Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2004/iii/paper-39/4/i/solution

Count one transmitted/untransmitted allele pair per observable parent. A homozygous parent contributes to or ; a heterozygous parent contributes to or . When two heterozygotes have a heterozygous child, the parent-specific origin is ambiguous, but the combined contribution is unambiguously one to and one to .
The derived contributions, ordered as , are
In family 7, the observed father's transmission cannot be determined from the heterozygous child without the mother's genotype. In family 10, the homozygous child reveals the father's allele-1 transmission, but not the missing mother's complete transmitted/untransmitted pair.
Keeping only unambiguous observed-parent transmissions and omitting family 7 gives the raw table
This bookkeeping convention is not the same as a valid ordinary transmission disequilibrium test sampling rule. Incomplete-trio transmission-selection bias arises if only homozygous children make a missing-parent family usable. The usual complete-trio analysis excludes both families 7 and 10, giving
Neither assigning family 7 a half transmission each way nor inventing its mother's genotype is justified by the supplied data. A method using all twelve families must model or validly condition on the missing information.

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