Assume that a large number n of d-dimensional samples has been chosen from a multidimensional Gaussian, is an arbitrary positive definite covariance matrix.
(a) Prove that the distribution of the criterion function Je(1) given in Eq. 82 is normal with mean ndσ2. Express σ in terms of Σ.
(b) Prove that the variance of this distribution is
(c) Consider a suboptimal partition of the Gaussian by a hyperplane through the sample mean. Show that for large n, the sum of squared error for this partiction is approximately normal with mean and variance where σ is given in part (a).