Please see the problem in the attachment.

2. Estimation of Gaussian Vector [10 points] Consider an ndimensional signal X modeled as a jointly Gaussian vector with zero mean and covariance matrix EX. 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 X m, and N is the noise vector which is modeled as jointly Gaussian with zero mean and covariance matrix 2 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