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Consider the pair of bivariate Gaussian random variables, X and Y, where µX = 0. The MMSE estimator for Y in terms of X is YMMSE(X) = 2.
(a) What is E[Y]?
(b) Specify whether X and Y are correlated, uncorrelated, or there isn't enough information to make this determination. Explain.
(c) Specify whether X and Y are independent, dependent, or there isn't enough information to make this determination. Explain.
(d) What is the MMSE estimator of X in terms of Y, XMMSE(Y)?
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