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...

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

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

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

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

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

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...

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

In probability theory, a martingale is a stochastic process in which the expected value of the next observation, given all prior observations, is equal...

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

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...

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

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

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...

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...

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

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...

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

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

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]...

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

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

In probability theory and statistics, a Markov chain or Markov process is a stochastic process describing a sequence of possible events in which the probability...

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

In probability theory, the total variation distance is a statistical distance between probability distributions, and is sometimes called the statistical...

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...