Exotic probabilities

Quasiprobability distribution

A quasiprobability distribution is a mathematical object similar to a probability distribution but which relaxes some of Kolmogorov's axioms of probability theory. Quasiprobabilities share several of general features with ordinary probabilities, such as, crucially, the ability to yield expectation values with respect to the weights of the distribution. They can however violate the σ-additivity axiom: integrating them over does not necessarily yield probabilities of mutually exclusive states. Indeed, quasiprobability distributions also counterintuitively have regions of negative probability density, contradicting the first axiom. Quasiprobability distributions arise naturally in the study of quantum mechanics when treated in phase space formulation, commonly used in quantum optics, time-frequency analysis, and elsewhere. (Wikipedia).

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From playlist Probability Distributions

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From playlist The Normal Distribution

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From playlist MIT 8.422 Atomic and Optical Physics II, Spring 2013

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From playlist Statistics

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From playlist Machine Learning

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From playlist OCR MEI Statistics Minor G: Discrete Uniform Distributions

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From playlist OCR MEI Statistics Minor I: Binomial Distribution

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EPR paradox | Unit vector | Weierstrass transform | Diagonal matrix | C-number | Negative probability | Optical equivalence theorem | Order of integration (calculus) | Wigner quasiprobability distribution | Gaussian function | Fokker–Planck equation | Gamma function | Dirac delta function | Orthonormal basis | Overcompleteness | Probability distribution | Cohen's class distribution function | Convolution | Quantum entanglement | Hilbert space | Master equation | Fourier transform | Probability axioms | Characteristic function (probability theory)