Solution

Past exam of the mathematics course of the University of Cambridge / 2019 / ia / Paper 2 / 11F / b / Solution

Every linear combination $a^TX$ of the coordinates of a <multivariate Gaussian distribution>[jointly normal random vector] is a <normal random variable>. Its mean is $a^T\mu$ and its variance is $a^T\Sigma a$.

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 Incoming links: Linear combination of jointly normal random variables