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

axioms formalise probability in terms of a probability space, which assigns a measure taking values between 0 and 1, termed the probability measure, to a...

In probability and statistics, a probability mass function (sometimes called probability function or frequency function) is a function that gives the...

random phenomenon in terms of its sample space and the probabilities of events (subsets of the sample space). For instance, if X is used to denote the...

In probability theory, the sample space (also called sample description space, possibility space, or outcome space) of an experiment or random trial is...

In probability theory, a standard probability space, also called Lebesgue–Rokhlin probability space or just Lebesgue space (the latter term is ambiguous)...

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

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...

(\Omega ,F,P)} is a probability space, with sample space Ω {\displaystyle \Omega } , event space F {\displaystyle F} and probability measure P {\displaystyle...

Probability is the branch of mathematics and statistics concerning events and numerical descriptions of how likely they are to occur. The probability...

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

mathematical object usually defined as a family of random variables in a probability space, where the index of the family often has the interpretation of time...

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

pairs of outputs of two random variables that are defined on the same probability space. The joint distribution can just as well be considered for any given...

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 particularly in the Malliavin calculus, a Gaussian probability space is a probability space together with a Hilbert space of mean...

defined as a measurable function from a probability measure space (called the sample space) to a measurable space. This allows consideration of the pushforward...

a measure space is a probability space. A measurable space consists of the first two components without a specific measure. A measure space is a triple...

{\displaystyle \Sigma _{*}} and probability measure P {\displaystyle \mathbb {P} } if Σ∗ is a filtration of the underlying probability space (Ω, Σ,  P {\displaystyle...

are called transition probabilities. The process is characterized by a state space, a transition matrix describing the probabilities of particular transitions...

described or modeled by a mathematical construct known as a probability space. A probability space is constructed and defined with a specific kind of experiment...

In probability theory, a Markov kernel (also known as a stochastic kernel or probability kernel) is a map that in the general theory of Markov processes...

measure must assign value 1 to the entire space. Intuitively, the additivity property says that the probability assigned to the union of two disjoint (mutually...

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...

linear spaces, topological spaces, Hilbert spaces, or probability spaces, it does not define the notion of "space" itself. A space consists of selected mathematical...

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

Probability measure, a real-valued function on a probability space Probability mass function Probability distribution function (disambiguation) This disambiguation...

given two measurable spaces and measures on them, one can obtain a product measurable space and a product measure on that space. Conceptually, this is...

likely. Event (probability theory) – In statistics and probability theory, set of outcomes to which a probability is assigned Sample space – Set of all...

In probability theory and statistics, the conditional probability distribution is a probability distribution that describes the probability of an outcome...