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Mathematics course of the University of Cambridge

Past exam of the mathematics course of the University of Cambridge

2022

Paper 4

Generate $U\sim\operatorname{Uniform}[0,1]$ and set
$$
X=-\log U.
$$
For $x\geq0$,
$$
\mathbb P(X\leq x)
=\mathbb P(U\geq e^{-x})
=1-e^{-x},
$$
which is the distribution function of an <exponential distribution> with rate one. This is <inverse transform sampling>.

Solution

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

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

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

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