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History Of Probability
Probability has a dual aspect: on the one hand the likelihood of hypotheses given the evidence for them, and on the other hand the behavior of stochastic processes such as the throwing of dice or coins. The study of the former is historically older in, for example, the law of evidence, while the mathematical treatment of dice began with the work of Cardano, Pascal, Fermat and Christiaan Huygens between the 16th and 17th century. Probability is distinguished from statistics; see history of statistics. While statistics deals with data and inferences from it, (stochastic) probability deals with the stochastic (random) processes which lie behind data or outcomes. Etymology ''Probable'' and ''probability'' and their cognates in other modern languages derive from medieval learned Latin ''probabilis'', deriving from Cicero and generally applied to an opinion to mean ''plausible'' or ''generally approved''. The form ''probability'' is from Old French (14 c.) and directly from Latin (no ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty."Kendall's Advanced Theory of Statistics, Volume 1: Distribution Theory", Alan Stuart and Keith Ord, 6th Ed, (2009), .William Feller, ''An Introduction to Probability Theory and Its Applications'', (Vol 1), 3rd Ed, (1968), Wiley, . The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%). These con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Insurance
Insurance is a means of protection from financial loss in which, in exchange for a fee, a party agrees to compensate another party in the event of a certain loss, damage, or injury. It is a form of risk management, primarily used to hedge against the risk of a contingent or uncertain loss. An entity which provides insurance is known as an insurer, insurance company, insurance carrier, or underwriter. A person or entity who buys insurance is known as a policyholder, while a person or entity covered under the policy is called an insured. The insurance transaction involves the policyholder assuming a guaranteed, known, and relatively small loss in the form of a payment to the insurer (a premium) in exchange for the insurer's promise to compensate the insured in the event of a covered loss. The loss may or may not be financial, but it must be reducible to financial terms. Furthermore, it usually involves something in which the insured has an insurable interest established by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Carl Friedrich Gauss
Johann Carl Friedrich Gauss (; german: Gauß ; la, Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields in mathematics and science. Sometimes referred to as the ''Princeps mathematicorum'' () and "the greatest mathematician since antiquity", Gauss had an exceptional influence in many fields of mathematics and science, and he is ranked among history's most influential mathematicians. Also available at Retrieved 23 February 2014. Comprehensive biographical article. Biography Early years Johann Carl Friedrich Gauss was born on 30 April 1777 in Brunswick (Braunschweig), in the Duchy of Brunswick-Wolfenbüttel (now part of Lower Saxony, Germany), to poor, working-class parents. His mother was illiterate and never recorded the date of his birth, remembering only that he had been born on a Wednesday, eight days before the Feast of the Ascension (which occurs 39 days after Easter). Ga ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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. According to the law, the average of the results obtained from a large number of trials should be close to the expected value and tends to become closer to the expected value as more trials are performed. The LLN is important because it guarantees stable long-term results for the averages of some random events. For example, while a casino may lose money in a single spin of the roulette wheel, its earnings will tend towards a predictable percentage over a large number of spins. Any winning streak by a player will eventually be overcome by the parameters of the game. Importantly, the law applies (as the name indicates) only when a ''large number'' of observations are considered. There is no principle that a small number of observations will coincide with the expected value or that a streak of one value will immediately be "balance ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Doctrine Of Chances
''The Doctrine of Chances'' was the first textbook on probability theory, written by 18th-century French mathematician Abraham de Moivre and first published in 1718.. De Moivre wrote in English because he resided in England at the time, having fled France to escape the persecution of Huguenots. The book's title came to be synonymous with ''probability theory'', and accordingly the phrase was used in Thomas Bayes' famous posthumous paper ''An Essay towards solving a Problem in the Doctrine of Chances'', wherein a version of Bayes' theorem was first introduced. Editions The full title of the first edition was ''The doctrine of chances: or, a method for calculating the probabilities of events in play''; it was published in 1718, by W. Pearson, and ran for 175 pages. Published in 1738 by Woodfall and running for 258 pages, the second edition of de Moivre's book introduced the concept of normal distributions as approximations to binomial distributions. In effect de Moivre proved a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abraham De Moivre
