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