Question: Let X be a random variable having cumulative dis- tribution function F. Show that (i) E[X|? < o implies f{F(t)[1- F(t)]}P/2dt < o for

Let X be a random variable having cumulative dis- tribution function F.

Let X be a random variable having cumulative dis- tribution function F. Show that (i) E[X|? < o implies f{F(t)[1- F(t)]}P/2dt < o for p> 1; (ii) E|X|2+6 < o with some o > 0 implies f{F(t)[1 - F(t)]}/2dt

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