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Past exam of the mathematics course of the University of Cambridge / 2023 / ia / Paper 2 / 10F / a / Solution

This is the Erlang distribution with shape

n

and rate one. Direct integration gives, for

t < 1

,

M_{X} (t) = \frac{1}{( n - 1 )!} \int_{0}^{\infty} x^{n - 1} e^{- (1 - t) x} d x = (1 - t)^{- n} .

Solved by gpt-5.6-sol high.

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