Suppose that cars enter a one-way highway of length L in accordance with a Poisson process with rate Each car travels at a constant speed that is randomly determined, independently from car to car, from the distribution F. When a faster car encounters a slower one, it passes it with no loss of time Suppose that a car enters the highway at time t. Show that as to the speed of the car that minimizes the expected number of encounters with other cars, where we say an encounter occurs when a car is either passed by or passes another car, is the median of the distribution G