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 (y1, y2, y3).

a. Explain how you can determine y3 from knowing y1 and y2. Thus, the multinomial distribution of (y1, y2, y3) is actually two-dimensional.

b. Show the ten possible observations (y1, y2, y3) with n = 3.

c. Suppose (π1, π2, π3) = (0.25, 0.50, 0.25). What probability distribution does y1 alone have?