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Informally, probable is one of several words applied to uncertain events or knowledge, being more or less interchangeable with likely, risky, hazardous, uncertain, and doubtful, depending on the context. Chance, odds, and bet are other words expressing similar notions. As with the theory of mechanics which assigns precise definitions to such everyday terms as work and force, so the theory of probability attempts to quantify the notion of probable.
The scientific study of probability is a modern development. Gambling shows that there has been an interest in quantifying the ideas of probability for millennia, but exact mathematical descriptions of use in those problems only arose much later.
The doctrine of probabilities dates to the correspondence of Pierre de Fermat and Blaise Pascal (1654). Christiaan Huygens (1657) gave the first scientific treatment of the subject. Jakob Bernoulli's Ars Conjectandi (posthumous, 1713) and Abraham de Moivre's Doctrine of Chances (1718) treated the subject as a branch of mathematics.
The theory of errors may be traced back to Roger Cotes's Opera Miscellanea (posthumous, 1722), but a memoir prepared by Thomas Simpson in 1755 (printed 1756) first applied the theory to the discussion of errors of observation. The reprint (1757) of this memoir lays down the axioms that positive and negative errors are equally probable, and that there are certain assignable limits within which all errors may be supposed to fall; continuous errors are discussed and a probability curve is given.
Pierre-Simon Laplace (1774) made the first attempt to deduce a rule for the combination of observations from the principles of the theory of probabilities. He represented the law of probability of errors by a curve , being any error and its probability, and laid down three properties of this curve: (1) It is symmetric asto the -axis; (2) the -axis is an asymptote, the probability of the error being 0; (3) the area enclosed is 1, it being certain that an error exists. He deduced a formula for the mean of three observations. He also gave (1781) a formula for the law of facility of error (a term due to Lagrange, 1774), but one which led to unmanageable equations. Daniel Bernoulli (1778) introduced the principle of the maximum product of the probabilities of a system of concurrent errors.
The method of least squares is due to Adrien-Marie LegendreAdrien-Marie Legendre ( September 18 1752 January 10 1833) was a French mathematician. He made important contributions to statistics, number theory, abstract algebra and mathematical analysis. Most of his work was brought to perfection by others: his work (1805), who introduced it in his Nouvelles méthodes pour la détermination des orbites des comètes. In ignorance of Legendre's contribution, an Irish-American writer, Robert AdrainRobert Adrain ( September 30, 1775 August 10, 1843) was a scientist and mathematician. He was born in Carrickfergus, Ireland, but left Ireland after the failure of the uprising of the United Irishmen in 1798 and moved to Princeton, New Jersey. He taught m, editor of "The Analyst" (1808), first deduced the law of facility of error,
1856), and Morgan Crofton (1870). Other contributors were Ellis (1844), De MorganAugustus De Morgan ( June 27, 1806 March 18, 1871) was an Indian-born British mathematician and logician. He formulated De Morgan's laws and was the first to introduce the term, and make rigorous the idea of mathematical induction 1. Biography Childhood A (1864), GlaisherGlaisher may mean James Glaisher the meteorologist; James Whitbread Lee Glaisher, the mathematician. (1872), and Giovanni SchiaparelliGiovanni Virginio Schiaparelli ( March 14, 1835 July 4, 1910) was an Italian astronomer. He studied at the University of Turin and Berlin Observatory and worked for over forty years at Brera Observatory. He observed objects in the solar system, and after (1875). Peters's (1856) formula for , the probable error of a single observation, is well known.
In the nineteenth century authors on the general theory included Laplace, Sylvestre Lacroix (1816), Littrow (1833), Adolphe Quetelet (1853), Richard Dedekind (1860), Helmert (1872), Hermann Laurent (1873), Liagre, Didion, and Karl Pearson. Augustus De Morgan and George Boole improved the exposition of the theory.
On the geometric side (see integral geometry) contributors to The Educational Times were influential (Miller, Crofton, McColl, Wolstenholme, Watson, and Artemas Martin).
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