ABSTRACT
Consider the experiment of tossing two fair dice described in Example 2.1. Suppose x represents the sum of the toss. Define X as a variable that takes on only values given by x. If the sum of the toss is 2 then X = 2; if the sum of the toss is 3 then X = 3; if the sum of the toss is 7 then X = 7. Numerical values of X are associated with events defined from the sample space for this experiment, which was given in Table 2.1. In particular,
X = 2 is associated with only this simple event {(1, 1)}∗ X = 3 is associated with only these two simple events {(1, 2)}, {(2, 1)} X = 7 is associated with only these six simple events {(1, 6)}, {(2, 5)},
{(3, 4)}, {(4, 3)}, {(5, 2)}, {(6, 1)}
Here, we say X is a random variable. This is illustrated in Figure 3.1. Formally, a random variable is a real-valued function defined over a sample space. The sample space is the domain of a random variable. Traditionally, random variables are denoted by capital letters such as X,W, and Z.
