A DNA nucleotide has any of four values. A standard model for a mutational change of...

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A DNA nucleotide has any of four values. A standard model for a mutational change of the nucleotide at a specific location is a Markov chain model that sup- poses that in going from period to period the nucleotide does not change with probability 1-3a, and if it does change then it is equally likely to change to any of the other three values, for some 0 < a < }. (a) Show that P = +(1-4a)". (b) What is the long-run proportion of time the chain is in each state? A DNA nucleotide has any of four values. A standard model for a mutational change of the nucleotide at a specific location is a Markov chain model that sup- poses that in going from period to period the nucleotide does not change with probability 1-3a, and if it does change then it is equally likely to change to any of the other three values, for some 0 < a < }. (a) Show that P = +(1-4a)". (b) What is the long-run proportion of time the chain is in each state?