Lecture E1 (2020-09-24): Random Number Generation

This lecture surrounds random number generation. The topic is motivated by the need for generating samples from arbitrary random variables, which can be accomplished through transforming random numbers uniformly distributed between 0 and 1. We describe the key properties of a good pseudo-random number generator (uniformity and independence), discuss some historical random number generators, and then a more modern pseudo-random number generator. We close with descriptions of tests for uniformity (Chi-square and Kolmogorov-Smirnov) and independence (autocorrelation and runs tests).