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3.9. [Uniform and exponential distribution I] A fire station is to be build along a street of length L. (a) If fires will occur at points uniformly chosen on (0,L), 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[Xa], when X is uniformly distributed over (0,L). (b) Now suppose the street is of infinite length- stretching from point 0 outward to . If the distance of a fire from point 0 is exponentially distributed with rate , where should the fire station now be located?.

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3.9. [Uniform and exponential distribution I] A fire station is to be build along a street of length L. (a) If fires will occur at points uniformly chosen on (0,L), 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[Xa], when X is uniformly distributed over (0,L). (b) Now suppose the street is of infinite length- stretching from point 0 outward to . If the distance of a fire from point 0 is exponentially distributed with rate , where should the fire station now be located?

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