Help with the work thank you

Exercise 4. Let X and Y be two standard independent Brownian motions. Suppose we model the position of a molecule moving in a plane by (X, Y). Let Rt = VX? + Y? be its distance from the origin at time t. 1. The location of the molecule is described by (R, ) E R+ x [0, 2x] where X = R cos() and Y = R sin(O). Show that Rt and Ot are in- depenent and find their cumulative distributions functions and prob- ability densities ( for example, P(R. (arcsin(x) - xV1 - x2) for |x|