Let Xn be the WrightFisher model with no mutation defined in Example 1.9. (a) Show that Xn

Question:

Let Xn be the Wright–Fisher model with no mutation defined in Example 1.9.

(a) Show that Xn is a martingale and use Theorem 5.14 to conclude that Px.VN <

V0/ D x=N.

(b) Showthat Yn D Xn.N  Xn/=.1  1=N /n is a martingale.

(c) Use this to conclude that

.N  1/ 

x.N  x/.1  1=N /n Px.0 < Xn < N/ 

N2 4

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