Let X and Y be jointly continuous with density f X,Y . Let (R, ) be the polar coordinates of (X, Y). (a) Give a

Let X and Y be jointly continuous with density f_X,Y. Let (R, Θ) be the polar coordinates of (X, Y).
(a) Give a general expression for the joint density of R and Θ.
(b) Suppose X and Y are independent with common density function f(x) = 2x, for 0 < x < 1. Use your result to find the probability that (X, Y) lies inside the circle of radius one centered at the origin.