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.