient states and recurrent states. (e) Compute E; [Ti] = E[Ti|Xo = i] for each i≥ 0, where T; is the (usual) first return time.
5. Consider a Markov chain (Xn) with the state space S = {0, 1, 2,...} of non-negative integers and the one-step transition probabilities given by p(i, i + 1) =p and p(i, 0) = 1-p for i > 0, where p= (0, 1). (a) Identify the closed irreducible sets. (b) Is the Markov chain aperiodic? (c) Is there a stationary distribution? Is it unique? Compute the stationary distribution if it exists. (d) Find the transient states and recurrent states. (e) Compute E; [Ti] = E[Ti|Xo = i] for each i≥ 0, where T; is the (usual) first return time.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![5. Consider a Markov chain (Xn) with the state space S = {0, 1, 2,...} of non-negative integers
and the one-step transition probabilities given by p(i, i + 1) = p and p(i, 0) = 1 - p for i ≥ 0,
where p € (0, 1).
(a) Identify the closed irreducible sets.
(b) Is the Markov chain aperiodic?
(c) Is there a stationary distribution? Is it unique? Compute the stationary distribution if
it exists.
(d) Find the transient states and recurrent states.
(e) Compute E; [Ti] = E[Ti|Xo = i] for each i≥ 0, where T; is the (usual) first return time.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffdd2c166-8196-40eb-9536-745216d6fb07%2F5adeb716-4795-44db-afdf-e59111aa3f2d%2Fjk0vsnt_processed.jpeg&w=3840&q=75)
Transcribed Image Text:5. Consider a Markov chain (Xn) with the state space S = {0, 1, 2,...} of non-negative integers
and the one-step transition probabilities given by p(i, i + 1) = p and p(i, 0) = 1 - p for i ≥ 0,
where p € (0, 1).
(a) Identify the closed irreducible sets.
(b) Is the Markov chain aperiodic?
(c) Is there a stationary distribution? Is it unique? Compute the stationary distribution if
it exists.
(d) Find the transient states and recurrent states.
(e) Compute E; [Ti] = E[Ti|Xo = i] for each i≥ 0, where T; is the (usual) first return time.
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