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101 relations: Absolute continuity, Almost surely, Andrey Kolmogorov, Average, Axiomatic system, Belmont, California, Bernoulli distribution, Berry–Esseen theorem, Bertrand paradox (probability), Beta distribution, Binomial distribution, Blaise Pascal, Borel set, Brownian motion, Bruno de Finetti, Cantor distribution, Catalog of articles in probability theory, Central limit theorem, Christiaan Huygens, Classical definition of probability, Coin, Coin flipping, Combinatorics, Continuous function, Convergence of random variables, Countable set, Counting measure, Cumulative distribution function, David Williams (mathematician), Determinism, Dice, Dimension, Dirac delta function, Discrete uniform distribution, Elementary event, Event (probability theory), Expected value, Exponential distribution, Exponential family, Fat-tailed distribution, Function (mathematics), Fuzzy logic, Fuzzy measure theory, Game of chance, Gamma distribution, Geometric distribution, Gerolamo Cardano, Glossary of probability and statistics, Heavy-tailed distribution, Henk Tijms, ..., Independence (probability theory), Law of large numbers, Lebesgue measure, Likelihood function, List of important publications in statistics, List of probabilistic proofs of non-probabilistic theorems, List of probability topics, List of statistics articles, Mathematical analysis, Mathematics, Mean, Measure (mathematics), Monotonic function, Negative binomial distribution, Normal distribution, Notation in probability and statistics, Olav Kallenberg, Patrick Billingsley, Physics, Pierre de Fermat, Pierre-Simon Laplace, Playing card, Poisson distribution, Power set, Predictive modelling, Probabilistic logic, Probability, Probability axioms, Probability density function, Probability distribution, Probability interpretations, Probability mass function, Probability measure, Probability space, Problem of points, Quantity, Quantum mechanics, Radon–Nikodym theorem, Random variable, Random walk, Real number, Richard von Mises, Sample space, Sigma-algebra, Statistical mechanics, Statistics, Stochastic process, Subjective logic, Subset, Uniform distribution (continuous), Variance. Expand index (51 more) »
Absolute continuity
In calculus, absolute continuity is a smoothness property of functions that is stronger than continuity and uniform continuity.
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Almost surely
In probability theory, one says that an event happens almost surely (sometimes abbreviated as a.s.) if it happens with probability one.
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Andrey Kolmogorov
Andrey Nikolaevich Kolmogorov (a, 25 April 1903 – 20 October 1987) was a 20th-century Soviet mathematician who made significant contributions to the mathematics of probability theory, topology, intuitionistic logic, turbulence, classical mechanics, algorithmic information theory and computational complexity.
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Average
In colloquial language, an average is a middle or typical number of a list of numbers.
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Axiomatic system
In mathematics, an axiomatic system is any set of axioms from which some or all axioms can be used in conjunction to logically derive theorems.
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Belmont, California
Belmont is a city in San Mateo County in the U.S. state of California.
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Bernoulli distribution
In probability theory and statistics, the Bernoulli distribution, named after Swiss mathematician Jacob Bernoulli, is the discrete probability distribution of a random variable which takes the value 1 with probability p and the value 0 with probability q.
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Berry–Esseen theorem
In probability theory, the central limit theorem states that, under certain circumstances, the probability distribution of the scaled mean of a random sample converges to a normal distribution as the sample size increases to infinity.
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Bertrand paradox (probability)
The Bertrand paradox is a problem within the classical interpretation of probability theory.
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Beta distribution
In probability theory and statistics, the beta distribution is a family of continuous probability distributions defined on the interval parametrized by two positive shape parameters, denoted by α and β, that appear as exponents of the random variable and control the shape of the distribution.
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Binomial distribution
In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a sequence of n independent experiments, each asking a yes–no question, and each with its own boolean-valued outcome: a random variable containing a single bit of information: success/yes/true/one (with probability p) or failure/no/false/zero (with probability q.
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Blaise Pascal
Blaise Pascal (19 June 1623 – 19 August 1662) was a French mathematician, physicist, inventor, writer and Catholic theologian.
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Borel set
In mathematics, a Borel set is any set in a topological space that can be formed from open sets (or, equivalently, from closed sets) through the operations of countable union, countable intersection, and relative complement.
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Brownian motion
Brownian motion or pedesis (from πήδησις "leaping") is the random motion of particles suspended in a fluid (a liquid or a gas) resulting from their collision with the fast-moving molecules in the fluid.
