Please answer the following question: Information: - Geology (from the Ancient Greek , "g", i.e. "earth" and -o, "-logia", i.e. "study of, discourse") is an earth science comprising the study of solid Earth, the rocks of which it is composed, and the processes by which they change. Geology can also refer generally to the study of the solid features of any terrestrial planet (such as the geology of the Moon or Mars). - In probability and statistics, a random variable, random quantity, aleatory variable, or stochastic variable is a variable quantity whose possible values depend, in random manner, on a set of random outcomes events. It is common that the outcome depends on some physical variables that are not well understood. For example, when you toss a coin (or a die), it falls on its edge, and the final outcome formula_1 or formula_2 depends on the uncertain physics. What is not uncertain are the possible outcomes. Of course the coin could get caught in a crack in the floor, but that is not a consideration. Essential to the definition of a random variable is the outcome space typically defined in terms of set theory or a set. In the case of the coin, the set is binary. The member of the set are each labelled by a probability formula_3 where formula_4 labels the possible outcome values. Thus for the coin example, there are formula_5 such that formula_6. The only outcomes allowed are those from the set, thus one of these outcomes must have some measurable (non-zero) probability. - Debt, AIDS, Trade, Africa (DATA) was a multinational non-government organization founded in January 2002 in London by U2's Bono along with Bobby Shriver and activists from the Jubilee 2000 Drop the Debt campaign. - An experiment is a procedure carried out to support, refute, or validate a hypothesis. Experiments provide insight into cause-and-effect by demonstrating what outcome occurs when a particular factor is manipulated. Experiments vary greatly in goal and scale, but always rely on repeatable procedure and logical analysis of the results. There also exists natural experimental studies. - Water is a transparent and nearly colorless chemical substance that is the main constituent of Earth's streams, lakes, and oceans, and the fluids of most living organisms. Its chemical formula is HO, meaning that its molecule contains one oxygen and two hydrogen atoms, that are connected by covalent bonds. Water strictly refers to the liquid state of that substance, that prevails at standard ambient temperature and pressure; but it often refers also to its solid state (ice) or its gaseous state (steam or water vapor). It also occurs in nature as snow, glaciers, ice packs and icebergs, clouds, fog, dew, aquifers, and atmospheric humidity. - The median is the value separating the higher half of a data sample, a population, or a probability distribution, from the lower half. In simple terms, it may be thought of as the "middle" value of a data set. For example, in the data set {1, 3, 3, 6, 7, 8, 9}, the median is 6, the fourth number in the sample. The median is a commonly used measure of the properties of a data set in statistics and probability theory. - The water cycle, also known as the hydrological cycle, describes the continuous movement of water on, above and below the surface of the Earth. The mass of water on Earth remains fairly constant over time but the partitioning of the water into the major reservoirs of ice, fresh water, saline water and atmospheric water is variable depending on a wide range of climatic variables. The water moves from one reservoir to another, such as from river to ocean, or from the ocean to the atmosphere, by the physical processes of evaporation, condensation, precipitation, infiltration, surface runoff, and subsurface flow. In doing so, the water goes through different phases: liquid, solid (ice) and vapor. - A flood is an overflow of water that submerges land which is usually dry. The European Union (EU) Floods Directive defines a flood as a covering by water of land not normally covered by water. In the sense of "flowing water", the word may also be applied to the inflow of the tide. - The Environment Agency (EA) is a non-departmental public body, established in 1995 and sponsored by the United Kingdom government's Department for Environment, Food and Rural Affairs (DEFRA), with responsibilities relating to the protection and enhancement of the environment in England (and until 2013 also Wales). - A one-hundred-year flood is a flood event that has a 1% probability of occurring in any given year. The 100-year flood is also referred to as the 1% flood, since its annual exceedance probability is 1%. For river systems, the 100-year flood is generally expressed as a flowrate. Based on the expected 100-year flood flow rate, the flood water level can be mapped as an area of inundation. The resulting floodplain map is referred to as the 100-year floodplain. Estimates of the 100-year flood flowrate and other streamflow statistics for any stream in the United States are available. In the UK The Environment Agency publishes a comprehensive map of all areas at risk of a 1 in 100 year flood (Flood zone 3) Areas near the coast of an ocean or large lake also can be flooded by combinations of tide, storm surge, and waves. Maps of the riverine or coastal 100-year floodplain may figure importantly in building permits, environmental regulations, and flood insurance. - Tides are the rise and fall of sea levels caused by the combined effects of the gravitational forces exerted by the Moon and the Sun and the rotation of the Earth. - Statistics is the study of the collection, analysis, interpretation, presentation, and organization of data. In applying statistics to, e.g., a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model process to be studied. Populations can be diverse topics such as "all people living in a country" or "every atom composing a crystal". Statistics deals with all aspects of data including the planning of data collection in terms of the design of surveys and experiments. - A floodplain or flood plain is an area of land adjacent to a stream or river that stretches from the banks of its channel to the base of the enclosing valley walls and experiences flooding during periods of high discharge. It includes the floodway, which consists of the stream channel and adjacent areas that actively carry flood flows downstream, and the flood fringe, which are areas inundated by the flood, but which do not experience a strong current. In other words, a floodplain is an area near a river or a stream which floods when the water level reaches flood stage. - Flood insurance denotes the specific insurance coverage against property loss from flooding. To determine risk factors for specific properties, insurers will often refer to topographical maps that denote lowlands, floodplains