I have a pdf of two random variables given as $\displaystyle f(x,y) = \frac{K}{x}$ if $\displaystyle 0<y<x \mbox{; and ;} 0<x<2$, and 0 otherwise.

I found out the value of K by integrating the pdf equal to 1, that is:

$\displaystyle \int_0^2 \int_0^x \frac{K}{x} \mbox{dy} \mbox{dx} = 1$

and got k = 1/2

then I found of the marginal pdf of x by:

$\displaystyle f_{X}(x) = \int_0^x \frac{1}{2x} dy = \frac{1}{2}$

but when I tried to find the marginal pdf of y by doing:

$\displaystyle f_{Y}(x) = \int_0^2 \frac{1}{2x} dx$, I am getting infinity!!

Is that correct or did I make a mistake while finding the marginal pdf of Y??

Thanks.