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

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

(\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 a branch of mathematics and statistics concerning events and numerical descriptions of how likely they are to occur. The probability of...

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

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

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

{\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...

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

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

on the same probability space, the multivariate or joint probability distribution for X , Y , … {\displaystyle X,Y,\ldots } is a probability distribution...

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...

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

more formal probability theory, a random variable is a function X defined from a sample space Ω to a measurable space called the state space. If an element...

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

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...

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

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...

A prior probability distribution of an uncertain quantity, simply called the prior, is its assumed probability distribution before some evidence is taken...

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