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/yes/true/one or failure/no/false/zero. 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.
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. The figure on the right illustrates the geometric relationship. 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 and published in his 1912 paper Variability and Mutability.
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 instead used in many languages, such as French, Italian, Russian, Romanian 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. 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.
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, quantum field theory, quantum technology, and quantum information science.
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. Informally, 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 .
The ideal gas law, also called the general gas equation, is the equation of state of a hypothetical ideal gas. It is a good approximation of the behavior of many gases under many conditions, although it has several limitations. It was first stated by Benoît Paul Émile Clapeyron in 1834 as a combination of the empirical Boyle's law, Charles's law, Avogadro's law, and Gay-Lussac's law. The ideal gas law is often written in an empirical form:
2 (two) is a number, numeral, and glyph. 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.
A single-player video game is a video game where input from only one player is expected throughout the course of the gaming session. A single-player game is usually a game that can only be played by one person, while "single-player mode" is usually a game mode designed to be played by a single-player, though the game also contains multi-player modes.
α,N,N-Trimethyltryptamine is a psychoactive drug of the tryptamine chemical class which acts as a psychedelic hallucinogen. It is similar in structure to the other psychedelics of the tryptamine class such as dimethyltryptamine (DMT) and α-methyltryptamine (α-MT).
5-Fluoro-α-methyltryptamine (5-Fluoro-αMT), also known as PAL-544, is a putative stimulant, entactogen, and psychedelic tryptamine derivative related to α-methyltryptamine (αMT). It has been found to act as a well-balanced serotonin-norepinephrine-dopamine releasing agent, a 5-HT2A receptor agonist, and a potent and specific MAO-A inhibitor. It produces a strong head-twitch response in mice, and this effect is known to correlate with psychedelic effects in humans, which suggests that 5-fluoro-αMT could be an active psychedelic in humans, although it is not known to have been tested in humans and could be dangerous due to its strong inhibition of MAO-A.
In mathematics, a rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. Since q may be equal to 1, every integer is a rational number. The set of all rational numbers, often referred to as "the rationals", the field of rationals or the field of rational numbers is usually denoted by a boldface Q ; it was thus denoted in 1895 by Giuseppe Peano after quoziente, Italian for "quotient".
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.
