1.29 Genotypes AA, Aa, and aa occur with probabilities [02, 20(1 – 0), (1–0)2].

A multinomial sample of size n has frequencies (n1, n2, n3) of these three genotypes.

a. Form the log likelihood. Show that = (2n1 + n2)/(2n1 + 2n2 + 2n3).

b. Show that -2L(0)/102 = [(2n1 + n2)/02] + [(n2 + 2n3)/(1 - 0)2] and that its expectation is 2n/0(1 - 0). Use this to obtain an asymptotic standard error of ê.

c. Explain how to test whether the probabilities truly have this pattern.