Take two orthogonal vectors u, v ε R". u v, and let X = (Xi, , X,) be a vector of n iid standard Gaussians. Xi ~ N(0, 1), yl E「r

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3 years ago

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Take two orthogonal vectors u, v ε R". u v, and let X = (Xi, , X,) be a vector of n iid standard Gaussians. Xi ~ N(0, 1), yl E「r

). Let llr-〈II, X〉 and vr-(v, X〉, Are ux and vr independent? Hin: First try to see if they are correlated; you may use the fact that jointly normal random variables are independent iff. they are uncorrelated.

Mathematics

1 answer:

Semenov [28] · Answer 1 · 2022-03-28T01:27:40+03:00

Semenov [28]3 years ago

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Attached is the complete solution.