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Consider a Markov chain {X,:n>0} with transition probability matrix: 1 2 3 4 states 0.3 0.7 1 P= 2 0.8 0.2 0.5 0.5 3 0.9 0.1 4 0.1 0.2 0 0.3 0.4 The limiting TT's are: TTo = 29 / 80, TI = 11 / 80, T2 = 7/ 32, TT3 = 9/ 32, TT4= 0 a) Determine the classes of this Markov chain. For each class state whether the class is transient or recurrent. Also, state the period of each class. CLASS PERIOD TRANSIENT or RECURRENT b) If we start in state 2, on average, how many transitions will it take to return to Express as an exact fraction. state 2?

Consider a Markov chain {X,:n>0} with transition probability matrix: 1 2 3 4 states 0.3 0.7 1 P= 2 0.8 0.2 0.5 0.5 3 0.9 0.1 4 0.1 0.2 0 0.3 0.4 The limiting TT's are: TTo = 29 / 80, TI = 11 / 80, T2 = 7/ 32, TT3 = 9/ 32, TT4= 0 a) Determine the classes of this Markov chain. For each class state whether the class is transient or recurrent. Also, state the period of each class. CLASS PERIOD TRANSIENT or RECURRENT b) If we start in state 2, on average, how many transitions will it take to return to Express as an exact fraction. state 2?

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Consider a Markov chain {X„:n>0} with transition probability matrix: 1 2 3 4 states 0.3 0.7 1 P = 2 0.8 0.2 0.5 0.5 3 0.9 0.1 4 0.1 0.2 0.3 0.4 The limiting TT's are: TTo = 29 / 80, TI = 11 / 80, TT2 = 7/ 32, TT3 = 9/32, TT4 = 0 a) Determine the classes of this Markov chain. For each class state whether the class is transient or recurrent. Also, state the period of each class. CLASS PERIOD TRANSIENT or RECURRENT b) If we start in state 2, on average, how many transitions will it take to return to state 2? Express as an exact fraction.
Transcribed Image Text:Consider a Markov chain {X„:n>0} with transition probability matrix: 1 2 3 4 states 0.3 0.7 1 P = 2 0.8 0.2 0.5 0.5 3 0.9 0.1 4 0.1 0.2 0.3 0.4 The limiting TT's are: TTo = 29 / 80, TI = 11 / 80, TT2 = 7/ 32, TT3 = 9/32, TT4 = 0 a) Determine the classes of this Markov chain. For each class state whether the class is transient or recurrent. Also, state the period of each class. CLASS PERIOD TRANSIENT or RECURRENT b) If we start in state 2, on average, how many transitions will it take to return to state 2? Express as an exact fraction.
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