RANDOM VARIABLES
A random variable is a variable that can have multiple values, and where each value has an associated probability of occurrence. For example, if X is a random variable whose values are the outcomes of tossing a well-balanced die, then the values of X are the numbers in the set {1,2,3,4,5,6}. Moreover, each of those values can occur with equal probability (which is 1/6).
In the case of two well-balanced dice, let X be a random variable whose values can be any of the numbers in the set {2,3,4, . . . , 12}. The set of associated probabilities for the different values for X are listed here:
{1/36,2/36,3/36,4/36,5/36,6/36,5/36,4/36,3/26,2/36,1/36}
Discrete Versus Continuous Random Variables
The preceding section contains examples of discrete random variables because the list of possible values is either finite or countably infinite (such as the set of integers). As an aside, the set of rational numbers is also countably infinite, but the set of irrational numbers and also...
