Let X denote an n dimensional random vector with a multivariate normal distribution with mean vector 0 and covariance matrix give by 2 l n Let M 1 and M 2 denote orthogonal linear subspace or R n and let P j denote the matrix representation orthogonal projection onto M j , j 1,2 Find the distribution of XT PIX XT PX

Question: Let X denote an n-dimensional random vector with a multivariate normal distribution with mean vector 0 and covariance matrix give by ? 2 l n

Let X denote an n-dimensional random vector with a multivariate normal distribution with mean vector 0 and covariance matrix give by ? ² l _n . Let M ₁ and M ₂ denote orthogonal linear subspace or R ⁿ and let P _jdenote the matrix representation orthogonal projection onto M _j , j=1,2. Find the distribution of

XT PIX XT PX

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