3. The transition matrix for a three-state Markov chain is 0 ||1 0 r llo q p+r Р P = q Where p, q> 0, r≥ 0 and p + q + r = 1 a. Draw the directed graph of the chain. b. Is the set {2,3} closed? Why or why not? c. Find the expression for Pn). Then verify that state 1 is positive recurrent. d. Show that the process has a unique stationary probability distribution = (1₁, 1₂, 13) tr

3. The transition matrix for a three-state Markov chain is 0 ||1 0 r llo q p+r Р P = q Where p, q> 0, r≥ 0 and p + q + r = 1 a. Draw the directed graph of the chain. b. Is the set {2,3} closed? Why or why not? c. Find the expression for Pn). Then verify that state 1 is positive recurrent. d. Show that the process has a unique stationary probability distribution = (1₁, 1₂, 13) tr

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.7: Applications

Problem 9EQ

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