Simon goes to his University class every weekday by using a train that leaves at 8:00 a.m. We assume that the duration of the journey, in minutes, is a random variable following the uniform distribution in the interval [58, 63]. Further, suppose that from the train platform he needs a 15-minute walk to enter the classroom and that his class starts precisely at 9:15a.m.
(i) What is the probability that Simon arrives in time for his class?
(ii) What is the probability that he arrives at the class at least two minutes after it has begun?
(iii) Find Simon’s expected arrival time in the class.