 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ii/paper-4/27k/c/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

E S = \int_{R^{d}} g (u) λ (u) d u .

Expanding

S^{2}

separates equal and distinct Poisson points. The factorial-moment formula gives

E S^{2} = \int g (u)^{2} λ (u) d u + (\int g (u) λ (u) d u)^{2} .

Subtracting the square of the mean yields

var S = \int_{R^{d}} g (u)^{2} λ (u) d u .

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