Rulertown wants to minimize the average distance between, Ask an Expert

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"The city of Rulertown consists of the unit interval [0,1]. Rulertown needs to determine where to build the city's only firestation. It knows that for a small Delta X, the probability that a given fire occurs at a location between x and delta x is 2x(delta x). Rulertown wants to minimize the average distance between the fire station and a fire. Where should the fire station be located?

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