Question: Let X be a non-degenerate random variable realizing only positive values, such that X and Y = 1/X both have finite second moments. Show that

Let X be a non-degenerate random variable realizing only positive values, such that X and Y = 1/X both have finite second moments. Show that the correlation XY is negative.

Thus, although correlation is a measure of linear association, some non-linear associations

can be detected. Hint: Use Jensen's inequality to relate E[Y ] to E[X].

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