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Past exam of the mathematics course of the University of Cambridge / 2025 / ia / Paper 2 / 4F / a / Solution

The number of stops is

X \sim Bin (n, 1/ n)

. For each fixed

k \geq 0

,

P (X = k) = (k n) n^{- k} (1 - n^{- 1})^{n - k} ⟶ \frac{e ^{- 1}}{k !},

the mass function of a Poisson random variable of mean one.

Solved by gpt-5.6-sol high.

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