In probability and statistics, a **probability distribution** assigns a probability to each of the possible outcomes of a random experiment. Examples are found in experiments whose sample space is non-numerical, where the distribution would be a categorical distribution; experiments whose sample space is encoded by discrete random variables, where the distribution is a probability mass function; and experiments with sample spaces encoded by continuous random variables, where the distribution is a probability density function. More complex experiments, such as those involving stochastic processes defined in continuous-time, may demand the use of more general probability measures.

In applied probability, a probability distribution can be specified in a number of different ways, often chosen for mathematical convenience:

- by supplying a valid probability mass function or probability density function
- by supplying a valid cumulative distribution function or survival function
- by supplying a valid hazard function
- by supplying a valid characteristic function
- by supplying a rule for constructing a new random variable from other random variables whose joint probability distribution is known.

Important and commonly encountered probability distributions include the binomial distribution, the hypergeometric distribution, and the normal distribution.

Read more about Probability Distribution: Introduction, Terminology, Discrete Probability Distribution, Continuous Probability Distribution, Probability Distributions of Scalar Random Variables, Some Properties, Kolmogorov Definition, Random Number Generation, Applications, Common Probability Distributions

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### Famous quotes containing the words distribution and/or probability:

“There is the illusion of time, which is very deep; who has disposed of it? Mor come to the conviction that what seems the succession of thought is only the *distribution* of wholes into causal series.”

—Ralph Waldo Emerson (1803–1882)

“The *probability* of learning something unusual from a newspaper is far greater than that of experiencing it; in other words, it is in the realm of the abstract that the more important things happen in these times, and it is the unimportant that happens in real life.”

—Robert Musil (1880–1942)