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Year 1 of the computer science course of the University of Oxford

Past exam of the year 1 of the computer science course of the University of Oxford

2016

Discrete mathematics, continuous mathematics and probability

Use the <covariance> identity and the <moments> from (ii):
$$
\operatorname{Cov}(X,X^2)=\mathbb E(X^3)-\mathbb E(X)\mathbb E(X^2)
=\frac14-\frac12\cdot\frac13=\boxed{\frac1{12}}.
$$
The positive value is consistent with both $X$ and $X^2$ increasing together on $[0,1]$.

Solution

Past exam of the year 1 of the computer science course of the University of Oxford / 2016 / Discrete mathematics, continuous mathematics and probability / 9 / a / iii / Solution

Past exam of the year 1 of the computer science course of the University of Oxford / 2016 / Discrete mathematics, continuous mathematics and probability / 9 / a / iii / Solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2016 / Discrete mathematics, continuous mathematics and probability / 9 / a / iii / Solution

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