Probability Theory (ii): Many Random Variables

Abstract

In almost every application of statistical methods we deal with the analysis of many observations. For example, if we wish to test whether a certain die is fair, we would roll it many times before making our assessment. Perhaps the most basic issue concerning many random variables is that of independence. The numbers appearing on the various rolls of a die are taken as independent random variables, as discussed below in Section 2.1.1. On the other hand, the random variables Y _i , i = 1, ..., 6, giving the respective numbers of times that i appears in a fixed number of rolls, comprise a dependent set of six random variables, since knowing the value of any five of them determines the sixth.