Probability distribution

For other uses, see Distribution.

In probability theory and statistics, a probability distribution is a function that gives the probabilities of occurrence of possible events for an experiment. It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events (subsets of the sample space).

Each random variable has a probability distribution. For instance, if X is used to denote the outcome of a coin toss ("the experiment"), then the probability distribution of X would take the value 0.5 (1 in 2 or 1/2) for X = heads, and 0.5 for X = tails (assuming that the coin is fair). More commonly, probability distributions are used to compare the relative occurrence of many different random values.

In practice, probability distributions are often described using cumulative distribution functions, probability mass functions or probability density functions. In probability theory, probability distributions are represented by probability measures, and the term probability distribution is often used in reference to probability measures associated with random variables. Probability distributions of particular importance are given specific names.

This article is issued from Wikipedia. The text is available under Creative Commons Attribution-Share Alike 4.0 unless otherwise noted. Additional terms may apply for the media files.