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February 14th, 2013, 12:41 AM  #1 
Newbie Joined: Feb 2013 Posts: 1 Thanks: 0  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? 
February 14th, 2013, 01:02 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,756 Thanks: 696  Re: Markov Chains problem
Have you checked the eigenvector? It doesn't look right to me. (Check Ax = x).


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