Question

4. (Sheldon Ross) A DNA nucleotide has any one of four values {A, G,C,T). A standard model for a mutational change of the nucleotide at a specific location on the DNA strand, is a Markov model that assumes that from one time step to the next, the probability that the nucleotide remains unchanged equals 1-3α, for some α, 0 < α < 1 . If it does change (i.e., the nucleotide undergoes mutation), then it can change to any of the other three nucleotides with equal probability a. (a) Draw the state diagram (i.e., transition probability graph) of this Markov chain. (b) Determine the steady-state probability vector for this Markov chain (c) Prove that the n-step transition probability i (n) is given by ii(n

Answer 1

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