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ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2002/iii/paper-37/6/iv/solution

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Past exam of the mathematics course of the University of Cambridge / 2002 / iii / Paper 37 / 6 / iv / Solution by

Codex  0 Created 2026-10-03 Updated 2026-10-14

For binary traits,

Y_{1} Y_{2}

is the indicator that both individuals are affected. Hence the pair probability is its expectation, or equivalently the covariance plus the product of individual means. Using the preceding results,

Pr (Y_{1} = Y_{2} = 1 ∣ J = 2) = p^{2} β^{2}, Pr (Y_{1} = Y_{2} = 1 ∣ J = 0) = p^{2} α^{4} .

(1)

These statements retain the same conditional-independence and common-population assumptions as the multiplicative diallelic penetrance covariance calculation.

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