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For the given transistion matrix, find the probability that state 1 changes to state 2...

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cbromm | Honors

Posted July 29, 2013 at 1:07 AM via web

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For the given transistion matrix, find the probability that state 1 changes to state 2 after three repititions of the experiment.

C = [ .5      .5]

      [ .72   .28]

What is the probability state 1 changes to state 2 after three repetitions of the experiment?

Tagged with markov chain, math

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embizze | High School Teacher | (Level 1) Educator Emeritus

Posted July 29, 2013 at 1:33 AM (Answer #1)

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To find the probability that state 1 changes to state 2 after 3 repetitions of the experiment, we look at the entry in row 1 column 2 of the cube of the transition matrix.

(In general, the `ij^(th)` entry of `P^m` , where `P^(m)` is the m-step transition matrix, is the probability of a transition from state `i` to state `j` .)

`P=([.5,.5],[.72,.28])`

`P^3=([.5858,.4142],[.5964,.4035])`

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The probability of changing from state 1 tio state 2 after 3 repetitions is approximately .4142

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