Suppose x has a symmetric distribution about zero and

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Suppose X has a symmetric distribution about zero, and let Y X 2 . Then E Y | X X 2 E Y Var X (a number). But Cov X , Y E X 3 0. At this point, we can summarize what we know about the three kinds of dependence we have discussed: X and Y independent E Y | X E Y E Y | X E Y Cov X , Y 0 But neither of the reverse implications holds. 50
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