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February 14th, 2013, 12:41 AM   #1
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Markov Chains problem

Suppose a gene in a chromosome is of type A or type B. Assume that the probability that a gene of type A will mutate to type B in one generation is 10^-4 and that the gene of type B will mutate to type A is 10^-6.

(i) What is the transition matrix?

99.9999 0.0001
0.000001 99.999999

(ii) After many generations, what is the probability that the gene will be of type A? Of type B?

I have to find the stationary matrix.
This is the stationary matrix that I got:

[1.000000101 -0.100000101]

The stationary matrix looks really strange to me because there is one entry (Type A Gene) that has MORE THAN 100% chance of happening. Is this possible?
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February 14th, 2013, 01:02 PM   #2
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Re: Markov Chains problem

Have you checked the eigenvector? It doesn't look right to me. (Check Ax = x).
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