Finding the distribution of a random variable from its moment function
Otwombe, Naviava Kennedy
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Consider the problem of r + l randomly distributed points in a unit n-ball and the convex hull created by these points. Let “ n" be r! Times the r-content of an r-simplex whose p vertices are in the interior and r + 1-p vertices on the boundary of a unit n-ball. Explicit expressions for the exact distribution functions of " n" are given when r + 1 points are independently, and identically distributed according to the Uniform distribution. The exact distributions are obtained using the technique is illustrated for the general case p = r + 1 and a particular case p = 3, r = 2. Various representations of the distributions in psi and the generalized zeta functions are given. These representations are also given in the most general case as an H-function distribution.