Estimation of Gaussian Vector Consider an n-dimensional signal X modeled as a jointly Gaussian vector with zero mean and covariance matrix X. Let Y denote the observation which is an n-dimensional vector and is related to X as Y = HX + N, where H is a known deterministic matrix of size n m, and N is the noise vector which is modeled as jointly Gaussian with zero mean and covariance matrix N . H can be thought of as the transfer function of the noisy medium that takes X and produces Y. It is assumed that X and N are independent. Find the MMSE estimate of X from Y.