Problem 2. Amy is waiting for Jake at a train that is undergoing repair before for leaving. Amy is certain that the departure time for the train is sometime in the next hour starting from right at this moment and is modeled as a random variable X ~Unif orm[0,1] (in hours). Amy has determined that Jake's arrival time from this same moment is exponentially distributed as Y~Exp(1) (i.e., )1 = 1). X and Y are independent. (a) Find the probability that Jake arrives in time to catch the train. (i.e., P(Y S X )) (b) At 30 minutes from when Amy started counting, Jake still hasn't arrived so she gets on the train which leaves promptly 30 minutes later (i.e., exactly 1 hour after she started counting). What is the probability that Jake arrives within 15 minutes of the train departing? (NOTE: Assume Jake makes it on the train)