Key Concepts

• The probability for each value in a probability distribution is between 0 and 1, inclusive.
• The sum of the probabilities in a probability distribution is 1.

Glossary

probability distribution function (PDF): a mathematical description of a discrete random variable (RV), given either in the form of an equation (formula) or in the form of a table listing all the possible outcomes of an experiment and the probability associated with each outcome.

random variable (RV): a characteristic of interest in a population being studied; common notation for variables are upper case Latin letters [latex]X, Y, Z,[/latex]…; common notation for a specific value from the domain (set of all possible values of a variable) are lower case Latin letters [latex]x, y, and z[/latex]. For example, if [latex]X[/latex] is the number of children in a family, then [latex]x[/latex] represents a specific integer [latex]0, 1, 2, 3,[/latex]…. Variables in statistics differ from variables in intermediate algebra in the two following ways:

• The domain of the random variable (RV) is not necessarily a numerical set; the domain may be expressed in words; for example, if [latex]X=[/latex] hair color then the domain is {black, blond, gray, green, orange}.
• We can tell what specific value [latex]x[/latex] the random variable [latex]X[/latex] takes only after performing the experiment.