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Coupon Collector Problem
In probability theory, the coupon collector's problem describes "collect all coupons and win" contests. It asks the following question: If each box of a brand of cereals contains a coupon, and there are ''n'' different types of coupons, what is the probability that more than ''t'' boxes need to be bought to collect all ''n'' coupons? An alternative statement is: Given ''n'' coupons, how many coupons do you expect you need to draw with replacement before having drawn each coupon at least once? The mathematical analysis of the problem reveals that the expected number of trials needed grows as \Theta(n\log(n)). For example, when ''n'' = 50 it takes about 225E(50) = 50(1 + 1/2 + 1/3 + ... + 1/50) = 224.9603, the expected number of trials to collect all 50 coupons. The approximation n\log n+\gamma n+1/2 for this expected number gives in this case 50\log 50+50\gamma+1/2 \approx 195.6011+28.8608+0.5\approx 224.9619. trials on average to collect all 50 coupons. Solution Calcula ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coupon Collector Problem
In probability theory, the coupon collector's problem describes "collect all coupons and win" contests. It asks the following question: If each box of a brand of cereals contains a coupon, and there are ''n'' different types of coupons, what is the probability that more than ''t'' boxes need to be bought to collect all ''n'' coupons? An alternative statement is: Given ''n'' coupons, how many coupons do you expect you need to draw with replacement before having drawn each coupon at least once? The mathematical analysis of the problem reveals that the expected number of trials needed grows as \Theta(n\log(n)). For example, when ''n'' = 50 it takes about 225E(50) = 50(1 + 1/2 + 1/3 + ... + 1/50) = 224.9603, the expected number of trials to collect all 50 coupons. The approximation n\log n+\gamma n+1/2 for this expected number gives in this case 50\log 50+50\gamma+1/2 \approx 195.6011+28.8608+0.5\approx 224.9619. trials on average to collect all 50 coupons. Solution Calcula ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alfréd Rényi
Alfréd Rényi (20 March 1921 – 1 February 1970) was a Hungarian mathematician known for his work in probability theory, though he also made contributions in combinatorics, graph theory, and number theory. Life Rényi was born in Budapest to Artúr Rényi and Borbála Alexander; his father was a mechanical engineer, while his mother was the daughter of philosopher and literary critic Bernhard Alexander; his uncle was Franz Alexander, a Hungarian-American psychoanalyst and physician. He was prevented from enrolling in university in 1939 due to the anti-Jewish laws then in force, but enrolled at the University of Budapest in 1940 and finished his studies in 1944. At this point, he was drafted to forced labour service, from which he escaped. He then completed his PhD in 1947 at the University of Szeged, under the advisement of Frigyes Riesz. He married Katalin Schulhof (who used Kató Rényi as her married name), herself a mathematician, in 1946; their daughter Zsuzsanna was bor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gambling Mathematics
Experiments, events and probability spaces The technical processes of a game stand for experiments that generate aleatory events. Here are a few examples: * Throwing the dice in craps is an experiment that generates events such as occurrences of certain numbers on the dice, obtaining a certain sum of the shown numbers, and obtaining numbers with certain properties (less than a specific number, higher than a specific number, even, uneven, and so on). The sample space of such an experiment is for rolling one die or for rolling two dice. The latter is a set of ordered pairs and counts 6 x 6 = 36 elements. The events can be identified with sets, namely parts of the sample space. For example, the event ''occurrence of an even number'' is represented by the following set in the experiment of rolling one die: . * Spinning the roulette wheel is an experiment whose generated events could be the occurrence of a certain number, of a certain color or a certain property of the numbers (low, high ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Articles Containing Proofs
Article often refers to: * Article (grammar), a grammatical element used to indicate definiteness or indefiniteness * Article (publishing), a piece of nonfictional prose that is an independent part of a publication Article may also refer to: Government and law * Article (European Union), articles of treaties of the European Union * Articles of association, the regulations governing a company, used in India, the UK and other countries * Articles of clerkship, the contract accepted to become an articled clerk * Articles of Confederation, the predecessor to the current United States Constitution *Article of Impeachment, a formal document and charge used for impeachment in the United States * Articles of incorporation, for corporations, U.S. equivalent of articles of association * Articles of organization, for limited liability organizations, a U.S. equivalent of articles of association Other uses * Article, an HTML element, delimited by the tags and * Article of clothing, an ite ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Doron Zeilberger
Doron Zeilberger (דורון ציילברגר, born 2 July 1950 in Haifa, Israel) is an Israeli mathematician, known for his work in combinatorics. Education and career He received his doctorate from the Weizmann Institute of Science in 1976, under the direction of Harry Dym, with the thesis "New Approaches and Results in the Theory of Discrete Analytic Functions." He is a Board of Governors Professor of Mathematics at Rutgers University. Contributions Zeilberger has made contributions to combinatorics, hypergeometric identities, and q-series. Zeilberger gave the first proof of the alternating sign matrix conjecture, noteworthy not only for its mathematical content, but also for the fact that Zeilberger recruited nearly a hundred volunteer checkers to "pre-referee" the paper. In 2011, together with Manuel Kauers and Christoph Koutschan, Zeilberger proved the ''q''-TSPP conjecture, which was independently stated in 1983 by George Andrews and David P. Robbins. Zeilberger is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wolfram Demonstrations Project
