Properties of random variables

Abstract

In this chapter, the behavior of random variables is summarized using the concepts of expectation, variance, and covariance. The expectation is a measurement of the location of a random variable’s distribution. The variance and its square root, the standard deviation, are measurements of the spread of a random variable’s distribution. Covariance and correlation are measurements of the extent of linear relationship between two random variables. The chapter also describe two important theorems that describe the distribution of means of samples from a distribution. As the sample size becomes larger, the distribution of the sample mean becomes bunched more tightly around the expectation—this is the law of large numbers—and the distribution of the sample mean approaches the shape of a normal distribution—this is the central limit theorem. Finally, a model describing a linear relationship between two random variables is considered, and the properties of those two random variables are analyzed.