Past exam of the mathematics course of the University of Cambridge / 2006 / iii / Paper 45 / 1 / d / Solution

Call the parent genotype $g$ and child genotype $h$, each in $\{0,1\}$. DefineThere is one pedigree founder and one nonfounder, soExplicitly this is $a_0{p}_0{b}_0{t}_{0\mid 0}+a_0{p}_0{b}_1{t}_{1\mid 0}+a_1{p}_1{b}_0{t}_{0\mid 1}+a_1{p}_1{b}_1{t}_{1\mid 1}$. The genotype-transmission model can be arbitrary for the single-parent species; no two-parent Mendelian assumption is being introduced.