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Math Help - marginal density..and other..

  1. #1
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    Exclamation marginal density..and other..

    Hello..
    Im having some difficulties in my statistics questions..

    Consider the function f() given by f(x,y)=k(k−1)(y−x)^(k−2), 0<x<y<1.

    -Verify that if k ≥ 2 is an integer, f() is a bivariate density.
    -Find the marginal densities of X and Y .
    -Find E(X|Y ).
    -Find E(X^2|Y = y) and V ar(X|Y ).

    ...it will be great if you help me at least one question.. : )...

    Thank you!!
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  2. #2
    MHF Contributor matheagle's Avatar
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    You need to integrate to find k.
    I prefer 0's in my bounds so I'll integrate first wrt x

    1=k(k-1)\int_0^1\int_0^y(y-x)^{k-2}dxdy

    then f_X(x)=\int_0^yf_{XY}(x,y)dy

    and f_Y(y)=\int_x^1f_{XY}(x,y)dx
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  3. #3
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    Thank you!!
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