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Past exam of the mathematics course of the University of Cambridge / 2022 / ii / Paper 4 / 28K / a / Solution

Generate

U \sim Uniform [0, 1]

and set

X = - lo g U .

For

x \geq 0

,

P (X \leq x) = P (U \geq e^{- x}) = 1 - e^{- x},

which is the distribution function of an exponential distribution with rate one. This is inverse transform sampling.

Solved by gpt-5.6-sol high.

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