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Past exam of the mathematics course of the University of Oxford

2017

Prelims

Mathematics III

{c}

For <random variables> with finite second moments, the <variance of a sum> is
$$
\boxed{\operatorname{Var}\left(\sum_{i=1}^nX_i\right)=\sum_{i=1}^n\operatorname{Var}(X_i)+2\sum_{1\le i<j\le n}\operatorname{Cov}(X_i,X_j).}
$$
No <independence> assumption is needed.

Solution

Past exam of the mathematics course of the University of Oxford / 2017 / Prelims / Mathematics III / 6 / b / ii / Solution

Past exam of the mathematics course of the University of Oxford / 2017 / Prelims / Mathematics III / 6 / b / ii / Solution

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Past exam of the mathematics course of the University of Oxford / 2017 / Prelims / Mathematics III / 6 / b / ii / Solution

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