Problem 4 (9 pts) A chord of a circle is a line segment connecting two points on the circle. To pick a point uniformly in the unit circle means that you are randomly throwing a dart at the unit circle. Pick a point Q uniformly at random in the unit circle, radius 0 5 R S 1 from the origin, and pick any chord of the circle with that point as the midpoint. Let L be the length of this chord. In the following steps, you will nd ]E[L]. l. (3 pts) Notice that if we rotate the circle, we can assume that the chord is always vertical with non-negative horizontal coordinate (i.e. assume Q=(R,0) for R 2 0). Show that the GDP of R is F 30!\") = r2. (Hint: What is the probability that the radius R of the point Q is less than T?) 2. (3 pts) Find the density of R. 3. (3 pts) Find ]E[L]