Probability Distribution

Definition: A probability distribution may be defined as a non-negative real function of all possible outcomes of some random event. The sum of the probabilities of all possible outcomes is defined as 1, and probabilities can never be negative.

Example: A coin toss has two outcomes, ``heads'' (H) or ``tails'' (T), which are equally likely if the coin is ``fair''. In this case, the probability distribution is

where denotes the probability of outcome . That is, the total ``probability mass'' is divided equally between the two possible outcomes heads or tails.

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written by Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.