"If X is non-negative, then E(X) = Integral(0 to infinity) of (1-F(x))dx, where F(x) is the cumulative distribution function of X."(adsbygoogle = window.adsbygoogle || []).push({});

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First of all, does X have to be acontinuousrandom variable here? Or will the above result hold for both continuous and discrete random variable X?

Secondly, the source that states this result gives no proof of it. I searched the internet but was unable to find a proof of it. I know that by definition, since X is non-negative, we have E(X) = Integral(0 to infinity) of x f(x)dx where f(x) is the density function of X. What's next?

Thanks for any help!

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# Statistics: E(X) = Integral(0 to infinity) of (1-F(x))dx

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