Probability theory

Probability theory or probability calculus is the branch of <a href="/facts/Mathematics/pxTouaz4">mathematics</a> concerned with <a href="/facts/Probability/fgYvMhwb">probability</a>. Although there are several different <a href="/facts/Probability_interpretations/qmuEgkIU">probability interpretations</a>, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of <a href="/facts/Axioms_of_probability/j6IkXsIT">axioms</a>. Typically these axioms formalise probability in terms of a <a href="/facts/Probability_space/dEcv2VrU">probability space</a>, which assigns a <a href="/facts/Measure_(mathematics)/yCq7zlI4">measure</a> taking values between 0 and 1, termed the <a href="/facts/Probability_measure/8BjhgoPR">probability measure</a>, to a set of outcomes called the <a href="/facts/Sample_space/WVldkN4F">sample space</a>. Any specified subset of the sample space is called an <a href="/facts/Event_(probability_theory)/aJ0l4oQb">event</a>.
Central subjects in probability theory include discrete and continuous <a href="/facts/Random_variable/TwTBXnLT">random variables</a>, <a href="/facts/Probability_distributions/EpsKKVRu">probability distributions</a>, and <a href="/facts/Stochastic_process/Ng1n1dnB">stochastic processes</a> (which provide mathematical abstractions of <a href="/facts/Determinism/NhvNlAbe">non-deterministic</a> or uncertain processes or measured <a href="/facts/Quantity/E2jCKetq">quantities</a> that may either be single occurrences or evolve over time in a random fashion).
Although it is not possible to perfectly predict random events, much can be said about their behavior. Two major results in probability theory describing such behaviour are the <a href="/facts/Law_of_large_numbers/X3Bjcy3v">law of large numbers</a> and the <a href="/facts/Central_limit_theorem/0gc2L0Wd">central limit theorem</a>.
As a mathematical foundation for <a href="/facts/Statistics/DNPsKGYU">statistics</a>, probability theory is essential to many human activities that involve quantitative analysis of data. Methods of probability theory also apply to descriptions of complex systems given only partial knowledge of their state, as in <a href="/facts/Statistical_mechanics/6zMsNYYG">statistical mechanics</a> or <a href="/facts/Sequential_estimation/EKm4Amrl">sequential estimation</a>. A great discovery of twentieth-century <a href="/facts/Physics/a7aH2y08">physics</a> was the probabilistic nature of physical phenomena at atomic scales, described in <a href="/facts/Quantum_mechanics/BRc3Mzgr">quantum mechanics</a>.

Probability theory open-in-new

Probability theory