. For the Wright-Fisher Markov chain in Section 13.7.2, show that the probability that allele A becomes fixed is its initial relative frequency. [Hint: define πi = P(Xreaches 2N before reaching 0|X0 =...

.
For the Wright-Fisher Markov chain in Section 13.7.2, show that

the probability that allele A becomes fixed is its initial relative frequency.

[Hint: define

πi = P(Xreaches 2N before reaching 0|X0 = i),

with π0 = 0, π2N = 1. By conditioning on the value of X1, justify the following

equation satisfied by the πi:

and verify that πj = j/(2N) solves the equation.]

.
For the Wright-Fisher Markov chain in Section 13.7.2, find the

variance of Xn, and use this to verify (13.21).