3. Genotypes AA, Aa and aa occur with probabilities (?1, ?2, ?3). 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-dimentional.
b. Show the set of all possible observations, (n1,n2,n3) with n=3
c. Suppose (x1,x2,x3) = (0.25,0.5,0.25). 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