Question: Problem 3 (LMS estimation) 3+3=6 points X is a standard Gaussian (Normal) random variable, i.e., X ~ N(0, 1). U is a standard Gaussian (Normal)

Problem 3 (LMS estimation) 3+3=6 points X is a standard Gaussian (Normal) random variable, i.e., X ~ N(0, 1). U is a standard Gaussian (Normal) random variable, i.e., U ~ N(0, 1), and is independent of X . Let Y = X + U . (a) What is the least mean-squared error (LMS) estimator for X given Y? (b) What is the variance of the estimation error

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