Probability theory: Difference between revisions

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{{Probability fundamentals}}

'''Probability theory''' is the branch of [[mathematics]] concerned within the [[probability]]. Although there are several different [[probability interpretations]], probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of [[axioms of probability|axioms]]. Typically these axioms formalise probability in terms of a [[probability space]], which assigns a [[measure (mathematics)|measure]] taking values between 0 and 1, termed the [[probability measure]], to a set of outcomes called the [[sample space]]. Any specified subset of the sample space is called an [[event (probability theory)|event]].

Central subjects in probability theory include discrete and continuous [[random variable]]s, [[probability distributions]], and [[stochastic process]]es (which provide mathematical abstractions of [[determinism|non-deterministic]] or uncertain processes or measured [[Quantity|quantities]] 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 [[law of large numbers]] and the [[central limit theorem]].