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 pairwise independent collection of random variables is a set of random variables any two of which are independent. Any collection...

In probability theory, conditional independence describes situations wherein an observation is irrelevant or redundant when evaluating the certainty of...

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

total probability Bayes' theorem Independence (probability theory) (Related topics: measure theory) Sample spaces, σ-algebras and probability measures...

In probability theory and statistics, a collection of random variables is independent and identically distributed (i.i.d., iid, or IID) if each random...

vine is a graphical tool for labeling constraints in high-dimensional probability distributions. A regular vine is a special case for which all constraints...

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

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

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

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...

In probability theory, conditional dependence is a relationship between two or more events that are dependent when a third event occurs. For example, if...

In probability theory, comonotonicity mainly refers to the perfect positive dependence between the components of a random vector, essentially saying that...

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

catalog of articles in probability theory. For distributions, see List of probability distributions. For journals, see list of probability journals. For contributors...

statistics, Local independence is the underlying assumption of latent variable models (such as factor analysis and item response theory models). The observed...

Causal inference, Chapman & Hall/CRC monographs on statistics & applied probability, CRC, p. 70, ISBN 978-1-4200-7616-5 Julia M. Rohrer (2018-07-02). "Thinking...

(mathematical logic), logical independence Independence (probability theory), statistical independence Linear independence Independence (1976 film), a docudrama...

of truth Disposition Eclecticism Epistemic theories of truth Imagination Independence (probability theory) Invariant (mathematics) McNamara fallacy Normative...

In probability theory and statistics, subindependence is a weak form of independence. Two random variables X and Y are said to be subindependent if the...

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

possibilities, we find x 1 x 2 = { + 1  with probability  N + ( N + − 1 ) + N − ( N − − 1 ) N ( N − 1 ) − 1  with probability  2 N + N − N ( N − 1 ) {\displaystyle...

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

In statistics, a spurious relationship or spurious correlation is a mathematical relationship in which two or more events or variables are associated but...

In probability theory, the tail dependence of a pair of random variables is a measure of their comovements in the tails of the distributions. The concept...

In statistics, there is a negative relationship or inverse relationship between two variables if higher values of one variable tend to be associated with...

Statistical theory Population Statistic Probability distribution Sampling distribution Order statistic Empirical distribution Density estimation Statistical...

influence each other. Through propagation of independence, the independence of Ui implies independence of Yi, even though each Yi has a different expectation...

In probability theory, a random variable Y {\displaystyle Y} is said to be mean independent of random variable X {\displaystyle X} if and only if its conditional...