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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....

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 = σx2I and ∑w = σw2I 

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