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regular markov chains

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 a gene of type B will mutate to type A is 10^-6.

(A) What is the transition matrix?
(B) After how many generations, what is the probability that the gene will be of type A? of Type B? (Find the stationary matrix)

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This solution is comprised of a detailed explanation to answer what is the transition matrix.