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Probability theory. 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]
The law of total probability is [1] a theorem that states, in its discrete case, if is a finite or countably infinite set of mutually exclusive and collectively exhaustive events, then for any event. or, alternatively, [1] where, for any , if , then these terms are simply omitted from the summation since is finite.
Download as PDF; Printable version; ... Part of a series on statistics: Probability theory; Probability. Axioms; Determinism. System ... Bayes' theorem; Boole's ...
In probability theory, the Borel–Cantelli lemma is a theorem about sequences of events. In general, it is a result in measure theory. It is named after Émile Borel and Francesco Paolo Cantelli, who gave statement to the lemma in the first decades of the 20th century. [1][2] A related result, sometimes called the second Borel–Cantelli lemma ...
Wald's equation. In probability theory, Wald's equation, Wald's identity[1] or Wald's lemma[2] is an important identity that simplifies the calculation of the expected value of the sum of a random number of random quantities. In its simplest form, it relates the expectation of a sum of randomly many finite-mean, independent and identically ...
v. t. e. In probability theory, an event is a set 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 ...
Characterization of probability distributions. Chung–Erdős inequality. Condorcet's jury theorem. Continuous mapping theorem. Contraction principle (large deviations theory) Coupon collector's problem. Cox's theorem. Cramér–Wold theorem. Cramér's theorem (large deviations)
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.