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...

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 subset of outcomes of an experiment (a subset of the sample space) to which a probability is assigned. A single outcome...

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

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

In probability theory and statistics, a probability distribution is a function that gives the probabilities of occurrence of possible events for an experiment...

Frequentist probability or frequentism is an interpretation of probability; it defines an event's probability (the long-run probability) as the limit...

of probability or classical interpretation of probability is identified with the works of Jacob Bernoulli and Pierre-Simon Laplace: The probability of...

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...

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

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

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

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

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

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...

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

understood connections to other frameworks such as probability, possibility and imprecise probability theories. First introduced by Arthur P. Dempster in the...

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

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 density function (PDF), density function, or density of an absolutely continuous random variable, is a function whose...

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

In probability theory and statistics, the Poisson distribution (/ˈpwɑːsɒn/) is a discrete probability distribution that expresses the probability of a...

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

In probability theory, an outcome is a possible result of an experiment or trial. Each possible outcome of a particular experiment is unique, and different...