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Marginal probability?

  1. Jul 23, 2015 #1
    If there are X and Y two random variables. The pdf of Y is f(y), and conditional pdf of X is f(x|y). I want to find the marginal CDF of X, the F(x). Is this correct?
    [itex]F(x)=\int^{F(x|y)}_{-\infty}f(y)dy[/itex]

    [itex] \dfrac{d}{dx}\int^{F(x|y)}_{-\infty}f(y)dy=\int^{\infty}_{-\infty}f(x|y)f(y)dy=f(x)[/itex]?
     
    Last edited: Jul 23, 2015
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  3. Jul 23, 2015 #2

    mathman

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    The density function for x is [itex]\int_{-\infty}^{\infty}f(x|y)f(y)dy[/itex].
     
  4. Jul 23, 2015 #3
    Yes, I know your logic. But I found the marginal expression today. I put it here. I wanna know is it correct, or under what condition I can get F(x) that way?
     
  5. Jul 24, 2015 #4

    mathman

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    It is not obvious. [itex]F(x)=\int_{-\infty}^{\infty}F(x|y)f(y)dy[/itex]. I don't see how you got your integral.
     
  6. Jul 25, 2015 #5

    micromass

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    No. And I don't see any distribution for which it is correct.
     
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