Due to the health crisis, only 70 dorm students wish to go to campus every morning: 40 early birds, each arriving at the shuttle stop at a uniform continuous time between 9:00 and 9:15, and 30 late risers, each arriving at the shuttle stop at a uniform continuous time between 9:15 and 9:30. Correspondingly, just two shuttles run each morning, one departs the dorm at 9:10, 9:12, and 9:15 with probabilities 0.3, 0.5, and 0.2, respectively, and the other departs exactly fifteen minutes after the first: 9:25 if the first left at 9:10, and similarly 9:27, and 9:30. Each shuttle takes all students present when it departs, hence in particular, all early birds make it to school. Student arrival times are independent of each other and of the shuttle departure times. Let X and Y respectively be the random number of students taking the first and second shuttles on a given day. (a) Find E(X). (b) Find E(Y). (c) Use Chebyshev's Inequality to upper bound P(X > 35). (d) Use the Chernoff bound to upper bound P(X Y