Friday, August 30, 2019

probability - Expectation of nonnegative Random Variable





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Can someone help me give me some pointers as to how to prove this relation?


Answer



Let p be the probability measure. We have that 0[1F(x)]dx=0Pr[X>x]dx=0[1X>xdp]dx using Fubini's theorem we have 0[1X>xdp]dx=[01X>xdx]dp=Xdp=E[X]


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