An often forgotten formula for the mean of a random variable $X$ is given by:

$\displaystyle \mu=E(X)=\sum_{x=0}^{\infty} \Big(1-F(x)\Big)$

And for the continous case:

$\displaystyle \mu=E(X)=\int_{x=0}^{\infty} \Big(1-F(x)\Big)$

This blog post is going to illustrate how these formulas arise.

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