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Let X be a random variable with E(X2) < and let Y = |X|. Suppose the probability density function f(x) of X is symmetric about

Let X be a random variable with E(X2) < and let Y = |X|. Suppose the probability density function f(x) of X is symmetric about zero, that is , f(-x) = f(x) , - < x< . Show that X and Y are uncorrelated, but they are not independent.

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