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Classical Probability
The classical definition of probability or classical interpretation of probability is identified with the works of Jacob Bernoulli and Pierre-Simon Laplace: This definition is essentially a consequence of the principle of indifference. If elementary events are assigned equal probabilities, then the probability of a disjunction of elementary events is just the number of events in the disjunction divided by the total number of elementary events. The classical definition of probability was called into question by several writers of the nineteenth century, including John Venn and George Boole. The frequentist definition of probability became widely accepted as a result of their criticism, and especially through the works of R.A. Fisher. The classical definition enjoyed a revival of sorts due to the general interest in Bayesian probability, because Bayesian methods require a prior probability distribution and the principle of indifference offers one source of such a distribution. C ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dice (11015609)
A die (: dice, sometimes also used as ) is a small, throwable object with marked sides that can rest in multiple positions. Dice are used for generating Statistical randomness, random values, commonly as part of tabletop games, including List of dice games, dice games, board games, role-playing games, and Game of chance, games of chance. A traditional die is a cube with each of its six faces marked with a different number of dots (pip (counting), pips) from one to six. When thrown or rolled, the die comes to rest showing a random integer from one to six on its upper surface, with each value being equally likely. Dice may also have other polyhedron, polyhedral or irregular shapes, may have faces marked with numerals or symbols instead of pips and may have their numbers carved out from the material of the dice instead of marked on it. Loaded dice are specifically designed or modified to favor some results over others, for cheating or entertainment purposes. History Dice have bee ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pierre De Fermat
Pierre de Fermat (; ; 17 August 1601 – 12 January 1665) was a French mathematician who is given credit for early developments that led to infinitesimal calculus, including his technique of adequality. In particular, he is recognized for his discovery of an original method of finding the greatest and the smallest ordinates of curved lines, which is analogous to that of differential calculus, then unknown, and his research into number theory. He made notable contributions to analytic geometry, probability, and optics. He is best known for his Fermat's principle for light propagation and his Fermat's Last Theorem in number theory, which he described in a note at the margin of a copy of Diophantus' ''Arithmetica''. He was also a lawyer at the ''parlement'' of Toulouse, France. Biography Fermat was born in 1601 in Beaumont-de-Lomagne, France—the late 15th-century mansion where Fermat was born is now a museum. He was from Gascony, where his father, Dominique Fermat, was a wealthy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Frequentist Probability
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 frequency in infinitely many trials. Probabilities can be found (in principle) by a repeatable objective process, as in repeated sampling from the same population, and are thus ideally devoid of subjectivity. The continued use of frequentist methods in scientific inference, however, has been called into question. The development of the frequentist account was motivated by the problems and paradoxes of the previously dominant viewpoint, the classical interpretation. In the classical interpretation, probability was defined in terms of the principle of indifference, based on the natural symmetry of a problem, so, for example, the probabilities of dice games arise from the natural symmetric 6-sidedness of the cube. This classical interpretation stumbled at any statistical problem that has no natural symmetry f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Interpretations Of Probability
The word "probability" has been used in a variety of ways since it was first applied to the mathematical study of games of chance. Does probability measure the real, physical, tendency of something to occur, or is it a measure of how strongly one believes it will occur, or does it draw on both these elements? In answering such questions, mathematicians interpret the probability values of probability theory. There are two broad categories of probability interpretations which can be called "physical" and "evidential" probabilities. Physical probabilities, which are also called objective or frequency probabilities, are associated with random physical systems such as roulette wheels, rolling dice and radioactive atoms. In such systems, a given type of event (such as a yielding a six) tends to occur at a persistent rate, or "relative frequency", in a long run of trials. Physical probabilities either explain, or are invoked to explain, these stable frequencies. The two main kinds of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
A Philosophical Essay On Probabilities
A Philosophical Essay on Probabilities is a work by Pierre-Simon Laplace on the mathematical theory of probability. The book consists of two parts, the first with five chapters and the second with thirteen. Table of Contents *Part I - A Philosophical Essay on Probabilities #Introduction #Concerning Probability #General Principles of the Calculus of Probability #Concerning Hope #Analytical Methods of the Calculus of Probability *Part II - Application of the Calculus of Probabilities #Games of Chance #Concerning the Unknown Inequalities which may Exist among Chances Supposed to be Equal #Concerning the Laws of Probability which result from the Indefinite Multiplication of Events #Application of the Calculus of Probabilities to Natural Philosophy #Application of the Calculus of Probabilities to the Moral Sciences #Concerning the Probability of Testimonies #Concerning the Selections and Deliberations of Assemblies #Concerning the Probability of the Judgements of Tribunals #Concerning Tab ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Laplace
