The Basis of Monte Carlo

Publication year: 2012
Source: Exploring Monte Carlo Methods, 2012, Pages 21-46

William L., Dunn , J. Kenneth, Shultis

 Summary: The second chapter begins by defining the probability density function (PDF) and the cumulative distribution function (CDF) of a single continuous random variable. The population and sample means, variances, and standard deviations are also defined. Discrete random variables and their distributions are then introduced. Functions of several random variables and their joint and conditional probability distributions are then introduced. Finally, several key concepts for MC analysis are presented: (1) the mean and variance of a sum of random variables, (2) the law of large numbers, and, most important of all, (3) the central limit theorem. Examples of MC as quadrature,…