ProbabilityProbability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty. The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin.
Probability theoryProbability theory or probability calculus 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.
Probability distributionIn probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events (subsets of the sample space). For instance, if X is used to denote the outcome of a coin toss ("the experiment"), then the probability distribution of X would take the value 0.5 (1 in 2 or 1/2) for X = heads, and 0.
Probability spaceIn probability theory, a probability space or a probability triple is a mathematical construct that provides a formal model of a random process or "experiment". For example, one can define a probability space which models the throwing of a die. A probability space consists of three elements: A sample space, , which is the set of all possible outcomes. An event space, which is a set of events, , an event being a set of outcomes in the sample space. A probability function, , which assigns each event in the event space a probability, which is a number between 0 and 1.
Probability axiomsThe Kolmogorov axioms are the foundations of probability theory introduced by Russian mathematician Andrey Kolmogorov in 1933. These axioms remain central and have direct contributions to mathematics, the physical sciences, and real-world probability cases. An alternative approach to formalising probability, favoured by some Bayesians, is given by Cox's theorem. The assumptions as to setting up the axioms can be summarised as follows: Let be a measure space with being the probability of some event , and .
Conditional probabilityIn probability theory, conditional probability is a measure of the probability of an event occurring, given that another event (by assumption, presumption, assertion or evidence) has already occurred. This particular method relies on event B occurring with some sort of relationship with another event A. In this event, the event B can be analyzed by a conditional probability with respect to A. If the event of interest is A and the event B is known or assumed to have occurred, "the conditional probability of A given B", or "the probability of A under the condition B", is usually written as P(AB) or occasionally P_B(A).
Bayesian probabilityBayesian probability (ˈbeɪziən or ˈbeɪʒən ) is an interpretation of the concept of probability, in which, instead of frequency or propensity of some phenomenon, probability is interpreted as reasonable expectation representing a state of knowledge or as quantification of a personal belief. The Bayesian interpretation of probability can be seen as an extension of propositional logic that enables reasoning with hypotheses; that is, with propositions whose truth or falsity is unknown.
AeroplanktonAeroplankton (or aerial plankton) are tiny lifeforms that float and drift in the air, carried by wind. Most of the living things that make up aeroplankton are very small to microscopic in size, and many can be difficult to identify because of their tiny size. Scientists collect them for study in traps and sweep nets from aircraft, kites or balloons. The study of the dispersion of these particles is called aerobiology.
MicroorganismA microorganism, or microbe, is an organism of microscopic size, which may exist in its single-celled form or as a colony of cells. The possible existence of unseen microbial life was suspected from ancient times, such as in Jain scriptures from sixth century BC India. The scientific study of microorganisms began with their observation under the microscope in the 1670s by Anton van Leeuwenhoek. In the 1850s, Louis Pasteur found that microorganisms caused food spoilage, debunking the theory of spontaneous generation.
Seed dispersalIn spermatophyte plants, seed dispersal is the movement, spread or transport of seeds away from the parent plant. Plants have limited mobility and rely upon a variety of dispersal vectors to transport their seeds, including both abiotic vectors, such as the wind, and living (biotic) vectors such as birds. Seeds can be dispersed away from the parent plant individually or collectively, as well as dispersed in both space and time.
Frequentist probabilityFrequentist probability or frequentism is an interpretation of probability; it defines an event's probability as the limit of its relative frequency in many trials (the long-run probability). Probabilities can be found (in principle) by a repeatable objective process (and are thus ideally devoid of opinion). The continued use of frequentist methods in scientific inference, however, has been called into question. The development of the frequentist account was motivated by the problems and paradoxes of the previously dominant viewpoint, the classical interpretation.
Probability interpretationsThe word probability has been used in a variety of ways since it was first applied to the mathematical study of games of chance. Does probability measure the real, physical, tendency of something to occur, or is it a measure of how strongly one believes it will occur, or does it draw on both these elements? In answering such questions, mathematicians interpret the probability values of probability theory. There are two broad categories of probability interpretations which can be called "physical" and "evidential" probabilities.
