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Bean Machine
The Galton board, also known as the Galton box or quincunx or bean machine (or incorrectly Dalton board), is a device invented by Francis Galton to demonstrate the central limit theorem, in particular that with sufficient sample size the binomial distribution approximates a normal distribution. Galton designed it to illustrate his idea of Regression toward the mean, regression to the mean, which he called "reversion to mediocrity" and made part of his Eugenics, eugenist ideology. Description The Galton board consists of a vertical board with interleaved rows of pegs. Beads are dropped from the top and, when the device is level, bounce either left or right as they hit the pegs. Eventually they are collected into bins at the bottom, where the height of bead columns accumulated in the bins approximate a normal distribution, bell curve. Overlaying Pascal's triangle onto the pins shows the number of different paths that can be taken to get to each bin. Large-scale working models of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
YouTube
YouTube is an American social media and online video sharing platform owned by Google. YouTube was founded on February 14, 2005, by Steve Chen, Chad Hurley, and Jawed Karim who were three former employees of PayPal. Headquartered in San Bruno, California, it is the second-most-visited website in the world, after Google Search. In January 2024, YouTube had more than 2.7billion monthly active users, who collectively watched more than one billion hours of videos every day. , videos were being uploaded to the platform at a rate of more than 500 hours of content per minute, and , there were approximately 14.8billion videos in total. On November 13, 2006, YouTube was purchased by Google for $1.65 billion (equivalent to $ billion in ). Google expanded YouTube's business model of generating revenue from advertisements alone, to offering paid content such as movies and exclusive content produced by and for YouTube. It also offers YouTube Premium, a paid subs ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pachinko
is a mechanical game originating in Japan that is used as an arcade game, and much more frequently for gambling. Pachinko fills a niche in Gambling in Japan, Japanese gambling comparable to that of the slot machine in the West as a form of low-stakes, low-strategy gambling. Pachinko parlors are widespread in Japan, and usually also feature a number of slot machines (called ''pachislo'' or pachislots) so these venues look and operate similarly to casinos. Modern pachinko machines have both mechanical and electrical components. Gambling for cash is illegal in Japan, but the widespread popularity of low-stakes pachinko in Japanese society has enabled a specific legal loophole allowing it to exist. Pachinko balls won from games cannot be exchanged directly for money in the parlor, nor can they be removed from the premises or exchanged with other parlors. However, they can be legally traded to the parlor for so-called "special prize" tokens (特殊景品 ''tokushu keihin''), whic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bagatelle
Bagatelle (from the Château de Bagatelle) is a billiards-derived indoor table game, the object of which is to get a number of balls (set at nine in the 19th century) past wooden pins (which act as obstacles) into holes that are guarded by wooden pegs; penalties are incurred if the pegs are knocked over. It probably developed from the table made with raised sides for ''trou madame'', which was also played with ivory balls and continued to be popular into the later 19th century, after which it developed into bar billiards, with influences from the French/Belgian game ' (with supposed Russian origins). A bagatelle variant using fixed metal pins, '' billard japonais'', eventually led to the development of pachinko and pinball. History Table games involving sticks and balls evolved from efforts to bring outdoor games like ground billiards, croquet, and bowling inside for play during inclement weather. They are attested in general by the 15th century, although the 19th-century ide ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quincunx (Galton Box) - Galton 1889 Diagram
A quincunx ( ) is a geometric pattern consisting of five points arranged in a cross, with four of them forming a square or rectangle and a fifth at its center. The same pattern has other names, including "in saltire" or "in cross" in heraldry (depending on the orientation of the outer square), the five-point stencil in numerical analysis, and the five dots tattoo. It forms the arrangement of five units in the pattern corresponding to the five-spot on six-sided dice, playing cards, and dominoes. It is represented in Unicode as or (for the die pattern) . Historical origins of the name The quincunx was originally a coin issued by the Roman Republic , whose value was five twelfths (''quinque'' and ''uncia'') of an as, the Roman standard bronze coin. On the Roman quincunx coins, the value was sometimes indicated by a pattern of five dots or pellets. However, these dots were not always arranged in a quincunx pattern. The ''Oxford English Dictionary'' (OED) dates the first appeara ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maximum Entropy Probability Distribution
In statistics and information theory, a maximum entropy probability distribution has entropy that is at least as great as that of all other members of a specified class of probability distributions. According to the principle of maximum entropy, if nothing is known about a distribution except that it belongs to a certain class (usually defined in terms of specified properties or measures), then the distribution with the largest entropy should be chosen as the least-informative default. The motivation is twofold: first, maximizing entropy minimizes the amount of prior information built into the distribution; second, many physical systems tend to move towards maximal entropy configurations over time. Definition of entropy and differential entropy If X is a continuous random variable with probability density p(x), then the differential entropy of X is defined as H(X) = - \int_^\infty p(x) \log p(x) \, dx ~. If X is a discrete random variable with distribution given by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Entropy
