Expectation of a non negative random variable
For any non negative continuous random variable having distribution function^{} $F(X)$ we have the followings:

1.
$E[X]={\int}_{0}^{\mathrm{\infty}}Pr[X>t]dt$

2.
$E[{X}^{r}]=r{\int}_{0}^{\mathrm{\infty}}{t}^{r1}Pr[X>t]dt$

3.
$E[\mathrm{min}(X,T)]=T{\int}_{0}^{\mathrm{\infty}}F(T)\mathit{d}t$

4.
$$ where $T$ is a constant.
Title  Expectation of a non negative random variable 

Canonical name  ExpectationOfANonNegativeRandomVariable 
Date of creation  20130322 19:10:52 
Last modified on  20130322 19:10:52 
Owner  georgiosl (7242) 
Last modified by  georgiosl (7242) 
Numerical id  7 
Author  georgiosl (7242) 
Entry type  Theorem 
Classification  msc 60C05 
Classification  msc 05A10 
Classification  msc 6000 