(Wright–Fisher model). Consider the chain described in Example 1.7.

p.x; y/ D N y !

.[1]x /y.1 [1] [1]x/N[1]y where [1]x D .1 [1] u/x=N C v.N [1] x/=N.

(a) Show that if u; v > 0, then limn!1 pn.x; y/ D .y/, where is the unique stationary distribution. There is no known formula for .y/, but you can

(b) compute the mean D Py y.y/ D limn!1 ExXn.