1 The City of Rulertown consists of the unit interval [0, 1] (see Figure 2). Rulertown needs to determine where to build the city’s only fire station. It knows that for small x, the probability that a given fire occurs at a location between x and x + x is 2x(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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FIGURE 2 0 x x + Ax 1