Show that if X and Y are independent, then Cov(X, Y) = Corr(X, Y) = 0.
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Now let's compute the covariance: $\text{Cov}(X, Y) = E[(X - E[X])(Y - E[Y])]$ $= E[XY - XE[Y] - E[X]Y + E[X]E[Y]]$ $= E[XY] - E[X]E[Y] - E[X]E[Y] + E[X]E[Y]$ Show more…
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