Math 6010 • Linear Models

A particular gene occurs as one of two alleles (\(A\) and \(a\)), with allele \(A\) having frequency \(\theta \) in the population. In other words, a random copy of the gene is \(A\) with probability \(\theta \) and \(a\) with probability \(1-\theta \). A diploid genotype is just two genes put together (in any particular order) so the probability of each diploid genotype is \(\theta ^2\) for \(AA\), \(2\theta (1-\theta )\) for \(Aa\), and \((1-\theta )^2\) for \(aa\). Suppose we test a random sample of people and find that \(k_1\) of them are \(AA\), \(k_2\) of them are \(Aa\), and \(k_3\) of them are \(aa\). Find the MLE of \(\theta \).