= Solution
Call the parent <genotype> $g$ and child <genotype> $h$, each in $\{0,1\}$. Define
$$
a_g=P(X_p\mid G_p=g),\quad p_g=P(G_p=g),\quad
b_h=P(X_c\mid G_c=h),\quad t_{h\mid g}=P(G_c=h\mid G_p=g).
$$
There is one <pedigree founder> and one nonfounder, so
$$
\boxed{L=\sum_{g=0}^1\sum_{h=0}^1 a_gp_gb_ht_{h\mid g}.}
$$
Explicitly this is $a_0p_0b_0t_{0\mid0}+a_0p_0b_1t_{1\mid0}+a_1p_1b_0t_{0\mid1}+a_1p_1b_1t_{1\mid1}$. The genotype-transmission model can be arbitrary for the single-parent species; no two-parent Mendelian assumption is being introduced.
Back to article page
