 Solution

Let $G$ count copies of allele $2$. Under Hardy-Weinberg equilibrium, $G$ has a binomial distribution with parameters $2,\varphi$, and the penetrance is $q_G=p{\theta }^G$. ConsequentlyThus the overall penetrance isThe multiplicative diallelic penetrance model requires $0\le \varphi \le 1$, $p\ge 0$, $\theta \ge 0$, and each occupied genotype's value $p{\theta }^G$ to be at most one. These are probabilities, not unrestricted relative-risk scores.