Question: Let X 0 a.s. be a random variable on some probability space (, F, P ). Let : [0, ) R be absolutely continuous i.e.,

Let X 0 a.s. be a random variable on some probability space (, F, P ). Let : [0, ) R be absolutely continuous i.e., (x) = x 0 (t) dt. Using the approach we used in class (via Fubini's theorem) show the following version of transformation formula: E[ (X) ] = 0 P[ X > t ] (t) dt = 0 P[ X t ] (t) d

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