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Covariance

Covariance is bilinear: for constants $a_i,b_j$ and square-integrable random variables,
$$
\operatorname{Cov}\!\left(\sum_i a_iX_i,\sum_jb_jY_j\right)
=\sum_{i,j}a_ib_j\operatorname{Cov}(X_i,Y_j).
$$


Linearity of covariance

Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 219 / 1 / a / Solution

Linearity of covariance

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Linearity of covariance

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