# Expectation of a non negative random variable

For any non negative continuous random variable having distribution function $F(X)$ we have the followings:

1. 1.

$E[X]=\int_{0}^{\infty}Pr[X>t]dt$

2. 2.

$E[X^{r}]=r\int_{0}^{\infty}t^{r-1}Pr[X>t]dt$

3. 3.

$E[\min(X,T)]=T-\int_{0}^{\infty}F(T)dt$

4. 4.

$E[X|X where $T$ is a constant.

Title Expectation of a non negative random variable ExpectationOfANonNegativeRandomVariable 2013-03-22 19:10:52 2013-03-22 19:10:52 georgiosl (7242) georgiosl (7242) 7 georgiosl (7242) Theorem msc 60C05 msc 05A10 msc 60-00