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...

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

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

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...

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 as...

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

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...

keystroke or mouse click Event (philosophy), an object in time, or an instantiation of a property in an object Event (probability theory), a set of outcomes...

In probability theory, an elementary event, also called an atomic event or sample point, is an event which contains only a single outcome in the sample...

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

The black swan theory or theory of black swan events is a metaphor that describes an event that comes as a surprise, has a major effect, and is often...

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, 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, the complement of any event A is the event [not A], i.e. the event that A does not occur. The event A and its complement [not A]...

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

probability space Random element Random compact set Dynkin system Probability axioms Event (probability theory) Complementary event Elementary event "Almost...

In probability theory, an event is said to happen almost surely (sometimes abbreviated as a.s.) if it happens with probability 1 (with respect to the...

compact set Dynkin system Probability axioms Normalizing constant Event (probability theory) Complementary event Elementary event Mutually exclusive Boole's...

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

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

measure theory as follows: Let ( X , Σ , μ ) {\displaystyle (X,\Sigma ,\mu )} be a probability space. Let A ∈ Σ {\displaystyle A\in \Sigma } be an event. The...

In probability theory and computer science, a log probability is simply a logarithm of a probability. The use of log probabilities means representing...

In probability theory and statistics, the Poisson distribution is a discrete probability distribution that expresses the probability of a given number...

In mathematics, a probability measure is a real-valued function defined on a set of events in a σ-algebra that satisfies measure properties such as countable...

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