Minimizing expected distance
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A fire station is to be located along a road of length A, A < ∞. If fires will 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...
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https://brainmass.com/statistics/central-tendency/minimizing-expected-distance-31286
Solution Summary
This shows how to use probability to minimize expected distance.
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