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  1. mathematics
  2. statistics
  3. consider the following markov chain: 0 1

Consider the following Markov chain: 0 1 2 3 0 0.3 0.5 0 0.2 1 0.5 0.2 0.2 0.1 2 0.2 0.3 0.4 0.1 3 0.1 0.2 0.4 0.3 What is the probability that the first passage time from 2 to...

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Question

Statistics

Consider the following Markov chain:

0

1

2

3

0

0.3

0.5

0

0.2

1

0.5

0.2

0.2

0.1

2

0.2

0.3

0.4

0.1

3

0.1

0.2

0.4

0.3

  1. What is the probability that the first passage timefrom 2 to 1 is 3?
  2. What is the expected first passage time from 2 to1?
  3. What is the expected first passage time from 2 to 2(recurrence time for 2)? What is the relation between thisexpectation and the steady-state probability of being at state2?

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