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 $X, Y, Z,$…; common notation for a specific value from the domain (set of all possible values of a variable) are lower case Latin letters $x, y, and z$. For example, if $X$ is the number of children in a family, then $x$ represents a specific integer $0, 1, 2, 3,$…. 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 $X=$ hair color then the domain is {black, blond, gray, green, orange}.
• We can tell what specific value $x$ the random variable $X$ takes only after performing the experiment.