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arXiv · 1112.0499

Mean Width of a Regular Cross-Polytope

Steven R. Finch
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Abstract

The expected range of a sample of n+1 normally distributed variables is known to be related to the mean width of a regular n-simplex. We show that the expected maximum mu_n of a sample of n half-normally distributed variables is related to the mean width of a regular n-crosspolytope. Both of these relations have mean square counterparts. An expression for mu_5 is found and is believed to be new.

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Steven R. Finch. 2016-03-12. Mean Width of a Regular Cross-Polytope. https://arxiv.org/abs/1112.0499

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