I'm having trouble solving the following problem:
Suppose you have a unit disk (x^2 + y^2 <= 1), and you pick a point randomly from the disk, then let X be the x coordinate and y be the Y coordinate. Are X and Y independent?
I'm pretty sure the joint distribution is 1/pi when x^2 + y^2 <= 1
And I know in order to prove independence you have to multiply the marginal distributions, but my problem is I dont know what I have to integrate over to get the marginal distributions. Any help would be greatly appreciated.