ABSTRACT
General moments and distributions of the volume contents of random simplices and random parallelotopes in Rn , the n-dimensional Euclidean space, when some general probability measures are associated with the vertices, are considered in this article. Usual methods available in the literature for dealing with such problems depend heavily on results from integral and differential geometry. Algebraic procedures based on properties of Jacobians of matrix transformations and functions of matrix argument, and no results from integral and differential geometry, will be used in the present article. Various types of results will be obtained when the vertices are preselected points or when the points arrive according to some stochastic processes.
