Question: 8.23. Suppose that X and Y are two random variables for which the LMMSE estimator n = ax +b of Y in terms of X

8.23. Suppose that X and Y are two random

8.23. Suppose that X and Y are two random variables for which the LMMSE estimator n = ax +b of Y in terms of X is i = 3X. For each of the following parts, say whether the given statement is true or false. For a true statement, give a brief but convincing explanation; for a false statement, give a counterexample or convincing explanation. (a) It must be the case that X and Y both have mean value 0. (b) It must be the case that the LMMSE estimator of X in terms of Y is We = {y. (c) It must be the case that E[Y|X = 2] = 6. (d) It must be the case that the LMMSE estimator of Z=2Y + 7 in terms of X is e = 6X +7. 8.23. Suppose that X and Y are two random variables for which the LMMSE estimator n = ax +b of Y in terms of X is i = 3X. For each of the following parts, say whether the given statement is true or false. For a true statement, give a brief but convincing explanation; for a false statement, give a counterexample or convincing explanation. (a) It must be the case that X and Y both have mean value 0. (b) It must be the case that the LMMSE estimator of X in terms of Y is We = {y. (c) It must be the case that E[Y|X = 2] = 6. (d) It must be the case that the LMMSE estimator of Z=2Y + 7 in terms of X is e = 6X +7

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