Random Variables

In an experiment, each outcome can be associated with a single number by using a rule of association, or random variable. By converting outcomes to numbers, we can use mathematics to give us insight into the experiment or study being conducted.

• Variable A rule which associates a single number with the outcome of an experiment (an event).
• Random Variable The random variable takes a countable number of values. In other words, it has a discrete sample space.
• Random Variable The random variable takes on values in an interval (it has a continuous sample space).

NOTE:\ We usually denote random variables with capital letters, e.g., the random variables X or Y.

EXAMPLE:\ Consider the following random variables:

• X = 1 (0) if a randomly selected person prefers Pepsi (Coke). (Categorical random variable.)
• X = # of Aggies attending a home football game. (Discrete random variable.)
• X = length of a rainbow trout. (Continuous random variable.)

• Mean and Variance of Random Variables