Nonuniform Random Number Distributions: Examples and Methods

This lecture covers the general formulation of nonuniform random number distributions, with examples such as the exponential and Gaussian distributions. It explores the application of the central limit theorem, the method of Box & Muller, and the rejection method of von Neumann for generating random variables. The lecture delves into the link between the functions f(x) and q(y), conservation of probability, and the transformation process to achieve desired distributions. Various techniques for generating random variables are discussed, including the procedure, proof, and implementation of the rejection method of von Neumann.