Past exam of the mathematics course of the University of Cambridge / 2003 / iii / Paper 40 / 6 / c / Solution

For the usual no-linkage reference model with unrelated, noninbred parents, define $J$ as the number of homologous allele copies shared identical by descent by two full siblings at the marker. The two siblings receive the same paternal copy with probability $1/2$, and independently receive the same maternal copy with probability $1/2$. Therefore Mendelian IBD sharing of full siblings givesHenceFor affected siblings, absence of genetic linkage makes the marker transmissions independent of selection by disease, so these are the relevant null moments. This is a fresh outbred reference calculation, not an application of these sharing probabilities to the inbred siblings $E,F$ in part (b). Without the outbred-parent assumption the three ordinary sharing probabilities require modification.