1. Genotypes AA, Aa and aa occur with probabilities [02/4,0(1 – 0/2), (1 – 0/2)²]. A multinomial sample of size n has frequencies (n1, N2, N3) of these three genotypes. (a) Write down and simplify the log-likelihood. (b) Show that the maximum likelihood estimate of 0 is Ô = the asymptotic standard error of ê. 2n1 +n2 == and find N1 N2 N3 (c) If n₁ = 12, n₂ = 20 and n3 = 18, conduct a score test of Ho: 0 = 1 against : H₁ 01 (reporting the test statistic and p-value), and find a score test based 95% confidence interval for 0.

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