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An Upper Bound for the Expected Range of a Random Sample

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Abstract:

We consider the expected range of a random sample of points chosen from the interval [0, 1] according to some probability distribution. We then use the notion of convexity to derive an upper bound for this expected range which is valid for all possible choices of this distribution. Finally we show that there is only one distribution for which this bound is achieved.

Document Type: Research Article

DOI: http://dx.doi.org/10.4169/074683410X475100

Publication date: January 1, 2010

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maa/cmj/2010/00000041/00000001/art00006
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