Entropy is a scientific concept, most commonly associated with states of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynamics, where it was first recognized, to the microscopic description of nature in statistical physics, and to the principles of information theory. It has found far-ranging applications in chemistry and physics, in biological systems and their relation to life, in cosmology, economics, sociology, weather science, climate change and information systems including the transmission of information in telecommunication. Entropy is central to the second law of thermodynamics, which states that the entropy of an isolated system left to spontaneous evolution cannot decrease with time. As a result, isolated systems evolve toward thermodynamic equilibrium, where the entropy is highest. A consequence of the second law of thermodynamics is that certain processes are irreversible. The thermodynami ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Standard Deviations
In statistics, the standard deviation is a measure of the amount of variation of the values of a variable about its mean. A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the values are spread out over a wider range. The standard deviation is commonly used in the determination of what constitutes an outlier and what does not. Standard deviation may be abbreviated SD or std dev, and is most commonly represented in mathematical texts and equations by the lowercase Greek letter σ (sigma), for the population standard deviation, or the Latin letter '' s'', for the sample standard deviation. The standard deviation of a random variable, sample, statistical population, data set, or probability distribution is the square root of its variance. (For a finite population, variance is the average of the squared deviations from the mean.) A useful property of the sta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
De Moivre–Laplace Theorem
In probability theory, the de Moivre–Laplace theorem, which is a special case of the central limit theorem, states that the normal distribution may be used as an approximation to the binomial distribution under certain conditions. In particular, the theorem shows that the probability mass function of the random number of "successes" observed in a series of n independent Bernoulli trials, each having probability p of success (a binomial distribution with n trials), converges to the probability density function of the normal distribution with expectation np and standard deviation \sqrt, as n grows large, assuming p is not 0 or 1. The theorem appeared in the second edition of '' The Doctrine of Chances'' by Abraham de Moivre, published in 1738. Although de Moivre did not use the term "Bernoulli trials", he wrote about the probability distribution of the number of times "heads" appears when a coin is tossed 3600 times. This is one derivation of the particular Gaussian function ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binomial Coefficient
In mathematics, the binomial coefficients are the positive integers that occur as coefficients in the binomial theorem. Commonly, a binomial coefficient is indexed by a pair of integers and is written \tbinom. It is the coefficient of the term in the polynomial expansion of the binomial power ; this coefficient can be computed by the multiplicative formula : \binom nk = \frac, which using factorial notation can be compactly expressed as : \binom = \frac. For example, the fourth power of is : \begin (1 + x)^4 &= \tbinom x^0 + \tbinom x^1 + \tbinom x^2 + \tbinom x^3 + \tbinom x^4 \\ &= 1 + 4x + 6 x^2 + 4x^3 + x^4, \end and the binomial coefficient \tbinom =\tfrac = \tfrac = 6 is the coefficient of the term. Arranging the numbers \tbinom, \tbinom, \ldots, \tbinom in successive rows for gives a triangular array called Pascal's triangle, satisfying the recurrence relation : \binom = \binom + \binom . The binomial coefficients occur in many areas of mathematics, and espe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Aitchison
John Aitchison (22 July 1926 – 23 December 2016) was a Scottish statistician. Career John Aitchison studied at the University of Edinburgh after being uncomfortable explaining to his headmaster that he didn’t plan to attend university. He graduated in 1947 with an MA in mathematics. After two years wherein he did actuarial work, he also attended Trinity College, Cambridge. He had a scholarship to do so, and graduated in 1951 with a BA focused on statistics. The year after he graduated, he joined the Department of Applied Economics at Cambridge as a statistician. He continued his work at Cambridge until 1956, when he was offered the position of Lecturer of Statistics at the University of Glasgow. During his time at Glasgow, he wrote ''The Lognormal Distribution, With Special Reference to its Uses in Economics (1957)'' with J A C Brown (who he met at Cambridge). However, he left Glasgow in 1962, when the University of Liverpool offered him the positions of Senior Lecturer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Groningen
The University of Groningen (abbreviated as UG; , abbreviated as RUG) is a Public university#Continental Europe, public research university of more than 30,000 students in the city of Groningen (city), Groningen, Netherlands. Founded in 1614, the university is the second oldest in the country (after Leiden University, Leiden). The University of Groningen has eleven Faculty (division), faculties, nine graduate schools, 27 research centres and institutes, and more than 175-degree programmes. The university's alumni and faculty include Johann Bernoulli, Aletta Jacobs, four Nobel Prize winners, nine Spinoza Prize winners, one Stevin Prize winner, various members of the Monarchy of the Netherlands, Dutch royal family, several politicians, the first president of the European Central Bank, and a secretary general of NATO. History The institution was founded as a college in 1614 in an initiative taken by the Regional Assembly of the city of Groningen and the ''Ommelanden'', or surroun ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
