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Probability: Probability Theory
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Probability is the topic of probability theory, a branch of mathematics concerned with analysis of random phenomena. Like algebra, geometry and other parts of mathematics, probability theory has its origins in the natural world. Humans routinely deal with incomplete and/or uncertain information in daily life: in decisions such as crossing the road ("will this approaching car respect the red light?"), eating food ("am I certain this food is not contaminated?"), and so on. Probability theory is a mathematical tool intended to formalize this ubiquitous mental process. The probability concept is a part of this theory, and is intended to formalize uncertainty.
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Probability is a mathematical theory of random events and random variables. It even extends to random functions of time (stochastic processes). Probability models occur in almost all areas of science: biology (genetics, epidemiology), economics (financial markets), physics (diffusion, theories of molecular matter), and so on, and it is essential for many statistical techniques. Relatively simple probability principles lead to astonishing results. One that has been famous for centuries is the Gaussian or normal curve (the bell-shaped curve). It is an almost universal solution to problems involving independence or weak dependence.
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Electronic Communications in Probability (ECP) publishes short notes, review papers and research announcements in probability theory. Its sister journal, the Electronic Journal of Probability (EJP), publishes full-sized articles in probability theory. Short papers, less than 12 pages, should be submitted to ECP first.
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Probability provides a mathematical description of randomness. A phenomenon is called random if the outcome of an experiment is uncertain. However, random phenomena often follow recognizable patterns. This long-run regularity of random phenomena can be described mathematically. The mathematical study of randomness is called probability theory.
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Probability axioms form the basis for mathematical probability theory. Calculation of probabilities can often be determined using combinatorics or by applying the axioms directly. Probability applications include even more than statistics, which is usually based on the idea of probability distributions and the central limit theorem.
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Probability is the likelihood or chance that something is the case or will happen. Probability theory is used extensively in areas such as statistics, mathematics, science and philosophy to draw conclusions about the likelihood of potential events and the underlying mechanics of complex systems.
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Probability Theory