Exercise. The average waiting time for the commuter train is 15 minutes . What is the probability that Joe will wait for more than 10 minutes, given that he has already waited for 5 minutes ?

Exercise. Suppose that the length of a phone call in minutes is an exponential r.v with average length 8 minutes. What is the probability of your phone call being more than 10 minutes ?

Honors exercise.  A hospital is to be located along a road of infinite length. If the population density is exponentially distributed along the road, where should the station be located to minimize the expected distance to travel to the hospital? That is, find an a to minimize E|X − a|, where X is exponential with rate λ.