Question: A point is generated on a unit disk in the following way: The radius, R, is uniform on [0, 1], and the angle is uniform on [0, 2π] and is independent of R.
a. Find the joint density of X = R cos and Y = R sin .
b. Find the marginal densities of X and Y .
c. Is the density uniform over the disk? If not, modify the method to produce a uniform density.