Note on the probability distribution of a small number of vectors

Abstract

In this note the problem of random flights is considered for the case of a small number of vectors, each vector possessing the same constant magnitude. A formula is developed which permits the calculation of the probability function of the sum of N + 1 such vectors if the function of the sum of N vectors is known. The formulae for the probability distributions up to N = 8 are quoted and some of their practical applications mentioned.