# How to prove the folowing theorem in probablity? [duplicate]

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.

## marked as duplicate by Shaun, Dilip Sarwate, kingW3, Davide Giraudo, apnortonJan 30 '15 at 14:56

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