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Mathematics course of the University of Cambridge

Past exam of the mathematics course of the University of Cambridge

2023

Paper 320

Average the phase probability over the <thermal eccentricity distribution>:
$$
f_{\rm unbound}
=\int_0^1 2e\left(\frac12-\frac e\pi\right)de.
$$
Therefore
$$
\boxed{
f_{\rm unbound}=\frac12-\frac{2}{3\pi}
\simeq0.288}.
$$

Solution

Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 320 / 1 / d / Solution

Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 320 / 1 / d / Solution

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Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 320 / 1 / d / Solution

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