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Math Help - If two random variable have teh joint density

  1. #1
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    If two random variable have teh joint density

    If two random variable have the joint density given by

    f(x,y) = \begin{cases} 2e^{-2y} e^{-x}  & 0<x< \infty , o<y<\infty\\<br />
0 & otherwise \end{cases}

    Are X and Y independent ?
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  2. #2
    Moo
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    Hello,

    If you can write the joint pdf as the product of a function which only depends on x, and a function which only depends on y, then they're independent.
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    MHF Contributor matheagle's Avatar
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    You can see that they are indep by inspection and that the mariginal densities are

    f_X(x)=e^{-x}I(x>0)

    and

    f_Y(y)=2e^{-2y}I(y>0)

    an exponential and a gamma.
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  4. #4
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    Quote Originally Posted by Moo View Post
    Hello,

    If you can write the joint pdf as the product of a function which only depends on x, and a function which only depends on y, then they're independent.
    i didnt understand .......could u please elaborate
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  5. #5
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    Quote Originally Posted by wolfyparadise View Post
    i didnt understand .......could u please elaborate
    You have been told how to do this. You are expected to have sufficient understanding of things so that explanations such as those given make sense.

    Go back to your textbook or class notes and review this material. Also, click on 5.2 here: Probability density function - Wikipedia, the free encyclopedia
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  6. #6
    MHF Contributor matheagle's Avatar
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    Quote Originally Posted by wolfyparadise View Post
    i didnt understand .......could u please elaborate
    no mite
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