Probability question - calculating marginal pdfs

jaejoon89
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Homework Statement



Calculate the marginal probability distribution function of X given joint pdf

f(x,y) = 15x^2 y for 0 <= x <= y <= 1
f(x,y) = 0 otherwise

Homework Equations

f_x (x) = integral of f(x,y) dy

The Attempt at a Solution



I've got no idea what the bounds are for this integral.

Also, would it be easier to do it in polar coordinates?
 
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0<=x<=y<=1. For a fixed value of x, doesn't y go from x to 1? I'm not sure why this is confusing you and I don't think polar coordinates will help one bit.
 

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