In probability theory, a probability space or a probability triple ( Ω , F , P ) {\displaystyle (\Omega ,{\mathcal {F}},P)} is a mathematical construct...
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In probability and statistics, a probability mass function (sometimes called probability function or frequency function) is a function that gives the...
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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...
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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...
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In probability theory, a standard probability space, also called Lebesgue–Rokhlin probability space or just Lebesgue space (the latter term is ambiguous)...
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In probability theory, the sample space (also called sample description space, possibility space, or outcome space) of an experiment or random trial is...
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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...
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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...
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(\Omega ,F,P)} is a probability space, with sample space Ω {\displaystyle \Omega } , event space F {\displaystyle F} and probability measure P {\displaystyle...
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Stochastic process (redirect from Version (probability theory))
mathematical object usually defined as a sequence of random variables in a probability space, where the index of the sequence often has the interpretation of time...
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Probability is the branch of mathematics[dubious – discuss] concerning events and numerical descriptions of how likely they are to occur. The probability...
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Independence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes. Two events are independent, statistically...
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variables that are defined on the same probability space, the joint probability distribution is the corresponding probability distribution on all possible pairs...
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In probability theory, the law (or formula) of total probability is a fundamental rule relating marginal probabilities to conditional probabilities. It...
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Convergence of random variables (redirect from Convergence in probability)
In probability theory, there exist several different notions of convergence of sequences of random variables, including convergence in probability, convergence...
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In probability theory, conditional probability is a measure of the probability of an event occurring, given that another event (by assumption, presumption...
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In probability theory particularly in the Malliavin calculus, a Gaussian probability space is a probability space together with a Hilbert space of mean...
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defined as a measurable function from a probability measure space (called the sample space) to a measurable space. This allows consideration of the pushforward...
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spaces, such as Euclidean spaces, linear spaces, topological spaces, Hilbert spaces, or probability spaces, it does not define the notion of "space"...
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Markov chain (redirect from Transition probability)
are called transition probabilities. The process is characterized by a state space, a transition matrix describing the probabilities of particular transitions...
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Markov kernel (redirect from Probability kernel)
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...
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{\displaystyle \Sigma _{*}} and probability measure P {\displaystyle \mathbb {P} } if Σ∗ is a filtration of the underlying probability space (Ω, Σ, P {\displaystyle...
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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...
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likely. Event (probability theory) – In statistics and probability theory, set of outcomes to which a probability is assigned Sample space – Set of all...
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Probability measure, a real-valued function on a probability space Probability mass function Probability distribution function (disambiguation) This disambiguation...
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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...
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function as the probability amplitude is a pillar of the Copenhagen interpretation of quantum mechanics. In fact, the properties of the space of wave functions...
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Lebesgue space may refer to: Lp space, a special Banach space of functions (or rather, equivalence classes of functions) Standard probability space, a non-pathological...
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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...
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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...
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