# Marginal Distribution for x [closed]

I want to calculate the marginal distribution of $$X$$ given that the joint probability density function of $$(X,Y)$$ is given by $$f(x,y)=2592(x^2-y^2)e^{-2x} \qquad 0

My problem is to determine the bounds of integration for the marginal density. Are they going to be from $$-x$$ to $$0$$ and then from $$0$$ to $$x$$? Or just from $$0$$ to $$x$$ since $$x$$ can only assume positive values?

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The support of $$Y$$ conditional on the value of $$X=x$$ is $$(-x,x)$$ so that should be your region of integration.