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Sep 5, 2019 at 13:38 comment added jld @JuanCorredor that is correct, they just need to have a diagonal covariance matrix which means they're uncorrelated. They certainly could also be independent but it's not required. I chose to use a multivariate Gaussian so in this case they are both uncorrelated and independent but independence wasn't required
Sep 5, 2019 at 13:37 comment added Juan Corredor So, the answer to my question is that $X_1,\ldots,X_r$ do not have to be independent?Thanks jld.
Sep 5, 2019 at 13:33 history answered jld CC BY-SA 4.0