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This answer explains how to calculate the variance of an average of n correlated random variables. How can I do it for a weighted average of n correlated random variables? My random variables are jointly multivariate Gaussian distributed.

This Answer explains how to do it for a weighted average of different realisations of a single random variable, where the weights are also realisations of a random variable. My weights are not random variables, but fixed numbers, so the problem is different.

I know that this is most likely a matter of pen-and-paper math, but I fear this problem is beyond my skills.

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