# [SOLVED] Expectation and Cumulative Distribution Function

• October 31st 2008, 06:32 AM
akolman
[SOLVED] Expectation and Cumulative Distribution Function
I need help with the following problem.

Let $X$ be a continuous random variable with pdf $f(x)$ that is positive provided $0, and is equal to zero elsewhere. Show that

$E(X)= \int ^b _0 [1-F(x)]dx$ where $F(x)$ is the cdf of $X$.

• October 31st 2008, 01:59 PM
mr fantastic
Quote:

Originally Posted by akolman
I need help with the following problem.

Let $X$ be a continuous random variable with pdf $f(x)$ that is positive provided $0, and is equal to zero elsewhere. Show that

$E(X)= \int ^b _0 [1-F(x)]dx$ where $F(x)$ is the cdf of $X$.