Question: 21. Let X be a continuous random variable with probability density function f . Show that if E(X) exists; that is, if #

21. Let X be a continuous random variable with probability density function f . Show that if E(X) exists; that is, if # ∞ −∞ |x|f (x) dx < ∞, then lim x→−∞ xP (X ≤ x) = lim x→∞ xP (X > x) = 0.

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