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Bruno de Finetti
Bruno de Finetti (13 June 1906 – 20 July 1985) was an Italian probabilist statistician and actuary, noted for the "operational subjective" conception of probability.
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Cantor distribution
The Cantor distribution is the probability distribution whose cumulative distribution function is the Cantor function.
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Catalog of articles in probability theory
This page lists articles related to probability theory.
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Central limit theorem
In probability theory, the central limit theorem (CLT) establishes that, in some situations, when independent random variables are added, their properly normalized sum tends toward a normal distribution (informally a "bell curve") even if the original variables themselves are not normally distributed.
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Christiaan Huygens
Christiaan Huygens (Hugenius; 14 April 1629 – 8 July 1695) was a Dutch physicist, mathematician, astronomer and inventor, who is widely regarded as one of the greatest scientists of all time and a major figure in the scientific revolution.
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Classical definition of probability
The classical definition or interpretation of probability is identified with the works of Jacob Bernoulli and Pierre-Simon Laplace.
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Coin
A coin is a small, flat, (usually) round piece of metal or plastic used primarily as a medium of exchange or legal tender.
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Coin flipping
Coin flipping, coin tossing, or heads or tails is the practice of throwing a coin in the air and checking which side is showing when it lands to choose between two alternatives, sometimes to resolve a dispute between two parties.
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Combinatorics
Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures.
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Continuous function
In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output.
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Convergence of random variables
In probability theory, there exist several different notions of convergence of random variables.
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Countable set
In mathematics, a countable set is a set with the same cardinality (number of elements) as some subset of the set of natural numbers.
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Counting measure
In mathematics, the counting measure is an intuitive way to put a measure on any set: the "size" of a subset is taken to be: the number of elements in the subset if the subset has finitely many elements, and ∞ if the subset is infinite.
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Cumulative distribution function
In probability theory and statistics, the cumulative distribution function (CDF, also cumulative density function) of a real-valued random variable X, or just distribution function of X, evaluated at x, is the probability that X will take a value less than or equal to x. In the case of a continuous distribution, it gives the area under the probability density function from minus infinity to x. Cumulative distribution functions are also used to specify the distribution of multivariate random variables.
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David Williams (mathematician)
David Williams FRS is a Welsh mathematician who works in probability theory.
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Determinism
Determinism is the philosophical theory that all events, including moral choices, are completely determined by previously existing causes.
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Dice
Dice (singular die or dice; from Old French dé; from Latin datum "something which is given or played") are small throwable objects with multiple resting positions, used for generating random numbers.
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Dimension
In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it.
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Dirac delta function
In mathematics, the Dirac delta function (function) is a generalized function or distribution introduced by the physicist Paul Dirac.
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Discrete uniform distribution
In probability theory and statistics, the discrete uniform distribution is a symmetric probability distribution whereby a finite number of values are equally likely to be observed; every one of n values has equal probability 1/n.
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Elementary event
In probability theory, an elementary event (also called an atomic event or simple event) is an event which contains only a single outcome in the sample space.
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Event (probability theory)
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.
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Expected value
In probability theory, the expected value of a random variable, intuitively, is the long-run average value of repetitions of the experiment it represents.
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Exponential distribution
No description.
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Exponential family
In probability and statistics, an exponential family is a set of probability distributions of a certain form, specified below.
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Fat-tailed distribution
A fat-tailed distribution is a probability distribution that has the property, along with the other heavy-tailed distributions, that it exhibits large skewness or kurtosis.
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Function (mathematics)
In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.
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Fuzzy logic
Fuzzy logic is a form of many-valued logic in which the truth values of variables may be any real number between 0 and 1.
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Fuzzy measure theory
In mathematics, fuzzy measure theory considers generalized measures in which the additive property is replaced by the weaker property of monotonicity.
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Game of chance
A game of chance is a game whose outcome is strongly influenced by some randomizing device, and upon which contestants may choose to wager money or anything of monetary value.
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Gamma distribution
In probability theory and statistics, the gamma distribution is a two-parameter family of continuous probability distributions.
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Geometric distribution
In probability theory and statistics, the geometric distribution is either of two discrete probability distributions.
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Gerolamo Cardano
Gerolamo (or Girolamo, or Geronimo) Cardano (Jérôme Cardan; Hieronymus Cardanus; 24 September 1501 – 21 September 1576) was an Italian polymath, whose interests and proficiencies ranged from being a mathematician, physician, biologist, physicist, chemist, astrologer, astronomer, philosopher, writer, and gambler.
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Glossary of probability and statistics
Most of the terms listed in Wikipedia glossaries are already defined and explained within Wikipedia itself.
