Variance for a Linear Transformation
How do we calculate $\mathrm{Var}(a^\top X)$?
Answer
If $X$ is a random vector with covariance matrix $\Sigma$, then
\[
\mathrm{Var}(a^\top X) = a^\top \Sigma a.
\]
Notes and comments
Comment 1: Basically the sum of all entries of the covariance matrix.