Chapter 2 - Probability and Risk

Abstract

This chapter covers most of the probability-based concepts needed for subsequent material in the book. The fundamental concepts of probability spaces, random variables, expected value and variance, conditional probability, and independent random variables are reviewed. Essential probability distributions are discussed and illustrated, including the binomial distribution, the uniform, normal, lognormal, and Poisson distributions. The central limit theorem is discussed carefully because it can be used to make the transition from the discrete binomial distribution to the normal distribution. Joint probability distributions are introduced and illustrated with emphasis on the bivariate normal distribution. This chapter concludes with the construction of a portfolio model and its associated optimization problem using Lagrange multipliers.