Quantitative Enterprise Risk Management

In this appendix, we review the major concepts, notation, and results from probability and statistics that are used in this book. We start with univariate random variables, their distributions, moments, and quantiles. We consider dependent random variables through conditional probabilities and joint density and distribution functions. We review some of the distributions that are most important in the text, including the normal, lognormal, Pareto, uniform, binomial, and Poisson distributions. We outline the maximum likelihood (ML) estimation process, and summarize key properties of ML estimators. We review Bayesian statistics, including the prior, posterior, and predictive distributions. We discuss Monte Carlo simulation, with a particular focus on estimation and uncertainty.