Afire station is to be located along a road of length a , a < [infinity] . if fires occur at points uniformly chosen on (0, a ), where should the station be located so as to minimize the expected distance from the fire? that is, choose a so as to minimize e [ | x − a | ] when x is uniformly distributed over (0, a ). now suppose that the road is of infinite length—stretching from point 0 outward to [infinity] . if the distance of a fire from point 0 is exponentially distributed with rate λ , where should the fire station now be located? that is, we want to minimize e [ | x − a | ] , where x is now exponential with rate λ