In a game. a player throws a dart at a target some distance away. Suppose that the dart lands at a location with a distance of R. in cm. from the centre of the target. Let the pdf of R be given by f0") = %(1 + ark'72, r > 0. If the dart lands at a distance within the radius of 2cm from the centre of the target. then the player will win a prize. (i) Show that the cdf of R is given by e"'2(3 + r) F(r) =1 3 r>0. (ii) If a dart is thrown at the target, nd the probability that the player wins a prize. (iii) If 3 darts are thrown at the target, nd the probability that the player will win a prize. (iv) Find the number of darts needed on average to win a prize