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Math Help - Uniform Distribution

  1. #1
    Newbie jaco's Avatar
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    Uniform Distribution

    Let X~UNIF(0,1) and Y~UNIF(0,1)

    then I know that X+X~UNIF(0,2)
    but how will X+Y be distributed?

    Is there an easy way to determine this? I think it should be a triangle distribution of some sort.

    If you look at the discrete uniform and think of 2 dice. If you throw the 2 dice there is 1 possible way to get 2. There are 2 ways to get 3. 3 ways to get 4 etc. up to 1 way to get 12. But how will this be adjusted for continuous uniform?
    Last edited by jaco; May 29th 2009 at 12:11 AM. Reason: typo
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  2. #2
    MHF Contributor matheagle's Avatar
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    By X+X you mean 2X, well that is U(0,2).

    For W=X+Y, wher you need independence, the classic way to do is solve via the CDF of W.
    Draw the unit square (0,1)X(0,1) and find F(w) where 0<w<1 and 1<w<2.

    The derivative will give you the density which is
    f(w)=w on (0,1) and f=2-w on [1,2) and 0 elsewhere.

    IS through=throw?
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