AtmosphereAn atmosphere () is a layer of gas or layers of gases that envelop a planet, and is held in place by the gravity of the planetary body. A planet retains an atmosphere when the gravity is great and the temperature of the atmosphere is low. A stellar atmosphere is the outer region of a star, which includes the layers above the opaque photosphere; stars of low temperature might have outer atmospheres containing compound molecules. The atmosphere of Earth is composed of nitrogen (78 %), oxygen (21 %), argon (0.
Extraterrestrial atmosphereThe study of extraterrestrial atmospheres is an active field of research, both as an aspect of astronomy and to gain insight into Earth's atmosphere. In addition to Earth, many of the other astronomical objects in the Solar System have atmospheres. These include all the gas giants, as well as Mars, Venus and Titan. Several moons and other bodies also have atmospheres, as do comets and the Sun. There is evidence that extrasolar planets can have an atmosphere.
Atmosphere of EarthThe atmosphere of Earth is the layer of gases, known collectively as air, retained by Earth's gravity that surrounds the planet and forms its planetary atmosphere. The atmosphere of Earth creates pressure, absorbs most meteoroids and ultraviolet solar radiation, warms the surface through heat retention (greenhouse effect), allowing life and liquid water to exist on the Earth's surface, and reduces temperature extremes between day and night (the diurnal temperature variation). As of 2023, by mole fraction (i.
Marine microorganismsMarine microorganisms are defined by their habitat as microorganisms living in a marine environment, that is, in the saltwater of a sea or ocean or the brackish water of a coastal estuary. A microorganism (or microbe) is any microscopic living organism or virus, that is too small to see with the unaided human eye without magnification. Microorganisms are very diverse. They can be single-celled or multicellular and include bacteria, archaea, viruses and most protozoa, as well as some fungi, algae, and animals, such as rotifers and copepods.
Atmosphere of MarsThe atmosphere of Mars is the layer of gases surrounding Mars. It is primarily composed of carbon dioxide (95%), molecular nitrogen (2.8%), and argon (2%). It also contains trace levels of water vapor, oxygen, carbon monoxide, hydrogen, and noble gases. The atmosphere of Mars is much thinner than Earth's. The average surface pressure is only about which is less than 1% of the Earth's value. The currently thin Martian atmosphere prohibits the existence of liquid water on the surface of Mars, but many studies suggest that the Martian atmosphere was much thicker in the past.
Atmosphere of VenusThe atmosphere of Venus is primarily of supercritical carbon dioxide and is much denser and hotter than that of Earth. The temperature at the surface is 740 K (467 °C, 872 °F), and the pressure is , roughly the pressure found underwater on Earth. The Venusian atmosphere supports opaque clouds of sulfuric acid, making optical Earth-based and orbital observation of the surface impossible. Information about the topography has been obtained exclusively by radar imaging. Aside from carbon dioxide, the other main component is nitrogen.
Atmosphere of the MoonThe atmosphere of the Moon is a very scant presence of gases surrounding the Moon. For most practical purposes, the Moon is considered to be surrounded by vacuum. The elevated presence of atomic and molecular particles in its vicinity compared to interplanetary medium, referred to as "lunar atmosphere" for scientific objectives, is negligible in comparison with the gaseous envelopes surrounding Earth and most planets of the Solar System. The pressure of this small mass is around , varying throughout the day, and in total mass less than 10 metric tonnes.
Biological dispersalBiological dispersal refers to both the movement of individuals (animals, plants, fungi, bacteria, etc.) from their birth site to their breeding site ('natal dispersal'), as well as the movement from one breeding site to another ('breeding dispersal'). Dispersal is also used to describe the movement of propagules such as seeds and spores. Technically, dispersal is defined as any movement that has the potential to lead to gene flow.
