Assume A (in cm) as the area of a circle that varies randomly (depicting a RV) with the cdf of A given by: F(A) = KA as As b. K is a positive constant = 1 -0 Azb otherwise Suppose r (in cm) is the radius of the circle and h (in cm) represents the altitude of an equilateral triangle inscribed in the circle, determine the following: (i) Expected value of A: (ii) expected value of r; (iii) expected value of the RV: h; (iv) pdf of the RV, S (in cm2) denoting the area of the triangle inscribed in the circle and (v) the range of the RV, S. Assume the following numerical values for (a, b and r) and choose the correct set of answers in the multiple-choices listed below: (a = 1.8; b -3.2 and r-5) Multiple-choices on the answer-set Multiple-choices on the answer-set (i) Choices (ii) E[r] (iii) E[h] (iv): pdf of (S) (v) Range of: S 2.50 0.0206 0.0268 1/((4x Pix (ba)) x (us)1/2), u (3/4) x (31/2) 2.44 0.0581 0.0218 2 1/((4x Pix (b-a)) x (us)1/2) u-(3/4) x (31/2) (ux a/Pi) to (u x b/Pi). u-(5/4) (31/2) (ux a/Pi) to (u x b/Pi). u = (1/4) x (31/2) 3 2.50 0.0205 0.0287 1/((4 x Pix (b-a)) x (us)1/2), u- (3/4) x (31/2) (ux a/Pi) to (ux b/Pi), u- (3/4) (31/2) 2.66 0.0453 0.0557 1/((4x Pix (b-a)) x (us)1/2), u-(3/4) (31/2) (ux a/Pi) to (ux b/Pi). u - (3/4) x (31/2) S 2.37 0.0334 0.0247 x 1/((4 x Pix (b-a)) * (us)1/2). u-(3/4) x (312) (ux a/Pi) to (ux b/Pi). u- (3/4) (31/2), x