I know that I'm integrating with respect to $y$ but am having a hard time understanding what my limits of integration are.
Marginal pdf with respect to $x$, $f_{XY}(X,Y)= xe^{-x-y}$, $x>0,$ $y>0$
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statistics
probability-distributions
1 Answers
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Then only restriction on $y$ is that it is positive. So when you integrate out $y$ to find the marginal pdf $f_X(x)$, you integrate over all possible $y$; i.e. $$ f_X(x) = \int_0^\infty f_{X,Y}(x,y) \; dy $$