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I'm looking at the joint pdf F(x,y) = (8+xy^3)/64) for -1<x<1 and -2<y<2

(A plot of it is here: https://www.wolframalpha.com/input/?i=(8+xy^3)/64+x+from+-1+to+1,+y+from+-2+to+2 ...sorry about the ugly url) and trying to find the marginal PDFs for X and Y.

I know I want to integrate the joint function with respect to Y and X in order to to get the marginal pdfs for X and Y, respectively. However, I'm running into trouble when I try to set the bounds for these integrals!

As far as I can tell, X and Y don't seem to depend on each other in this sense; i.e. for marginal(X) i would have Integral([JointPDF]dy), from -2 to 2, which comes out to 1/2.

(Similarly, integrating with respect to x from -1 to 1 yields 1/4).

When I integrate these from their respective bounds (x from -1 to 1, y from -2 to 2) both come out to 1, as a proper pdf should. However the fact that both are independent of x and y values makes me think something might be wrong...does anyone have any suggestions as to what I might be doing wrong?

Thanks so much!

Jamie

Edit: My apologies! Posted this to the wrong place! I can't figure out how to delete it though :x

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# Marginal PDF from Joint PDF

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