×

Systems of stochastically independent and normally distributed random points in the Euclidean space \(E_3\). (English) Zbl 0949.60026

Let \(P_1,P_2,P_3\) resp. \(Q_1,Q_2,Q_3,Q_4\) be independent random points in Euclidean 3-space \(E_3\) with standard normal distribution. The author studies the area \(A\) of the triangle spanned by \(P_1,P_2,P_3\) and the volume \(V\) of the tetrahedron spanned by \(Q_1,Q_2,Q_3,Q_4\) and determines explicitly the distribution of these random variables.
Reviewer: W.Weil (Karlsruhe)

MSC:

60D05 Geometric probability and stochastic geometry
52A22 Random convex sets and integral geometry (aspects of convex geometry)
52A38 Length, area, volume and convex sets (aspects of convex geometry)
PDF BibTeX XML Cite
Full Text: EuDML EMIS