(a) A fire station is to be located along a road of length A, A < ....
Question:
minimize E[|X − a|]
when X is uniformly distributed over (0, A).
(b) Now suppose that the road is of infinite length—stretching from point 0 outward to ∞. 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.
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