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Math Help - Proof of Expectation for Continuous Uniform Distribution

  1. #1
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    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) =

    Any help would be very much appreciated
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  2. #2
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    Re: Proof of Expectation for Continuous Uniform Distribution

    Which of the four equalities don't you understand?
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  3. #3
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    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.
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  4. #4
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    Re: Proof of Expectation for Continuous Uniform Distribution

    The second inequality uses the Fundamental Theorem of Calculus because (x^2/2)'=x. The notation [g(x)]_a^b meand g(b) - g(a). The last inequality holds because b^2-a^2=(b-a)(b+a).
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  5. #5
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    Re: Proof of Expectation for Continuous Uniform Distribution

    That is, \left[\frac{x^2}{2}\right]_a^b means \frac{b^2}{2}- \frac{a^2}{2}= \frac{b^2- a^2}{2}= \frac{(b-a)(b+a)}{2}
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