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Math Help - Marginal pdf of 2 dimensional random variables

  1. #1
    Junior Member
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    Marginal pdf of 2 dimensional random variables

    Hi everybody,

    Given is the following joint distribution of the 2-dimensional random variable (X1,X2).

    f(x1,x2)=(1/(2*x1); if 0<x2<x1 ;0<x1<2;
    0; otherwise

    How do I get the two marginal pdf f(x1) and f(x2)?

    Thanks for your help!
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  2. #2
    Grand Panjandrum
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    Re: Marginal pdf of 2 dimensional random variables

    Quote Originally Posted by Marmy View Post
    Hi everybody,

    Given is the following joint distribution of the 2-dimensional random variable (X1,X2).

    f(x1,x2)=(1/(2*x1); if 0<x2<x1 ;0<x1<2;
    0; otherwise

    How do I get the two marginal pdf f(x1) and f(x2)?

    Thanks for your help!
    It helps if you sketch the region over which the density is non-zero:

    f_{X_1}(x_1)=\int_R f(x_1, x_2) \; dx_2=\int_{x_2=0}^{x_1} f(x_1, x_2) \; dx_2

    f_{X_2}(x_2)=\int_R f(x_1, x_2) \; dx_1=\int_{x_1=x_2}^{2} f(x_1, x_2) \; dx_1

    CB
    Last edited by CaptainBlack; November 20th 2011 at 09:33 PM.
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  3. #3
    Junior Member
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    Re: Marginal pdf of 2 dimensional random variables

    Thank you very much!

    This helped a lot.
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