and floodways that are susceptible to flooding. - Physical geography (also known as geosystems or physiography) is one of the two major sub-fields of geography. Physical geography is that branch of natural science which deals with the study of processes and patterns in the natural environment like the atmosphere, hydrosphere, biosphere, and geosphere, as opposed to the cultural or built environment, the domain of human geography. - Analysis is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (384322 B.C.), though "analysis" as a formal concept is a relatively recent development. - Environmental science is an interdisciplinary academic field that integrates physical, biological and information sciences (including ecology, biology, physics, chemistry, zoology, mineralogy, oceanology, limnology, soil science, geology, atmospheric science, and geodesy) to the study of the environment, and the solution of environmental problems. Environmental science emerged from the fields of natural history and medicine during the Enlightenment. Today it provides an integrated, quantitative, and interdisciplinary approach to the study of environmental systems. - In statistics, a population is a set of similar items or events which is of interest for some question or experiment. A statistical population can be a group of actually existing objects (e.g. the set of all stars within the Milky Way galaxy) or a hypothetical and potentially infinite group of objects conceived as a generalization from experience (e.g. the set of all possible hands in a game of poker). A common aim of statistical analysis is to produce information about some chosen population. - Extreme value theory or extreme value analysis ( EVA ) is a branch of statistics dealing with the extreme deviations from the median of probability distributions . It seeks to assess , from a given ordered sample of a given random variable , the probability of events that are more extreme than any previously observed . Extreme value analysis is widely used in many disciplines , such as structural engineering , finance , earth sciences , traffic prediction , and geological engineering . For example , EVA might be used in the field of hydrology to estimate the probability of an unusually large flooding event , such as the 100 - year flood . Similarly , for the design of a breakwater , a coastal engineer would seek to estimate the 50 - year wave and design the structure accordingly . - In probability theory and statistics, a probability distribution is a mathematical function that, stated in simple terms, can be thought of as providing the probability of occurrence of different possible outcomes in an experiment. For instance, if the random variable 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 for formula_1, and 0.5 for formula_2. - A statistical model is a class of mathematical model, which embodies a set of assumptions concerning the generation of some sample data, and similar data from a larger population. A statistical model represents, often in considerably idealized form, the data-generating process. - A storm surge is a coastal flood or tsunami-like phenomenon of rising water commonly associated with low pressure weather systems (such as tropical cyclones and strong extratropical cyclones), the severity of which is affected by the shallowness and orientation of the water body relative to storm path, and the timing of tides. Most casualties during tropical cyclones occur as the result of storm surges. - Water resources are sources of water that are potentially useful. Uses of water include agricultural, industrial, household, recreational and environmental activities. The majority of human uses require fresh water. - Earth, otherwise known as the world, is the third planet from the Sun and the only object in the Universe known to harbor life. It is the densest planet in the Solar System and the largest of the four terrestrial planets. - The European Union (EU) is a political and economic union of member states that are located primarily in Europe. It has an area of , and an estimated population of over 510 million. The EU has developed an internal single market through a standardised system of laws that apply in all member states. EU policies aim to ensure the free movement of people, goods, services, and capital within the internal market, enact legislation in justice and home affairs, and maintain common policies on trade, agriculture, fisheries, and regional development. Within the Schengen Area, passport controls have been abolished. A monetary union was established in 1999 and came into full force in 2002, and is composed of 19 EU member states which use the euro currency. - Environmental engineering is the branch of engineering concerned with the application of scientific and engineering principles for protection of human populations from the effects of adverse environmental factors; protection of environments, both local and global, from potentially deleterious effects of natural and human activities; and improvement of environmental quality. - Probability and Statistics or also called Statistics and Probability are two related but separate academic disciplines. Statistical analysis often uses probability distributions, and the two topics are often studied together. However, probability theory contains much that is mostly of mathematical interest and not directly relevant to statistics. Moreover, many topics in statistics are independent of probability theory. - Probability theory is the branch of mathematics concerned with probability, the analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single occurrences or evolve over time in an apparently random fashion. - Hydrology is the scientific study of the movement, distribution, and quality of water on Earth and other planets, including the water cycle, water resources and environmental watershed sustainability. A practitioner of hydrology is a hydrologist, working within the fields of earth or environmental science, physical geography, geology or civil and environmental engineering. After reading the paragraphs above, choose the best answer for the entity that related to 'extreme value theory' with the relationship of 'part of'. Choices: - atmosphere - biology - body - building - chemical substance - chemistry - class - coin - country - data set - earth - engineering - england - europe - european union - event - experiment - galaxy - geology - government - human - human geography - insurance - legislation - liquid - logic - map - mars - mass - mathematics - may - milky way - moon - ocean - phenomenon - physical geography - physics - population - probability theory - process - river - science - sea - set theory - soil science - solar system - statistical population - statistics - sun - system - theory - trade - weather - word - year - zoology
A:
probability theory