Consider the revision L() = G1 Gn i Pen(Xi | Gi)1{Gi=g} j Prior(Gj ) {k,l,m} Tran(Gm | Gk, Gl) of

Consider the revision L(β) =

G1

···

Gn



i Pen(Xi | Gi)β1{Gi=g}

×



j Prior(Gj ) 

{k,l,m}

Tran(Gm | Gk, Gl)

of the likelihood expression (7.1), where β is an artificial parameter and g is a fixed genotype. Prove that d dβ lnL(1) is the expected number of people in the pedigree with genotype g conditional on the observed phenotypes in the pedigree. Note that this device is easy to implement in a good pedigree analysis program with the ability to compute partial derivatives numerically. Suggest at least one other interesting conditional expectation that one could compute by this technique.