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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 - Doctrine Of Chance - 1718
Abraham, ; ar, , , name=, group= (originally Abram) is the common Hebrew patriarch of the Abrahamic religions, including Judaism, Christianity, and Islam. In Judaism, he is the founding father of the special relationship between the Jews and God; in Christianity, he is the spiritual progenitor of all believers, whether Jewish or non-Jewish; and in Islam, he is a link in the chain of Islamic prophets that begins with Adam (see Adam in Islam) and culminates in Muhammad. His life, told in the narrative of the Book of Genesis, revolves around the themes of posterity and land. Abraham is called by God to leave the house of his father Terah and settle in the land of Canaan, which God now promises to Abraham and his progeny. This promise is subsequently inherited by Isaac, Abraham's son by his wife Sarah, while Isaac's half-brother Ishmael is also promised that he will be the founder of a great nation. Abraham purchases a tomb (the Cave of the Patriarchs) at Hebron to be S ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Central Limit Theorem
In probability theory, the central limit theorem (CLT) establishes that, in many situations, when independent random variables are summed up, their properly normalized sum tends toward a normal distribution even if the original variables themselves are not normally distributed. The theorem is a key concept in probability theory because it implies that probabilistic and statistical methods that work for normal distributions can be applicable to many problems involving other types of distributions. This theorem has seen many changes during the formal development of probability theory. Previous versions of the theorem date back to 1811, but in its modern general form, this fundamental result in probability theory was precisely stated as late as 1920, thereby serving as a bridge between classical and modern probability theory. If X_1, X_2, \dots, X_n, \dots are random samples drawn from a population with overall mean \mu and finite variance and if \bar_n is the sample mean of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1756 Books
Events January–March * January 16 – The Treaty of Westminster is signed between Great Britain and Prussia, guaranteeing the neutrality of the Kingdom of Hanover, controlled by King George II of Great Britain. *February 7 – Guaraní War: The leader of the Guaraní rebels, Sepé Tiaraju, is killed in a skirmish with Spanish and Portuguese troops. * February 10 – The massacre of the Guaraní rebels in the Jesuit reduction of Caaibaté takes place in Brazil after their leader, Noicola Neenguiru, defies an ultimatum to surrender by 2:00 in the afternoon. On February 7, Neenguiru's predecessor Sepé Tiaraju has been killed in a brief skirmish. As two o'clock arrives, a combined force of Spanish and Portuguese troops makes an assault on the first of the Seven Towns established as Jesuit missions. Defending their town with cannons made out of bamboo, the Guaraní suffer 1,511 dead, compared to three Spaniards and two Portuguese killed in battle. * Fe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1738 Books
Events January–March * January 1 – At least 664 African slaves drown, when the Dutch West Indies Company slave ship ''Leusden'' capsizes and sinks in the Maroni River, during its arrival in Surinam. The Dutch crew escapes, and leaves the slaves locked below decks to die. * January 3 – George Frideric Handel's opera '' Faramondo'' is given its first performance. * January 7 – After the Maratha Empire of India wins the Battle of Bhopal over the Jaipur State, Jaipur cedes the Malwa territory to the Maratha in a treaty signed at Doraha. * February 4 – Court Jew Joseph Süß Oppenheimer is executed in Württemberg. * February 11 – Jacques de Vaucanson stages the first demonstration of an early automaton, ''The Flute Player'' at the Hotel de Longueville in Paris, and continues to display it until March 30. * February 20 – Swedish Levant Company founded. * March 28 – Mariner Robert Jenkins presents a pickled ear, which he cla ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1718 Books
Events January – March * January 7 – In India, Sufi rebel leader Shah Inayat Shaheed from Sindh who had led attacks against the Mughal Empire, is beheaded days after being tricked into meeting with the Mughals to discuss peace. * January 17 – Jeremias III reclaims his role as the Ecumenical Patriarch of Constantinople, chief leader within the Eastern Orthodox Church, 16 days after the Metropolitan Cyril IV of Pruoza had engineered an election to become the Patriarch. * February 14 – The reign of Victor Amadeus over the principality of Anhalt-Bernburg (now within the state of Saxony-Anhalt in northeastern Germany) ends after 61 years and 7 months. He had ascended the throne on September 22, 1656. He is succeeded by his son Karl Frederick. * February 21 – Manuel II (Mpanzu a Nimi) becomes the new monarch of the Kingdom of Kongo (located in western Africa at present day Angola) when King Pedro IV (Nusamu a Mvemba) dies after a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics Books
