The classical definition of probability or classical interpretation of probability is identified with the works of Jacob Bernoulli and Pierre-Simon Laplace:...

the field of probability, championed by Pierre-Simon Laplace, is now known as the classical definition. Developed from studies of games of chance (such...

space: see Classical definition of probability. For example, if the event is "occurrence of an even number when a dice is rolled", the probability is given...

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

reformulation of the ideas of a classical Markov chain, replacing the classical definitions of probability with quantum probability. Very roughly, the theory of a...

gambling probability applications. In games of chance, most of the gambling probability calculus in which we use the classical definition of probability reverts...

Clark–Ocone theorem Class membership probabilities Classic data sets Classical definition of probability Classical test theory – psychometrics Classification...

A definition is a statement of the meaning of a term (a word, phrase, or other set of symbols). Definitions can be classified into two large categories:...

finite-dimensional. We first discuss the classical case. Suppose the probabilities of a finite sequence of events is given by the probability distribution P = {p1...pn}...

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

probability current (sometimes called probability flux) is a mathematical quantity describing the flow of probability. Specifically, if one thinks of...

probability. As with the classical Shannon entropy and its quantum generalization, the von Neumann entropy, one can define a conditional version of min-entropy...

In probability theory, a probability distribution is infinitely divisible if it can be expressed as the probability distribution of the sum of an arbitrary...

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...

quantum mechanics, a probability amplitude is a complex number used for describing the behaviour of systems. The square of the modulus of this quantity at...

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

a sum of free cumulants over the sum non-crossing partitions. This is the free analogue of the moment-cumulant formula in classical probability. See also...

known as the prior probability and marginal probability. Bayes' theorem may be derived from the definition of conditional probability: P ( A | B ) = P (...

measures the expected amount of information needed to describe the state of the variable, considering the distribution of probabilities across all potential states...

Modern Greek: φι fi [fi]) is the twenty-first letter of the Greek alphabet. In Archaic and Classical Greek (c. 9th to 4th century BC), it represented an...

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

subject to two physical constraints: The probabilities of all states add to unity (second axiom of probability): ∑ i ρ i = 1. {\displaystyle \sum _{i}\rho...

In probability theory and related fields, a stochastic (/stəˈkæstɪk/) or random process is a mathematical object usually defined as a family of random...

the process of deductive reasoning. Probability logic studies how the probability of the premises of an inference affects the probability of its conclusion...

equation relates the collection of probability amplitudes that pertain to one moment of time to the collection of probability amplitudes that pertain to another...

probability theory. The statistical entropy perspective was introduced in 1870 by Austrian physicist Ludwig Boltzmann, who established a new field of...

microstate has a certain probability of occurring during the course of the system's thermal fluctuations. In contrast, the macrostate of a system refers to...

transition probabilities or via the jump chain and holding times. As a prelude to a transition-probability definition, we first motivate the definition of a regular...

is a system comprising multiple qubits. It is the quantum analogue of the classical processor register. Quantum computers perform calculations by manipulating...

The probability of the outcome of an experiment is never negative, although a quasiprobability distribution allows a negative probability, or quasiprobability...