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Probability theory or probability calculus is the branch of mathematics concerned with 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 .
See Ian Hacking's The Emergence of Probability [4] and James Franklin's The Science of Conjecture [17] for histories of the early development of the very concept of mathematical probability. The theory of errors may be traced back to Roger Cotes's Opera Miscellanea (posthumous, 1722), but a memoir prepared by Thomas Simpson in 1755 (printed ...
In probability theory, an event is a subset of outcomes of an experiment (a subset of the sample space) to which a probability is assigned. [1] A single outcome may be an element of many different events, [2] and different events in an experiment are usually not equally likely, since they may include very different groups of outcomes. [3]
Independence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes.Two events are independent, statistically independent, or stochastically independent [1] if, informally speaking, the occurrence of one does not affect the probability of occurrence of the other or, equivalently, does not affect the odds.
The field of the history of probability itself was established by Isaac Todhunter's monumental A History of the Mathematical Theory of Probability from the Time of Pascal to that of Laplace (1865). Twentieth century
The certainty that is adopted can be described in terms of a numerical measure, and this number, between 0 and 1 (where 0 indicates impossibility and 1 indicates certainty) is called the probability. Probability theory is used extensively in statistics , mathematics , science and philosophy to draw conclusions about the likelihood of potential ...
The standard probability axioms are the foundations of probability theory introduced by Russian mathematician Andrey Kolmogorov in 1933. [1] These axioms remain central and have direct contributions to mathematics, the physical sciences, and real-world probability cases. [2] There are several other (equivalent) approaches to formalising ...
Categorical probability; Category of Markov kernels; Category of measurable spaces; Central tendency; Chain rule (probability) Chvátal–Sankoff constants; Collectively exhaustive events; Complete filtration; Complex random variable; Complex random vector; Contiguity (probability theory) Continuum percolation theory; Convergence of Probability ...