Proof of Expectation for Continuous Uniform Distribution

Hi everyone, I have been looking at some proofs recently and came across this one for the expectation of a Continuous Uniform Distribution. Not sure how it was done, and was wondering if anybody could guide me through the steps, and if there are any extra workings so that I can understand it better?

If X ~ U(a,b), then:

E(X) = http://www.mathsrevision.net/alevel/...xpectation.GIF

Any help would be very much appreciated

Re: Proof of Expectation for Continuous Uniform Distribution

Which of the four equalities don't you understand?

Re: Proof of Expectation for Continuous Uniform Distribution

the last three really. I am rusty with my calculus, and was hoping somebody could explain the process of how they moved from one to the next.

Re: Proof of Expectation for Continuous Uniform Distribution

The second inequality uses the Fundamental Theorem of Calculus because . The notation meand . The last inequality holds because .

Re: Proof of Expectation for Continuous Uniform Distribution

That is, **means**