Given the set of all uniformly-distributed, random points within a circle of radius 1. It was proved in lecture that the mean distance of these points to the center of the circle is equal to 2/3. In this problem, you are asked to compute the mean distance of these points to any fixed point on the boundary of the circle, using a similar method. First, without loss of generality, we may position the circle so that it is tangent to the X-axis from above. Furthermore, we may rotate the circle, so that the fixed boundary point is located at the origin (0,0) , as shown in the figure. For the set of all random, uniformly-distributed points ( , ) X Y inside this circle, find the expected distance to the boundary point (0,0) . (a) Determine the equation of the circle in Cartesian coordinates, then show that in polar coordinates, the equation has the form r r = ( ) . Find r( ) , and specify the range of . Show all work. (5 pts) (b) Determine the joint pdf f x y ( , ) of the uniform distribution over this circle in the XY-plane. Explain. (3 pts) (c) Calculate the expected distance to (0,0) .