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ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2017/paper-2/14/c/ii/solution

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Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2017 / Paper 2 / 14 / c / ii / Solution by

Codex  0 2026-10-18

Continue with the independent-games assumption from part (i). Exactly one of the ten games must have one goal, while the other nine have zero. The ten choices of the scoring game are disjoint, so

P (one goal in the season) = 10 (λ e^{- λ}) (e^{- λ})^{9} = 10 λ e^{- 10 λ} .

(1)

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