Monotonicity of the Sample Range of 3-D Data: Moments of Volumes of Random Tetrahedra

Stefan Kunis, Benjamin Reichenwallner, Matthias Reitzner

The sample range of uniform random points $X_1,\dots ,X_n$ chosen in a given convex set is the convex hull $\mathrm{conv}[X_1,\dots ,X_n]$. It is shown that in dimension three the…