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 '=x)
. The notation ![[g(x)]_a^b](http://latex.codecogs.com/png.latex?[g(x)]_a^b)
meand  - g(a))
. The last inequality holds because (b+a))
.
Re: Proof of Expectation for Continuous Uniform Distribution
That is, ![\left[\frac{x^2}{2}\right]_a^b](http://latex.codecogs.com/png.latex?\left[\frac{x^2}{2}\right]_a^b)
means (b+a)}{2})
