This thesis contains a brief review of some of the work that has been done concerning the generation and testing of pseudo-random numbers. Computer subroutine programs written in FORTRAN IV are given for the generation of pseudo-random numbers from 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 Pearson distribution may be specified either by the first four moments or from sample data, then the parameters of the fitted distribution are printed and, if desired, a graph of the distribution. A graph of the mixture of distributions may be obtained from 10,000 pseudo-random numbers from the mixture. The speed of generation varies from about 10,000 random numbers per minute (on the IBM 7040), for a Pearson distribution with moments calculated from the generated numbers, to more than 100,000 numbers per minute if mixtures are used. The subroutines are applied to a Monte Carlo investigation of the robustness of several methods of confidence interval estimation. / M.S.