7. (5pts) 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. The location of the molecule can also be described by (R, O) E R+ x [0, 27] where Xt = Rt cos(Of) and Yt = Rt sin(Ot). Show that Rt and Ot are indepdendent and find their CDFs and PDFs