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Heavy-tailed distribution
In probability theory, heavy-tailed distributions are probability distributions whose tails are not exponentially bounded: that is, they have heavier tails than the exponential distribution.
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Henk Tijms
Henk Tijms (Beverwijk, April 23, 1944) is a Dutch mathematician and Emeritus Professor of Operations Research at the VU University Amsterdam.
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Independence (probability theory)
In probability theory, two events are independent, statistically independent, or stochastically independent if the occurrence of one does not affect the probability of occurrence of the other.
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Law of large numbers
In probability theory, the law of large numbers (LLN) is a theorem that describes the result of performing the same experiment a large number of times.
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Lebesgue measure
In measure theory, the Lebesgue measure, named after French mathematician Henri Lebesgue, is the standard way of assigning a measure to subsets of n-dimensional Euclidean space.
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Likelihood function
In frequentist inference, a likelihood function (often simply the likelihood) is a function of the parameters of a statistical model, given specific observed data.
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List of important publications in statistics
This is a list of important publications in statistics, organized by field.
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List of probabilistic proofs of non-probabilistic theorems
Probability theory routinely uses results from other fields of mathematics (mostly, analysis).
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List of probability topics
This is a list of probability topics, by Wikipedia page.
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List of statistics articles
No description.
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Mathematical analysis
Mathematical analysis is the branch of mathematics dealing with limits and related theories, such as differentiation, integration, measure, infinite series, and analytic functions.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Mean
In mathematics, mean has several different definitions depending on the context.
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Measure (mathematics)
In mathematical analysis, a measure on a set is a systematic way to assign a number to each suitable subset of that set, intuitively interpreted as its size.
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Monotonic function
In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order.
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Negative binomial distribution
In probability theory and statistics, the negative binomial distribution is a discrete probability distribution of the number of successes in a sequence of independent and identically distributed Bernoulli trials before a specified (non-random) number of failures (denoted r) occurs.
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Normal distribution
In probability theory, the normal (or Gaussian or Gauss or Laplace–Gauss) distribution is a very common continuous probability distribution.
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Notation in probability and statistics
Probability theory and statistics have some commonly used conventions, in addition to standard mathematical notation and mathematical symbols.
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Olav Kallenberg
Olav Kallenberg is a probability theorist known for his work on exchangeable stochastic processes and for his graduate-level textbooks and monographs.
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Patrick Billingsley
Patrick Paul Billingsley (May 3, 1925 – April 22, 2011) was an American mathematician and stage and screen actor, noted for his books in advanced probability theory and statistics.
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Physics
Physics (from knowledge of nature, from φύσις phýsis "nature") is the natural science that studies matterAt the start of The Feynman Lectures on Physics, Richard Feynman offers the atomic hypothesis as the single most prolific scientific concept: "If, in some cataclysm, all scientific knowledge were to be destroyed one sentence what statement would contain the most information in the fewest words? I believe it is that all things are made up of atoms – little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another..." and its motion and behavior through space and time and that studies the related entities of energy and force."Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." Physics is one of the most fundamental scientific disciplines, and its main goal is to understand how the universe behaves."Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physics. (...) You will come to see physics as a towering achievement of the human intellect in its quest to understand our world and ourselves."Physics is an experimental science. Physicists observe the phenomena of nature and try to find patterns that relate these phenomena.""Physics is the study of your world and the world and universe around you." Physics is one of the oldest academic disciplines and, through its inclusion of astronomy, perhaps the oldest. Over the last two millennia, physics, chemistry, biology, and certain branches of mathematics were a part of natural philosophy, but during the scientific revolution in the 17th century, these natural sciences emerged as unique research endeavors in their own right. Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry, and the boundaries of physics are not rigidly defined. New ideas in physics often explain the fundamental mechanisms studied by other sciences and suggest new avenues of research in academic disciplines such as mathematics and philosophy. Advances in physics often enable advances in new technologies. For example, advances in the understanding of electromagnetism and nuclear physics led directly to the development of new products that have dramatically transformed modern-day society, such as television, computers, domestic appliances, and nuclear weapons; advances in thermodynamics led to the development of industrialization; and advances in mechanics inspired the development of calculus.
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Pierre de Fermat
Pierre de Fermat (Between 31 October and 6 December 1607 – 12 January 1665) was a French lawyer at the Parlement of Toulouse, France, and a mathematician who is given credit for early developments that led to infinitesimal calculus, including his technique of adequality.
