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Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 4 / 27K / c / Solution

Mark a virus at distance

r \leq R

if its uniform radius exceeds

r

, with probability

1 - r / R

. Marked Poisson thinning gives a Poisson count with mean

2 πλ \int_{0}^{R} r (1 - r / R) d r = λπ R^{2} /3.

Solved by gpt-5.6-sol high.

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