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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. As stated in Laplace's '' Théorie analytique des probabilités'', :The probability of an event is the ratio of the number of cases favorable to it, to the number of all cases possible when nothing leads us to expect that any one of these cases should occur more than any other, which renders them, for us, equally possible. 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, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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. 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 The taxonomy of probability interpretations given here is similar to that of the longer and more complete Interpretations of Probability article in the online Stanford Encyclopedia of Philosophy. References to that article include a parenthetic section number where appropriate. A partial outline of that article: * Section 2: Criteria of adequacy for the interpretations of probability * Section 3: ** 3.1 Classical Probability ** 3.2 Logical Probability ** 3.3 Subjective Probability ** 3.4 Frequency Interpretations ** 3.5 Propensity Interpretations "T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pierre De Fermat
Pierre de Fermat (; between 31 October and 6 December 1607 – 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 1607 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, Domin ... [...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 as the limit of its relative frequency in many trials (the long-run probability). Probabilities can be found (in principle) by a repeatable objective process (and are thus ideally devoid of opinion). 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, ''e.g.'' 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 for reasoning. Definition In the frequentist interpretation, probabilities are ... [...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 The taxonomy of probability interpretations given here is similar to that of the longer and more complete Interpretations of Probability article in the online Stanford Encyclopedia of Philosophy. References to that article include a parenthetic section number where appropriate. A partial outline of that article: * Section 2: Criteria of adequacy for the interpretations of probability * Section 3: ** 3.1 Classical Probability ** 3.2 Logical Probability ** 3.3 Subjective Probability ** 3.4 Frequency Interpretations ** 3.5 Propensity Interpretations "T ... [...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 scholar and polymath whose work was important to the development of engineering, mathematics, statistics, physics, astronomy, and philosophy. He summarized and extended the work of his predecessors in his five-volume ''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. In statistics, the 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 Laplacian differential operator, widely used in mathematics, is also named after him. He restated and developed the nebular hypothesis of the origin of the Solar System and was one of the first scientists to suggest ... [...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 attorney ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Encyclopédie
''Encyclopédie, ou dictionnaire raisonné des sciences, des arts et des métiers'' (English: ''Encyclopedia, or a Systematic Dictionary of the Sciences, Arts, and Crafts''), 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 Enlightenment. According to Denis Diderot in the article "Encyclopédie", the ''Encyclopédies aim was "to change the way people think" and for people (bourgeoisie) 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 dissemina ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Caramuel
Juan Caramuel y Lobkowitz (Juan Caramuel de Lobkowitz, 23 May 1606 in Madrid — 7 or 8 September 1682 in Vigevano) was a Spanish Catholic scholastic philosopher, ecclesiastic, mathematician and writer. He is believed to be a great-grandson of Jan Popel y Lobkowicz. Life Juan Caramuel was born in Madrid in 1606, the son of Count Lorenzo Caramuele and Caterina Frissea von Lobkowitz, a descendant of a German princely family. He was instructed in oriental languages by Archbishop Juan de Esron (Ezron). By the age of 17, he was studying at the University of Alcalá de Henares, where he took his degree in the humanities and philosophy. He was a precocious child, early delving into serious problems in mathematics and even publishing astronomical tables at the age of ten, ''Camuelis primus calamus'' (Madrid 1617). He studied Chinese. He was received into the Cistercian Order at the monastery of La Espina, in the diocese of Palencia in 1625, and after ordination entered upon a varied and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gilles De Roberval
Gilles Personne de Roberval (August 10, 1602 – October 27, 1675), French mathematician, was 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. Two years after that, in 1633, 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 till his death. Roberval was one of those mathematicians who, just before the invention of the infinitesimal calculus, occupied their attention with problems which are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Christiaan Huygens
Christiaan Huygens, Lord of Zeelhem, ( , , ; also spelled Huyghens; la, Hugenius; 14 April 1629 – 8 July 1695) was a Dutch mathematician, physicist, engineer, astronomer, and inventor, who is regarded as one of the greatest scientists of all time and a major figure in the Scientific Revolution. In physics, Huygens made groundbreaking contributions in optics and mechanics, while as an astronomer he is chiefly known for his studies of the rings of Saturn and the discovery of its moon Titan. As an engineer and inventor, he improved the design of telescopes and invented the pendulum clock, a breakthrough in timekeeping and the most accurate timekeeper for almost 300 years. An exceptionally talented mathematician and physicist, Huygens was the first to idealize a physical problem by a set of mathematical parameters, and the first to fully mathematize a mechanistic explanation of an unobservable physical phenomenon.Dijksterhuis, F.J. (2008) Stevin, Huygens and the Dutch republ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Luca Pacioli
Fra Luca Bartolomeo de Pacioli (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. Several of his works were plagiarised from Piero della Francesca, in what has been called "probably the first full-blown case of plagiarism in the history of mathematics". 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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