# 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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## 1 Answer

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

• Thank you very much for your reply I appreciate it. However, after I submitted this question I thought of this again and I computed the integral from -x to 0 and add this to the integral from 0 to x. Is this also true?Or is it just the integral from -x to x correct? I am sorry for asking so many questions but i am having some difficulties. Thank you for your help! – Thekla Oct 23 '20 at 6:57
• The integral is additive, so yes it's the same thing – MONODA43 Oct 23 '20 at 13:41