The main purpose of this study was to review and modify some of the work that has been done concerning the generation of pseudo-random numbers. The PURGE3, MIX1, and MIX2 subroutines, written in FORTRAN IV to be run on the IBM 360 computer system, are used for the generation of pseudo-random numbers from a family of Pearson distributions as well as from any combination of mixtures of two Pearson distributions, a normal distribution with arbitrary mean and variance and a uniform distribution on any finite interval. The primary improvement undertaken here was to increase the efficiency of operation by enabling the PURGE3 and MIX1 subroutines to be called in a single computer program. The Pearson distribution may be specified either by the first four moments or from sample data. The parameters of the fitted distribution are printed and, if desired, the moments and a graph of the distribution of the 100 pseudo-random numbers generated are printed. A graph of the mixture of distributions generated in the MIX1 subroutine may be obtained from 10,000 random numbers generated from the mixture. The MIX2 subroutine functions to generate random numbers only. The speed of generation varies from about 13,000 random numbers per minute for a Pearson distribution which computes and prints the moments from the generated numbers, to approximately 143,000 numbers per minute if mixtures are used without computing the moments from the generated numbers. / Master of Science