Abraham de Moivre FRS (; 26 May 166727 November 1754) was a French mathematician known for de Moivre's formula, a formula that links complex numbers and trigonometry, and for his work on the normal distribution and probability theory. He moved to England at a young age due to the religious persecution of Huguenots in France which reached a climax in 1685 with the Edict of Fontainebleau. He was a friend of Isaac Newton, Edmond Halley, and James Stirling. Among his fellow Huguenot exiles in England, he was a colleague of the editor and translator Pierre des Maizeaux. De Moivre wrote a book on probability theory, ''The Doctrine of Chances'', said to have been prized by gamblers. De Moivre first discovered Binet's formula, the closed-form expression for Fibonacci numbers linking the ''n''th power of the golden ratio ''φ'' to the ''n''th Fibonacci number. He also was the first to postulate the central limit theorem, a cornerstone of probability theory. Life Early years Abraham ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ars Conjectandi
(Latin for "The Art of Conjecturing") is a book on combinatorics and mathematical probability written by Jacob Bernoulli and published in 1713, eight years after his death, by his nephew, Niklaus Bernoulli. The seminal work consolidated, apart from many combinatorial topics, many central ideas in probability theory, such as the very first version of the law of large numbers: indeed, it is widely regarded as the founding work of that subject. It also addressed problems that today are classified in the twelvefold way and added to the subjects; consequently, it has been dubbed an important historical landmark in not only probability but all combinatorics by a plethora of mathematical historians. The importance of this early work had a large impact on both contemporary and later mathematicians; for example, Abraham de Moivre. Bernoulli wrote the text between 1684 and 1689, including the work of mathematicians such as Christiaan Huygens, Gerolamo Cardano, Pierre de Fermat, and Bla ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jacob Bernoulli
Jacob Bernoulli (also known as James or Jacques; – 16 August 1705) was one of the many prominent mathematicians in the Bernoulli family. He was an early proponent of Leibnizian calculus and sided with Gottfried Wilhelm Leibniz during the Leibniz–Newton calculus controversy. He is known for his numerous contributions to calculus, and along with his brother Johann, was one of the founders of the calculus of variations. He also discovered the fundamental mathematical constant . However, his most important contribution was in the field of probability, where he derived the first version of the law of large numbers in his work '' Ars Conjectandi''.Jacob (Jacques) Bernoulli [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Galileo
Galileo di Vincenzo Bonaiuti de' Galilei (15 February 1564 – 8 January 1642) was an Italian astronomer, physicist and engineer, sometimes described as a polymath. Commonly referred to as Galileo, his name was pronounced (, ). He was born in the city of Pisa, then part of the Duchy of Florence. Galileo has been called the "father" of observational astronomy, modern physics, the scientific method, and modern science. Galileo studied speed and velocity, gravity and free fall, the principle of relativity, inertia, projectile motion and also worked in applied science and technology, describing the properties of pendulums and " hydrostatic balances". He invented the thermoscope and various military compasses, and used the telescope for scientific observations of celestial objects. His contributions to observational astronomy include telescopic confirmation of the phases of Venus, observation of the four largest satellites of Jupiter, observation of Saturn's ring ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dante Alighieri
Dante Alighieri (; – 14 September 1321), probably baptized Durante di Alighiero degli Alighieri and often referred to as Dante (, ), was an Italian poet, writer and philosopher. His ''Divine Comedy'', originally called (modern Italian: ''Commedia'') and later christened by Giovanni Boccaccio, is widely considered one of the most important poems of the Middle Ages and the greatest literary work in the Italian language. Dante is known for establishing the use of the vernacular in literature at a time when most poetry was written in Latin, which was accessible only to the most educated readers. His ''De vulgari eloquentia'' (''On Eloquence in the Vernacular'') was one of the first scholarly defenses of the vernacular. His use of the Florentine dialect for works such as '' The New Life'' (1295) and ''Divine Comedy'' helped establish the modern-day standardized Italian language. His work set a precedent that important Italian writers such as Petrarch and Boccaccio would late ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hazard (game)
Hazard is an early English game played with two dice; it was mentioned in Geoffrey Chaucer's ''Canterbury Tales'' in the 14th century. Despite its complicated rules, hazard was very popular in the 17th and 18th centuries and was often played for money. At Crockford's Club in London, hazard was especially popular. In the 19th century, the game craps developed from hazard through a simplification of the rules. Craps is now popular in North America but neither game remains popular amongst the rest of the world. Rules Any number may play, but only one player – the caster – has the dice at any one time. In each round, the caster specifies a number between 5 and 9 inclusive: this is the main. They then throw two dice. * If they roll the main, they win (throwing in or nicking). * If they roll a 2 or a 3, they lose (throwing out or outing). * If they roll an 11 or 12, the result depends on the main: ** with a main of 5 or 9, they throw out with both an 11 a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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