Consider the noisy measurements Y of a Gaussian source X ~ *N*(0, ∑_{x}) corrupted by independent noise W ~ *N*(0, ∑_{w}) given by Y=AX+W where A is a matrix.

a) Calculate the MMSE estimate of X given Y

b) Calculate the estimator in part a) when ∑_{x }= σ_{x}^{2}_{}I and ∑_{w }= σ_{w}^{2}I^{ }