The Wolfram Demonstrations Project is an organized, open-source collection of small (or medium-size) interactive programs called Demonstrations, which are meant to visually and interactively represent ideas from a range of fields. It is hosted by Wolfram Research, whose stated goal is to bring computational exploration to a large population. At its launch, it contained 1300 demonstrations but has grown to over 10,000. The site won a Parents' Choice Award in 2008. Technology The Demonstrations run in '' Mathematica'' 6 or above and in '' Wolfram CDF Player'' which is a free modified version of Wolfram's ''Mathematica'' and available for Windows, Linux and macOS and can operate as a web browser plugin. They typically consist of a very direct user interface to a graphic or visualization, which dynamically recomputes in response to user actions such as moving a slider, clicking a button, or dragging a piece of graphics. Each Demonstration also has a brief description of the c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ed Pegg, Jr
Ed, ed or ED may refer to: Arts and entertainment * ''Ed'' (film), a 1996 film starring Matt LeBlanc * Ed (''Fullmetal Alchemist'') or Edward Elric, a character in ''Fullmetal Alchemist'' media * ''Ed'' (TV series), a TV series that ran from 2000 to 2004 Businesses and organizations * Ed (supermarket), a French brand of discount stores founded in 1978 * Consolidated Edison, from their NYSE stock symbol * United States Department of Education, a department of the United States government * Enforcement Directorate, a law enforcement and economic intelligence agency in India * European Democrats, a loose association of conservative political parties in Europe * Airblue (IATA code ED), a private Pakistani airline * Eagle Dynamics, a Swiss software company Places * Ed, Kentucky, an unincorporated community in the United States * Ed, Sweden, a town in Dals-Ed, Sweden * Erode Junction railway station, station code ED Health and medicine * Eating disorder, mental disorders def ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Undergraduate Texts In Mathematics
Undergraduate Texts in Mathematics (UTM) (ISSN 0172-6056) is a series of undergraduate-level textbooks in mathematics published by Springer-Verlag. The books in this series, like the other Springer-Verlag mathematics series, are small yellow books of a standard size. The books in this series tend to be written at a more elementary level than the similar Graduate Texts in Mathematics series, although there is a fair amount of overlap between the two series in terms of material covered and difficulty level. There is no Springer-Verlag numbering of the books like in the Graduate Texts in Mathematics Graduate Texts in Mathematics (GTM) (ISSN 0072-5285) is a series of graduate-level textbooks in mathematics published by Springer-Verlag. The books in this series, like the other Springer-Verlag mathematics series, are yellow books of a standard s ... series. The books are numbered here by year of publication. List of books # # # # # # # # # # # # # # # # # # # # # # # # # ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Mathematical Monthly
''The American Mathematical Monthly'' is a mathematical journal founded by Benjamin Finkel in 1894. It is published ten times each year by Taylor & Francis for the Mathematical Association of America. The ''American Mathematical Monthly'' is an expository journal intended for a wide audience of mathematicians, from undergraduate students to research professionals. Articles are chosen on the basis of their broad interest and reviewed and edited for quality of exposition as well as content. In this the ''American Mathematical Monthly'' fulfills a different role from that of typical mathematical research journals. The ''American Mathematical Monthly'' is the most widely read mathematics journal in the world according to records on JSTOR. Tables of contents with article abstracts from 1997–2010 are availablonline The MAA gives the Lester R. Ford Awards annually to "authors of articles of expository excellence" published in the ''American Mathematical Monthly''. Editors *2022– ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Birthday Problem
In probability theory, the birthday problem asks for the probability that, in a set of randomly chosen people, at least two will share a birthday. The birthday paradox is that, counterintuitively, the probability of a shared birthday exceeds 50% in a group of only 23 people. The birthday paradox is a veridical paradox: it appears wrong, but is in fact true. While it may seem surprising that only 23 individuals are required to reach a 50% probability of a shared birthday, this result is made more intuitive by considering that the comparisons of birthdays will be made between every possible pair of individuals. With 23 individuals, there are (23 × 22) / 2 = 253 pairs to consider, much more than half the number of days in a year. Real-world applications for the birthday problem include a cryptographic attack called the birthday attack, which uses this probabilistic model to reduce the complexity of finding a collision for a hash function, as well as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Watterson Estimator
In population genetics, the Watterson estimator is a method for describing the genetic diversity in a population. It was developed by Margaret Wu and G. A. Watterson in the 1970s. It is estimated by counting the number of polymorphic sites. It is a measure of the "population mutation rate" (the product of the effective population size and the neutral mutation rate) from the observed nucleotide diversity of a population. \theta = 4N_e\mu, where N_e is the effective population size and \mu is the per-generation mutation rate of the population of interest ( ). The assumptions made are that there is a sample of n haploid individuals from the population of interest, that there are infinitely many sites capable of varying (so that mutations never overlay or reverse one another), and that n \ll N_e. Because the number of segregating sites counted will increase with the number of sequences looked at, the correction factor a_n is used. The estimate of \theta, often denoted as \widehat _w, i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
McDonald's Monopoly
The McDonald's Monopoly game is a sales promotion run by fast food restaurant chain McDonald's, with a theme based on the Hasbro board game ''Monopoly''. The game first ran in the U.S. in 1987 and has since been used worldwide. The promotion has used other names, such as ''Monopoly: Pick Your Prize!'' (2001), ''Monopoly Best Chance Game'' (2003–2005), ''Monopoly/Millionaire Game'', ''Prize Vault'' (2013–2014), ''Money Monopoly'' (2016–present), ''Coast To Coast'' (2015–present) in Canada, ''Golden Chances'' (2015), ''Prize Choice'' (2016), ''Win Win'' (2017), ''Wiiiin!!'' (2018), ''V.I.P.'' (2021) and Double Peel (2022–present) in the UK. History The promotion has been offered in the United States, Canada, Australia, Austria, France, Germany, Hong Kong, the Netherlands, New Zealand, Poland, Portugal, Romania, Russia, Singapore, South Africa, Spain, Switzerland, Taiwan, and United Kingdom since 1987. Argentina and Brazil were included in 2013 as well as South Korea in 20 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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