On certain random simplices in n

The exact density is given for the r-content of the simplicial convex hull of r + 1 independent points in n, each having a type II [beta] distribution. The density is given in the form of an integral of Mellin-Barnes type, which even in the most general cases can be evaluated to give a series representation for the density. Some special cases are evaluated to observe the types of series that can arise. It is also shown that the r-content is asymptotically normal for large values of n, a result analogous to a result conjectured by R. E. Miles (1971, Adv. in Appl. Probab., 3 353-382).