Pierre-Simon, Marquis de Laplace (; ; 23 March 1749 – 5 March 1827) was a French polymath, a scholar whose work has been instrumental in the fields of physics, astronomy, mathematics, engineering, statistics, and philosophy. He summarized and extended the work of his predecessors in his five-volume Traité de mécanique céleste, ''Mécanique céleste'' (''Celestial Mechanics'') (1799–1825). This work translated the geometric study of classical mechanics to one based on calculus, opening up a broader range of problems. Laplace also popularized and further confirmed Isaac Newton, Sir Isaac Newton's work. In statistics, the Bayesian probability, Bayesian interpretation of probability was developed mainly by Laplace. Laplace formulated Laplace's equation, and pioneered the Laplace transform which appears in many branches of mathematical physics, a field that he took a leading role in forming. The Laplace operator, Laplacian differential operator, widely used in mathematic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Charles-Benjamin De Lubières
Charles-Benjamin de Langes de Montmirail, baron de Lubières, 1714, Berlin – 1 June 1790, was a Genevan mathematician. Charles-de Lubières Benjamin was the son of François de Lange de Montmirail de Lubières (1664–1720) and Marie Calandrini (1677–1762) from Geneva. In 1703, the father left the Principality of Orange. He first fled to Geneva then to Berlin. In 1732, he became a citizen of Geneva, and later gouverneur de Neuchâtel and in 1752, a member of the Council of Two Hundred (). 22 October 1764, he married Genève Olympe Camp (1709-1785) in Geneva. Lubières is the author of ''Éloge du mathématicien Gabriel Cramer'', ''Relation de voyage en Italie'', extracts from ''Essai analytique sur les facultés de l'âme, by Charles Bonnet'' and ''Considérations sur les corps organisés''. Lubières was a member of the Société des Gens de Lettres de Genève together with the mathematician and philosopher Gabriel Cramer, Jean-Louis Calandrini (1703-1758) and the attorn ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Encyclopédie
, better known as ''Encyclopédie'' (), was a general encyclopedia published in France between 1751 and 1772, with later supplements, revised editions, and translations. It had many writers, known as the Encyclopédistes. It was edited by Denis Diderot and, until 1759, co-edited by Jean le Rond d'Alembert. The ''Encyclopédie'' is most famous for representing the thought of the Age of Enlightenment, Enlightenment. According to Denis Diderot in the article "Encyclopédie", the ''Encyclopédie'' aim was "to change the way people think" and for people to be able to inform themselves and to know things. He and the other contributors advocated for the secularization of learning away from the Jesuits. Diderot wanted to incorporate all of the world's knowledge into the ''Encyclopédie'' and hoped that the text could disseminate all this information to the public and future generations. Thus, it is an example of democratization of knowledge. It was also the first encyclopedia to include ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gilles De Roberval
Gilles Personne de Roberval (August 10, 1602 – October 27, 1675) was a French mathematician born at Roberval near Beauvais, France. His name was originally Gilles Personne or Gilles Personier, with Roberval the place of his birth. Biography Like René Descartes, he was present at the Siege of La Rochelle in 1627. In the same year he went to Paris, and in 1631 he was appointed the philosophy chair at Gervais College, Paris. In 1634, he was also made the chair of mathematics at the Royal College of France. A condition of tenure attached to this particular chair was that the holder (Roberval, in this case) would propose mathematical questions for solution, and should resign in favour of any person who solved them better than himself. Notwithstanding this, Roberval was able to keep the chair until his death. Roberval was one of those mathematicians who, just before the invention of the infinitesimal calculus, occupied their attention with problems which are only soluble, or can ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Christiaan Huygens
Christiaan Huygens, Halen, Lord of Zeelhem, ( , ; ; also spelled Huyghens; ; 14 April 1629 – 8 July 1695) was a Dutch mathematician, physicist, engineer, astronomer, and inventor who is regarded as a key figure in the Scientific Revolution. In physics, Huygens made seminal contributions to optics and mechanics, while as an astronomer he studied the rings of Saturn and discovered its largest moon, Titan (moon), Titan. As an engineer and inventor, he improved the design of telescopes and invented the pendulum clock, the most accurate timekeeper for almost 300 years. A talented mathematician and physicist, his works contain the first idealization of a physical problem by a set of Mathematical model, mathematical parameters, and the first mathematical and mechanistic explanation of an unobservable physical phenomenon.Dijksterhuis, F.J. (2008) Stevin, Huygens and the Dutch republic. ''Nieuw archief voor wiskunde'', ''5'', pp. 100–10/ref> Huygens first identified the correct la ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Luca Pacioli
Luca Bartolomeo de Pacioli, O.F.M. (sometimes ''Paccioli'' or ''Paciolo''; 1447 – 19 June 1517) was an Italian mathematician, Franciscan friar, collaborator with Leonardo da Vinci, and an early contributor to the field now known as accounting. He is referred to as the father of accounting and bookkeeping and he was the first person to publish a work on the double-entry system of book-keeping on the continent. He was also called Luca di Borgo after his birthplace, Borgo Sansepolcro, Tuscany. Life Luca Pacioli was born between 1446 and 1448 in the Tuscan town of Sansepolcro where he received an abbaco education. This was education in the vernacular (''i.e.'', the local tongue) rather than Latin and focused on the knowledge required of merchants. His father was Bartolomeo Pacioli; however, Luca Pacioli was said to have lived with the Befolci family as a child in his birth town Sansepolcro. He moved to Venice around 1464, where he continued his own education while working ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
