Is the Marginal CDF of X Correctly Defined with Two Random Variables?

[zli034]

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?
$F(x)=\int^{F(x|y)}_{-\infty}f(y)dy$

$\dfrac{d}{dx}\int^{F(x|y)}_{-\infty}f(y)dy=\int^{\infty}_{-\infty}f(x|y)f(y)dy=f(x)$?

 

[mathman]

The density function for x is $\int_{-\infty}^{\infty}f(x|y)f(y)dy$.

 

[zli034]

Yes, I know your logic. But I found the marginal expression today. I put it here. I want to know is it correct, or under what condition I can get F(x) that way?

 

[mathman]

Yes, I know your logic. But I found the marginal expression today. I put it here. I want to know is it correct, or under what condition I can get F(x) that way?

It is not obvious. $F(x)=\int_{-\infty}^{\infty}F(x|y)f(y)dy$. I don't see how you got your integral.

 

[micromass]

Is this correct?

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