Q1 Let X ~ N(u, E) be a Gaussian random variable with mean / E Rd and covariance matrix E E Rdxd Assuming that E is invertible. Let a E Rd be a fixed vector, and Y = a X E R be a random variable. Calculate E[Y], Var(Y), E[X|Y = y], and Cov(X| Y = y) = E[XX |Y = y] - E[X|Y = y]E[X |Y = y]