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Math Help - Joint Density

  1. #1
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    Joint Density

    (X,Y) has density 3x^2 + 1/2 on [0,1]x[0,1].

    I need to compute the joint density of Y and Z where Z = XY.

    I tried substituting X = Z/Y into the (X,Y) but that didn't work...My next guess is to just multiply X*Y together, to get the density of Z. I'm lacking a formula to put that into to find the joint distribution of Z and Y, so maybe that isn't right.

    Some direction would be appreciated.
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  2. #2
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    Re: Joint Density

    Try to find the joint distribution F(y,z), after that take derivatives to find f(y,z)
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  3. #3
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    Re: Joint Density

    I'm not sure what you mean?
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  4. #4
    Junior Member MathTutor2013's Avatar
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    Re: Joint Density

    First try to find F(y,z) = Pr(Y<=y,Z<=z) making a graph
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  5. #5
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    Re: Joint Density

    f(x,y) = 3x^2 + 1/2
    Z = XY
    Use transformation of variable technique
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  6. #6
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