Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations...

Independence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes. Two events are independent, statistically...

In probability theory, a martingale is a sequence of random variables (i.e., a stochastic process) for which, at a particular time, the conditional expectation...

computer science, game theory, and philosophy to, for example, draw inferences about the expected frequency of events. Probability theory is also used to describe...

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. A single outcome...

Bayesian probability (/ˈbeɪziən/ BAY-zee-ən or /ˈbeɪʒən/ BAY-zhən) is an interpretation of the concept of probability, in which, instead of frequency or...

In probability theory and statistics, the characteristic function of any real-valued random variable completely defines its probability distribution. If...

In probability theory and related fields, a stochastic (/stəˈkæstɪk/) or random process is a mathematical object usually defined as a family of random...

In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of possible outcomes...

In probability theory and statistics, two real-valued random variables, X {\displaystyle X} , Y {\displaystyle Y} , are said to be uncorrelated if their...

In the theory of stochastic processes, a subdiscipline of probability theory, filtrations are totally ordered collections of subsets that are used to...

In probability theory, an experiment or trial (see below) is any procedure that can be infinitely repeated and has a well-defined set of possible outcomes...

In probability theory, a probability space or a probability triple ( Ω , F , P ) {\displaystyle (\Omega ,{\mathcal {F}},P)} is a mathematical construct...

In probability theory, the law (or formula) of total probability is a fundamental rule relating marginal probabilities to conditional probabilities. It...

The standard probability axioms are the foundations of probability theory introduced by Russian mathematician Andrey Kolmogorov in 1933. These axioms remain...

ideas since long before the invention of poker. The development of probability theory in the late 1400s was attributed to gambling; when playing a game...

Frequentist probability or frequentism is an interpretation of probability; it defines an event's probability as the limit of its relative frequency in...

Decision theory or the theory of rational choice is a branch of probability, economics, and analytic philosophy that uses the tools of expected utility...

In probability theory, Bernstein inequalities give bounds on the probability that the sum of random variables deviates from its mean. In the simplest...

Free probability is a mathematical theory that studies non-commutative random variables. The "freeness" or free independence property is the analogue of...

In probability theory, there exist several different notions of convergence of sequences of random variables, including convergence in probability, convergence...

In probability theory, conditional probability is a measure of the probability of an event occurring, given that another event (by assumption, presumption...

on probability theory and theoretical computer science. In essence, Solomonoff's induction derives the posterior probability of any computable theory, given...

mathematicians interpret the probability values of probability theory. There are two broad categories of probability interpretations which can be called...

In probability theory, the probability generating function of a discrete random variable is a power series representation (the generating function) of...

In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes...

(1995). Probability and Measure. John Wiley. ISBN 0-471-00710-2. Ash, Robert B.; Doléans-Dade, Catherine A. (1999). Probability & Measure Theory. Academic...

In probability theory, the total variation distance is a distance measure for probability distributions. It is an example of a statistical distance metric...

before an experiment is conducted. As a mathematical subject, the theory of probability arose very late—as compared to geometry for example—despite the...

In probability theory, a tree diagram may be used to represent a probability space. A tree diagram may represent a series of independent events (such...