Let X and Y be nonnegative random variables with an
Chapter , Problem 17(choose chapter or problem)
Let X and Y be nonnegative random variables with an arbitrary joint probability distribution function. Let I (x, y) = B 1 if X > x, Y > y 0 otherwise. (a) Show that E 0 E 0 I (x, y) dx dy = XY. (b) By calculating expected values of both sides of part (a), prove that E(XY ) = E 0 E 0 P (X > x, Y > y) dx dy. Note that this is a generalization of the result explained in Remark 6.4.
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