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 or failure. 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 number e, also known as Euler's number, is a mathematical constant approximately equal to 2.71828, and can be characterized in many ways. It is the base of the natural logarithm. It is the limit of (1 + 1/n)n as n approaches infinity, an expression that arises in the study of compound interest. It can also be calculated as the sum of the infinite series
In mathematics, the Fibonacci numbers, commonly denoted Fn, form a sequence, called the Fibonacci sequence, such that each number is the sum of the two preceding ones, starting from 0 and 1. That is,
In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Expressed algebraically, for quantities a and b with a > b > 0,
In economics, the Gini coefficient, sometimes called the Gini index or Gini ratio, is a measure of statistical dispersion intended to represent the income inequality or wealth inequality within a nation or any other group of people. It was developed by the Italian statistician and sociologist Corrado Gini.
N.W.A was an American hip hop group from Compton, California. They were among the earliest and most significant popularizers and controversial figures of the gangsta rap subgenre, and are widely considered one of the greatest and most influential groups in the history of hip hop music.
Nitrogen is the chemical element with the symbol N and atomic number 7. It was first discovered and isolated by Scottish physician Daniel Rutherford in 1772. Although Carl Wilhelm Scheele and Henry Cavendish had independently done so at about the same time, Rutherford is generally accorded the credit because his work was published first. The name nitrogène was suggested by French chemist Jean-Antoine-Claude Chaptal in 1790 when it was found that nitrogen was present in nitric acid and nitrates. Antoine Lavoisier suggested instead the name azote, from the Greek ἀζωτικός "no life", as it is an asphyxiant gas; this name is used instead in many languages, such as French, Italian, Russian, Romanian, Portuguese and Turkish, and appears in the English names of some nitrogen compounds such as hydrazine, azides and azo compounds.
In probability theory, a normaldistribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is
The number π is a mathematical constant. It is defined as the ratio of a circle's circumference to its diameter, and it also has various equivalent definitions. It appears in many formulas in all areas of mathematics and physics. The earliest known use of the Greek letter π to represent the ratio of a circle's circumference to its diameter was by Welsh mathematician William Jones in 1706. It is approximately equal to 3.14159. It has been represented by the Greek letter "π" since the mid-18th century, and is spelled out as "pi". It is also referred to as Archimedes' constant.
A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself. However, 4 is composite because it is a product in which both numbers are smaller than 4. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself or can be factorized as a product of primes that is unique up to their order.
In optics, the refractive index of a material is a dimensionless number that describes how fast light travels through the material. It is defined as
In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean of the set, while a high standard deviation indicates that the values are spread out over a wider range.
In mathematics, the Taylor series of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point. For most common functions, the function and the sum of its Taylor series are equal near this point. Taylor's series are named after Brook Taylor who introduced them in 1715.
In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its mean. In other words, it measures how far a set of numbers is spread out from their average value. Variance has a central role in statistics, where some ideas that use it include descriptive statistics, statistical inference, hypothesis testing, goodness of fit, and Monte Carlo sampling. Variance is an important tool in the sciences, where statistical analysis of data is common. The variance is the square of the standard deviation, the second central moment of a distribution, and the covariance of the random variable with itself, and it is often represented by , , or .
Big O notation is a mathematical notation that describes the limiting behavior of a function when the argument tends towards a particular value or infinity. Big O is a member of a family of notations invented by Paul Bachmann, Edmund Landau, and others, collectively called Bachmann–Landau notation or asymptotic notation.
2 (two) is a number, numeral and digit. It is the natural number following 1 and preceding 3. It is the smallest and only even prime number. Because it forms the basis of a duality, it has religious and spiritual significance in many cultures.
Radioactive decay is the process by which an unstable atomic nucleus loses energy by radiation. A material containing unstable nuclei is considered radioactive. Three of the most common types of decay are alpha decay, beta decay, and gamma decay, all of which involve emitting one or more particles or photons. The weak force is the mechanism that is responsible for beta decay, while the other two are governed by the usual electromagnetic and strong forces.
Guns N' Roses, often abbreviated as GNR, is an American hard rock band from Los Angeles, California, formed in 1985. When they signed to Geffen Records in 1986, the band comprised vocalist Axl Rose, lead guitarist Slash, rhythm guitarist Izzy Stradlin, bassist Duff McKagan, and drummer Steven Adler. The current lineup consists of Rose, Slash, McKagan, guitarist Richard Fortus, drummer Frank Ferrer and keyboardists Dizzy Reed and Melissa Reese.
Capricorn(♑︎) is the tenth astrological sign in the zodiac out of twelve total zodiac signs, originating from the constellation of Capricornus, the horned goat. It spans the 270–300th degree of the zodiac, corresponding to celestial longitude. Under the tropical zodiac, the sun transits this area from about December 21 to January 21 the following year, and under the sidereal zodiac, the sun transits the constellation of Capricorn from approximately January 16 to February 16. In astrology, Capricorn is considered an earth sign, negative sign, and one of the four cardinal signs. Capricorn is said to be ruled by the planet Saturn.
In probability theory and statistics, the Poisson distribution, named after French mathematician Siméon Denis Poisson, is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and independently of the time since the last event. The Poisson distribution can also be used for the number of events in other specified intervals such as distance, area or volume.
