Consider a Markov chain {Xn}n≥0 having the following transition diagram: For this chain, there are two recurrent classes R1 = {6, 7} and R2 = {1, 2, 5}, and one transient class R3 = {3, 4}. Find the period of state Find f33 and f22. Starting at state 3,
Consider a Markov chain {Xn}n≥0 having the following transition diagram: For this chain, there are two recurrent classes R1 = {6, 7} and R2 = {1, 2, 5}, and one transient class R3 = {3, 4}. Find the period of state Find f33 and f22. Starting at state 3,
A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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- Consider a Markov chain {Xn}n≥0 having the following transition diagram:
For this chain, there are two recurrent classes R1 = {6, 7} and R2 = {1, 2, 5}, and one transient class R3 = {3, 4}.
- Find the period of state
- Find f33 and f22.
- Starting at state 3, find the probability that the chain is absorbed into R1.
- Starting at state 3, find the mean absorbation time, i.e., the expected number of steps that the chain is absorbed into R1 or R2.
Note: there are missing transition probabilities for this chain, but no impact for your solution.
![1
2
5
1/2
1/4
3
4
1/2
1/4
7](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F08fa459e-ef9c-4a03-ae4d-eec34cd6e45d%2F6149c4eb-92bb-43ea-9a43-94fc63ca6e80%2Fn5bnsfg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1
2
5
1/2
1/4
3
4
1/2
1/4
7
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