**Beiträge zur Algebra und Geometrie <BR> Contributions to Algebra and GeometryVol. 40, No. 2, pp. 291-301 (1999)
**

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

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Elena Bosetto

Dipartimento di Matematica dell'Universita di Torino, Via C. Alberto, 10, I-10123 Torino, Italy

**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

**Full text of the article:**

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