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 ? 3?, for some ?, 0

| Sheldon Ross) A DNA nucleotide has any one of four values (A. G. C. I'. 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 - 3 0, for some {. O _ _ _ I . 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 graphs of this Markov chain . Ibj Determine the steady - state probability vector for this Markay chain . (c) Prove that the A - step transition probability my I !'' ) is given by = \\[ willy 2 + = 1 1 - 40)" , 1 = 1