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Feb 18, 2019 at 18:03 comment added Jochen Wengenroth That $E(X|Y)$ is Gaussian for a Gaussian $n+m$-dimensional vector $(X,Y)$ follows from the fact that uncorrelated components of $(X,Y)$ are independent -- no need to calculate densities. And I don't believe that sums of Gaussian distributed random variables are Gaussian (you need that the joint distribution is Gaussian).
Feb 18, 2019 at 13:57 answer added JPR timeline score: 1
Feb 18, 2019 at 11:39 comment added ABIM Updated, the trail of thought.... hopefully the proof sketch is clearer :)
Feb 18, 2019 at 11:38 history edited ABIM CC BY-SA 4.0
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Feb 18, 2019 at 10:24 history asked ABIM CC BY-SA 4.0