Hey mglen.
Hint: You need to define some attributes for the X and Y random variables. If everything is uniform and X and Y are independent random variables then the PDF is proportional to the area of the region.
Will somebody please help me in this problem.
A point is chosen at random from the interior of a circle whose equation is x^2 + y^2 ≤ 4. Let the random variables X and Y denote the x- and y-coordinates of the sampled point. Find fX,Y (x, y).
Thank you.
probability - Continuous uniform distribution over a circle with radius R - Mathematics Stack Exchange
just substitute 2 for R in the above derivation