# Marginal probability?

1. Jul 23, 2015

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

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

Last edited: Jul 23, 2015
2. Jul 23, 2015

### mathman

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

3. Jul 23, 2015

### zli034

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?

4. Jul 24, 2015

### mathman

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

5. Jul 25, 2015

### micromass

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