= Solution
Let $G$ count copies of allele $2$. Under <Hardy-Weinberg equilibrium>, $G$ has a <binomial distribution> with parameters $2,\phi$, and the <penetrance> is $q_G=p\theta^G$. Consequently
$$
\begin{aligned}
\Pr(Y=1)
&=p(1-\phi)^2+\theta p\,2\phi(1-\phi)+\theta^2p\phi^2\\
&=p[(1-\phi)+\phi\theta]^2
=p\alpha^2.
\end{aligned}
$$
Thus \b[the overall penetrance is]
$$
\boxed{K=p\alpha^2,\qquad\alpha=1+\phi(\theta-1).}
$$
The <multiplicative diallelic penetrance> model requires $0\leq\phi\leq1$, $p\geq0$, $\theta\geq0$, and each occupied genotype's value $p\theta^G$ to be at most one. These are probabilities, not unrestricted relative-risk scores.
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