Genotypes AA, Aa, and aa occur with probabilities (1, 2, 3). For n = 3 independent observations,

Genotypes AA, Aa, and aa occur with probabilities (π1, π2, π3). For n = 3 independent observations, the observed frequencies are (n1, n2, n3).

a. Explain how you can determine n3 from knowing n1 and n2. Thus, the multinomial distribution of (n1, n2, n3) is actually two-dimensional.

b. Show the set of all possible observations, (n1, n2, n3) with n = 3.

c. Suppose (π1, π2, π3) = (0.25, 0.50, 0.25). Find the multinomial probability that (n1, n2, n3) = (1, 2, 0).

d. Refer to (c). What probability distribution does n1 alone have? Specify the values of the sample size index and parameter for that distribution.