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Math Help - Expected length?

  1. #1
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    Expected length?

    Two points, X and Y , are chosen at random on a rod of length 1. What is the expected distance between these two points?

    Can anyone help me out with this question? Not exactly sure where to start?
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  2. #2
    Super Member Anonymous1's Avatar
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    []EDIT[] \color{red}{\text{Please delete.}}
    Last edited by Anonymous1; May 12th 2010 at 01:03 PM.
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  3. #3
    Super Member Anonymous1's Avatar
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    I think an easier approach is:

    E(|X-Y|) =\int \int |X-Y|f_{X,Y} dxdy

    Assuming......

    X ~ \text{Uniform(0,1);} Y ~ \text{Uniform(0,1) i.i.d.}

    ......makes this fairly simple, actually.
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