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Annuity (finance Theory)
In investment, an annuity is a series of payments made at equal intervals.Kellison, Stephen G. (1970). ''The Theory of Interest''. Homewood, Illinois: Richard D. Irwin, Inc. p. 45 Examples of annuities are regular deposits to a savings account, monthly home mortgage payments, monthly insurance payments and pension payments. Annuities can be classified by the frequency of payment dates. The payments (deposits) may be made weekly, monthly, quarterly, yearly, or at any other regular interval of time. Annuities may be calculated by mathematical functions known as "annuity functions". An annuity which provides for payments for the remainder of a person's lifetime is a life annuity. Types Annuities may be classified in several ways. Timing of payments Payments of an ''annuity-immediate'' are made at the end of payment periods, so that interest accrues between the issue of the annuity and the first payment. Payments of an ''annuity-due'' are made at the beginning of payment period ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theorem Of De Moivre–Laplace
In mathematics, a theorem is a statement that has been proved, or can be proved. The ''proof'' of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the theorem is a logical consequence of the axioms and previously proved theorems. In the mainstream of mathematics, the axioms and the inference rules are commonly left implicit, and, in this case, they are almost always those of Zermelo–Fraenkel set theory with the axiom of choice, or of a less powerful theory, such as Peano arithmetic. A notable exception is Wiles's proof of Fermat's Last Theorem, which involves the Grothendieck universes whose existence requires the addition of a new axiom to the set theory. Generally, an assertion that is explicitly called a theorem is a proved result that is not an immediate consequence of other known theorems. Moreover, many authors qualify as ''theorems'' only the most important results, and use the terms ''lemma'', ''proposition'' a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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: ''success'' (with probability ''p'') or ''failure'' (with probability q=1-p). A single success/failure experiment is also called a Bernoulli trial or Bernoulli experiment, and a sequence of outcomes is called a Bernoulli process; for a single trial, i.e., ''n'' = 1, the binomial distribution is a Bernoulli distribution. The binomial distribution is the basis for the popular binomial test of statistical significance. The binomial distribution is frequently used to model the number of successes in a sample of size ''n'' drawn with replacement from a population of size ''N''. If the sampling is carried out without replacement, the draws are not independent and so the resulting ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Theory
Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms. Typically these axioms formalise probability in terms of a probability space, which assigns a measure taking values between 0 and 1, termed the probability measure, to a set of outcomes called the sample space. Any specified subset of the sample space is called an event. Central subjects in probability theory include discrete and continuous random variables, probability distributions, and stochastic processes (which provide mathematical abstractions of non-deterministic or uncertain processes or measured quantities that may either be single occurrences or evolve over time in a random fashion). Although it is not possible to perfectly predict random events, much can be said about their behavior. Two major results in probab ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Normal Distribution
In statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is : f(x) = \frac e^ The parameter \mu is the mean or expectation of the distribution (and also its median and mode), while the parameter \sigma is its standard deviation. The variance of the distribution is \sigma^2. A random variable with a Gaussian distribution is said to be normally distributed, and is called a normal deviate. Normal distributions are important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose distributions are not known. Their importance is partly due to the central limit theorem. It states that, under some conditions, the average of many samples (observations) of a random variable with finite mean and variance is itself a random variable—whose distribution converges to a normal d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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