Answer Happy

14. [14 marks] In a long jump competition between Alvin and Benson, each player is allowed two jumps. The maximum distance of Alvin's two jumps will be compared with those of Benson. The one who jumps the larger maximum distance will win a prize. From past records, Alvin can jump a distance of X (in cm) which follows a uniform distribution on (650, 740). Benson can jump a distance of Y (in cm) which follows a uniform distribution on (640, 720). Denote the distances of Alvin's jumps by X, and X, and the distances of Benson's jumps by Y, and Y. Assume that all the random variables are independent. Follow the following steps to calculate the chance that Alvin will win the prize: (a) {4 marks) What is the density function of R=max (x,x)? (b) (2 marks) State the joint density function of Rand S, where S = max (Y,Y). (c) {8 marks) Compute the probability that Alvin will win the prize in the competition.