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?
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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7
![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F753a8867-c4f0-498a-816a-438208e50376%2F32d5c9c7-865b-487b-b2dd-6f0604af3f5e%2Fkppvy5e_processed.png&w=3840&q=75)
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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