There are 3 gene types S1, S2 and S3 in a large population. They each have the relative frequency of a^2, 2a(1-a) and (1-a)^2 respectively where "a" is the gene frequency. Suppose that in a random sample of size n, there x1, x2 and x3 of the three genotypes respectively. n=x1+x2+x3
What sort of distribution is this?
What is the probability function?
What is the likelihood, and loglikelihood of "a"?