Systems of Stochastically Independent and Normally Distributed Random Points in the Euclidean Space $E_3$

Abstract: We consider sets of three or four stochastically independent and normally distributed random points in $E_3$. We look at these points as the vertices of a triangle $\hbox{\cal T}_3$ or of a tetrahedron $\hbox{\cal T}_4$ and we study the random variables $\hbox{\cal A}$, area of $\hbox{\cal T}_3$, and $\hbox{\cal V}$, volume of $\hbox{\cal T}_4$. We also determine the probability that $\hbox{\cal T}_3$ is acute-angled.

Keywords: geometric probability, stochastic geometry, random sets; random convex sets and integral geometry

Classification (MSC91): 60D05, 52A22

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