Friday, 11 September 2015

integration - finding the marginal PDF of a random variable with undefined integral

The joint PDF of X and Y is



fX,Y(x,y)={1y,0<x<y,0<y<10,otherwise



To find the marginal PDF of Y seems straightforward enough:
fY(y)=y01ydx=[xy]x=yx=0=1




But when I try to find the marginal PDF of X I get stuck with what seems to be an undefined integral:



fX(x)=101ydy



Is there another way to find the marginal PDF of X?

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