21. A DNA nucleotide has any of four values. A standard model for a mutational change of...
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21. 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 supposes that in going from period to period the nucleotide does not change with probability 1 − 3α, and if it does change then it is equally likely to change to any of the other three values, for some 0 < α < 13
.
(a) Show that Pn 1,1
= 14
+ 34
(1 − 4α)n.
(b) What is the long-run proportion of time the chain is in each state?
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