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Let X and Y be independent but not identically distributed two p-dimensional normal random vectors such that X~Np(ux Ex) and Y~Np(uy,Ey) Further, X and Y

Let X and Y be independent but not identically distributed two p-dimensional normal random vectors such that X~Np(ux Ex) and Y~Np(uy,Ey) Further, X and Y have a zero- covariance matrix, that is E[(X - #x)(Y - @y)T] = Opxp where E[:] denotes the expectation operator. What is the distribution of X CY where C is ap Xp matrix:

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