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Pierre-Simon Laplace
Pierre-Simon, marquis de Laplace (23 March 1749 – 5 March 1827) was a French scholar whose work was important to the development of mathematics, statistics, physics and astronomy.
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Playing card
A playing card is a piece of specially prepared heavy paper, thin cardboard, plastic-coated paper, cotton-paper blend, or thin plastic, marked with distinguishing motifs and used as one of a set for playing card games.
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Poisson distribution
In probability theory and statistics, the Poisson distribution (in English often rendered), named after French mathematician Siméon Denis Poisson, is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant rate and independently of the time since the last event.
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Power set
In mathematics, the power set (or powerset) of any set is the set of all subsets of, including the empty set and itself, variously denoted as, 𝒫(), ℘() (using the "Weierstrass p"),,, or, identifying the powerset of with the set of all functions from to a given set of two elements,.
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Predictive modelling
Predictive modelling uses statistics to predict outcomes.
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Probabilistic logic
The aim of a probabilistic logic (also probability logic and probabilistic reasoning) is to combine the capacity of probability theory to handle uncertainty with the capacity of deductive logic to exploit structure of formal argument.
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Probability
Probability is the measure of the likelihood that an event will occur.
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Probability axioms
In Kolmogorov's probability theory, the probability P of some event E, denoted P(E), is usually defined such that P satisfies the Kolmogorov axioms, named after the Russian mathematician Andrey Kolmogorov, which are described below.
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Probability density function
In probability theory, a probability density function (PDF), or density of a continuous random variable, is a function, whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the random variable would equal that sample.
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Probability distribution
In probability theory and statistics, a probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment.
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Probability interpretations
The word probability has been used in a variety of ways since it was first applied to the mathematical study of games of chance.
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Probability mass function
In probability and statistics, a probability mass function (pmf) is a function that gives the probability that a discrete random variable is exactly equal to some value.
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Probability measure
In mathematics, a probability measure is a real-valued function defined on a set of events in a probability space that satisfies measure properties such as countable additivity.
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Probability space
In probability theory, a probability space or a probability triple (\Omega, \mathcal, P) is a mathematical construct that models a real-world process (or “experiment”) consisting of states that occur randomly.
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Problem of points
The problem of points, also called the problem of division of the stakes, is a classical problem in probability theory.
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Quantity
Quantity is a property that can exist as a multitude or magnitude.
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Quantum mechanics
Quantum mechanics (QM; also known as quantum physics, quantum theory, the wave mechanical model, or matrix mechanics), including quantum field theory, is a fundamental theory in physics which describes nature at the smallest scales of energy levels of atoms and subatomic particles.
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Radon–Nikodym theorem
In mathematics, the Radon–Nikodym theorem is a result in measure theory.
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Random variable
In probability and statistics, a random variable, random quantity, aleatory variable, or stochastic variable is a variable whose possible values are outcomes of a random phenomenon.
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Random walk
A random walk is a mathematical object, known as a stochastic or random process, that describes a path that consists of a succession of random steps on some mathematical space such as the integers.
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Real number
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
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Richard von Mises
Richard Edler von Mises (19 April 1883 – 14 July 1953) was a scientist and mathematician who worked on solid mechanics, fluid mechanics, aerodynamics, aeronautics, statistics and probability theory.
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Sample space
In probability theory, the sample space of an experiment or random trial is the set of all possible outcomes or results of that experiment.
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Sigma-algebra
In mathematical analysis and in probability theory, a σ-algebra (also σ-field) on a set X is a collection Σ of subsets of X that includes the empty subset, is closed under complement, and is closed under countable unions and countable intersections.
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Statistical mechanics
Statistical mechanics is one of the pillars of modern physics.
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Statistics
Statistics is a branch of mathematics dealing with the collection, analysis, interpretation, presentation, and organization of data.
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Stochastic process
--> In probability theory and related fields, a stochastic or random process is a mathematical object usually defined as a collection of random variables.
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Subjective logic
Subjective logic is a type of probabilistic logic that explicitly takes uncertainty and source trust into account.
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Subset
In mathematics, a set A is a subset of a set B, or equivalently B is a superset of A, if A is "contained" inside B, that is, all elements of A are also elements of B. A and B may coincide.
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Uniform distribution (continuous)
In probability theory and statistics, the continuous uniform distribution or rectangular distribution is a family of symmetric probability distributions such that for each member of the family, all intervals of the same length on the distribution's support are equally probable.
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Variance
In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its mean.
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References
[1] https://en.wikipedia.org/wiki/Probability_theory
