Systems of stochastically independent and normally distributed random points in the Euclidean space \(E_3\) (Q1567449)

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.