volume 33, issue 1, P125-142 2004
DOI: 10.1007/s00454-004-1109-3
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Abstract: Denote by K n the convex hull of n independent random points distributed uniformly in a convex body K in R d , by V n the volume of K n , by D n the volume of K \K n , and by N n the number of vertices of K n . A well-known identity due to Efron relates the expected volume ED n -and thus EV n -to the expected number EN n+1 . This identity is extended from expected values to higher moments.The planar case of the arising identity for the variances provides in a simple way the corrected version of a central limi…

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