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Math Help - Conditional Densities Question

  1. #1
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    Conditional Densities Question

    If fx,y(x,y) = 2, x greater than or equal to 0, y greater than or equal to 0, and x+y is less than or equal to 1:

    show that the conditional pdf of Y given x is uniform
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  2. #2
    MHF Contributor matheagle's Avatar
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    f_X(x)=\int_0^{1-x}2dy=2(1-x) on 0<x<1, which is a valid density, it's a beta

    so

    f(y|x)={f(x,y)\over f(x)}={1\over 1-x} on 0<y<1-x.

    Which is CONSTANT on the interval (0,1-x)
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