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Past exam of the mathematics course of the University of Cambridge / 2025 / ia / Paper 2 / 12F / a / Solution

Direct integration of the gamma density gives, for

t < 1

,

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

Solved by gpt-5.6-sol high.

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