6.2.19 (Hardy-Weinberg law) The Hardy-Weinberg law in genetics says that the proportions of genotypes AA, Aa, and aa are ? 2, 2? (1 ? ?), and (1 ? ? )2, respectively, where ? ? [0, 1]. Suppose that in a sample of n from the population (small relative to the size of the population), we observe x1 individuals of type AA, x2 individuals of type Aa, and x3 individuals of type aa. (a) What distribution do the counts (X1, X2, X3) follow? (b) Record the likelihood function, the log-likelihood function, and the score function for ?.

6.2.19 (Hardy-Weinberg law) The Hardy-Weinberg law in genetics says that the pro- portions of genotypes AA, Aa, and aa are 02, 20 (1 - 0), and (1 - 0), respectively, where O E [0, 1]. Suppose that in a sample of n from the population (small relative to the size of the population), we observe x1 individuals of type AA, x2 individuals of type Aa, and x3 individuals of type aa. (a) What distribution do the counts (X1, X2, X3) follow? (b) Record the likelihood function, the log-likelihood function, and the score function for O. (c) Record the form of the MLE for 0