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Past exam of the mathematics course of the University of Oxford

2023

Prelims

Mathematics III

{c}

For a <random variable> with a <probability density function>, a singleton has zero probability:
$$
\boxed{\mathbb P(X=x)=\int_{\{x\}}f(t)\,dt=0.}
$$
Equivalently, its <cumulative distribution function> is <continuous>, so it has no jump at $x$.

Solution

Past exam of the mathematics course of the University of Oxford / 2023 / Prelims / Mathematics III / 6 / a / ii / Solution

Past exam of the mathematics course of the University of Oxford / 2023 / Prelims / Mathematics III / 6 / a / ii / Solution

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Past exam of the mathematics course of the University of Oxford / 2023 / Prelims / Mathematics III / 6 / a / ii / Solution

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