# proof of expectation with CDF

• Mar 15th 2009, 05:08 AM
proof of expectation with CDF
Hey guys! I need help in completing the proof.
The proof starts like this
$E[X]=E[X^+]-E[X^-]=\int_{0}^{\infty} xdF_x^+(x)\, dx - \int_{0}^{\infty} xdF_x^-(x)\,dx$
$= \int_{-\infty}^{\infty} xdF_x(x)\, dx
$

I cant find the reason for the last line. Please give me a clue.
• Mar 16th 2009, 12:21 AM
$\int_a^b f(x)dx=-\int_b^a f(x)dx$, and try to work from there using the properties of the propability function ;)