Question: If two jointly Gaussian random vectors X and Y are uncorrelated, show that they are also independent. (BONUS) Will this be true if X

If two jointly Gaussian random vectors X and Y are uncorrelated, show

If two jointly Gaussian random vectors X and Y are uncorrelated, show that they are also independent. (BONUS) Will this be true if X and Y are not jointly Gaussian but marginally Gaussian?

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