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September 26th, 2013, 03:24 AM   #1
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Expected value and markov chains

I have a transition and initial state matrix -

[attachment=0:295kjxtl]Tmatrix.jpg[/attachment:295kjxtl]

Where the top row of the state matrix is the probability of seeing film A, and the bottom row the probability of seeing film B.

The question I have been given is - "Given that a couple initially see film B, what is the expected number of times that they will see film B together over the next 4 trips to the theater?" So rising the transition matrix to a power 'n' and multiplying it by the initial state will give me the probability of them seeing either film the 'nth' time they go to the theater. I wondering how to get the expected value out of that. Is it simply summing up the probabilities and multiplying that by 4?

Thanks in advance,
- deSitter
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September 28th, 2013, 01:08 AM   #2
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Re: Expected value and markov chains

Anybody have any thoughts? I would've thought the expected value would be fairly simple to find out, as a binomial distribution is just n * p.
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