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...

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

In probability theory and statistics, a copula is a multivariate cumulative distribution function for which the marginal probability distribution of each...

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, 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...

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 sequence of random...

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

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 and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different...

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

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...

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...

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

Decision theory (or the theory of choice) is a branch of applied probability theory and analytic philosophy concerned with the theory of making decisions...

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

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

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

In probability theory and statistics, the empirical probability, relative frequency, or experimental probability of an event is the ratio of the number...

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

term chance was also used in the mathematical sense of "probability" (and probability theory was called Doctrine of Chances). This word is ultimately...

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

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...

: vii  The field, in applied mathematics, is at the intersection of probability theory, statistics, computer science, statistical mechanics, information...

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