The Institute of Statistical Mathematics and the Graduate University for Advanced Studies, 4-6-7 Minami-Azabu Minato-ku, Tokyo 106, Japan
(Received March 31, 1993; Accepted June 14, 1994)
Keywords: Probability of Configuration, Random Symplex, Separation by Hyperplane
Abstract. We consider N + 2 points mutually independently distributed on a sphere of N-dimension. We calculate the probability of a configuration of the N + 2 points on the sphere. The probability is (1/2)N+1 which does not depend on the particular choice of the underlying distribution as long as it is central symmetric.