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2. [Linear MMSE Estimation] Suppose Y is estimated by a linear estimator, L(X1, X2) = a + bX1 + cX2, such that X1 and X2
2. [Linear MMSE Estimation] Suppose Y is estimated by a linear estimator, L(X1, X2) = a + bX1 + cX2, such that X1 and X2 have mean zero and are uncorrelated with each other. (a) Determine a, b and c to minimize the MSE, E[(Y - (a + bX1 + cX2))"]. Express your answer in terms of E[Y], the variances of X1 and X2, and the covariances Cov(Y, X1) and Cov(Y, X2). (b) Express the MSE for the estimator found in part (a) in terms of the variances of X1, X2, and Y and the covariances Cov(Y, X1) and Cov(Y, X2)
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