Question: (Symmetric normal distribution) The random vector X = ( X u ...,Xp) f is said to have a symmetric normal distribution if it is distributed

(Symmetric normal distribution) The random vector X = ( X u ...,Xp) f is said to have a symmetric normal distribution if it is distributed as Np(p-,2), where p. = (p-i and

|| p P a. 1 PP P

that is, var(A",) = cr2, cov(Xi,Xj) = pa2 for all i 7^ j = 1 Let 0 be an orthogonal p x p matrix and be defined by

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and let ’y = (Yu- ~,YP)' = OX. Find F(Y ), cov(Y) and show Y U...,YP are independent.

|| p P a. 1 PP P

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