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Show that for any continuous random variable $X$ that takes only positive real values $\int_{0}^{\infty}\text{Pr}(X\geq x)dx=\mu$ where $\mu$ is the mean.

Pp..
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hello world
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    This question has been discussed many times on this forum. See, for example, [Intuition behind using complementary CDF to compute expectation for nonnegative random variables](http://math.stackexchange.com/questions/64186/intuition-behind-using-complementary-cdf-to-compute-expectation-for-nonnegative) – Dilip Sarwate Jan 30 '15 at 14:25

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$\int_{0}^{+\infty}\text{Pr}(X\geq x) dx = \int_{0}^{+\infty} \mathbf{E}[\mathbf{1}_{\{X\geq x\}}] dx = \ldots$ What can you say after ?

Olórin
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