The starting time of a class is uniformly distributed between 10:00 and 10:05. If a student arrives early and has to wait t minutes for the class to start, then the student incurs a penalty of A1t, which accounts for the waste in the student's time. On the other hand, if the student arrives t minutes after the class has started, then the student incurs a penalty of A2t. which accounts for the information the student has missed. If the student arrives at x minutes after 10:00. what is the expected penalty incurred by the student? What value of x minimizes the expected penalty?