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For each of the following statements, explain whether it is true or false. If you think it is true, then prove why you think it

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For each of the following statements, explain whether it is true or false. If you think it is true, then prove why you think it is always true. If you believe it is false, then giving a counterexample is sufficient. (a) If the posterior distribution is symmetric, then the MAP and LMS estimators coincide. (b) Let X and Y be two discrete random variables. If P(X > Y ) > 0.5, then E[X] > E[Y ]

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