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Probability Distributions With Non-finite Variance
Probability is a branch of mathematics and statistics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an event is to occur."Kendall's Advanced Theory of Statistics, Volume 1: Distribution Theory", Alan Stuart and Keith Ord, 6th ed., (2009), .William Feller, ''An Introduction to Probability Theory and Its Applications'', vol. 1, 3rd ed., (1968), Wiley, . This number is often expressed as a percentage (%), ranging from 0% to 100%. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%). These concepts have been given an axiomatic mathematical formaliza ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dice Distribution (bar)
A die (: dice, sometimes also used as ) is a small, throwable object with marked sides that can rest in multiple positions. Dice are used for generating Statistical randomness, random values, commonly as part of tabletop games, including List of dice games, dice games, board games, role-playing games, and Game of chance, games of chance. A traditional die is a cube with each of its six faces marked with a different number of dots (pip (counting), pips) from one to six. When thrown or rolled, the die comes to rest showing a random integer from one to six on its upper surface, with each value being equally likely. Dice may also have other polyhedron, polyhedral or irregular shapes, may have faces marked with numerals or symbols instead of pips and may have their numbers carved out from the material of the dice instead of marked on it. Loaded dice are specifically designed or modified to favor some results over others, for cheating or entertainment purposes. History Dice have bee ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Game Theory
Game theory is the study of mathematical models of strategic interactions. It has applications in many fields of social science, and is used extensively in economics, logic, systems science and computer science. Initially, game theory addressed two-person zero-sum games, in which a participant's gains or losses are exactly balanced by the losses and gains of the other participant. In the 1950s, it was extended to the study of non zero-sum games, and was eventually applied to a wide range of Human behavior, behavioral relations. It is now an umbrella term for the science of rational Decision-making, decision making in humans, animals, and computers. Modern game theory began with the idea of mixed-strategy equilibria in two-person zero-sum games and its proof by John von Neumann. Von Neumann's original proof used the Brouwer fixed-point theorem on continuous mappings into compact convex sets, which became a standard method in game theory and mathematical economics. His paper was f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Experiment (probability Theory)
In probability theory, an experiment or trial (see below) is any procedure that can be infinitely repeated and has a well-defined set of possible outcomes, known as the sample space. An experiment is said to be ''random'' if it has more than one possible outcome, and ''deterministic'' if it has only one. A random experiment that has exactly two (mutually exclusive) possible outcomes is known as a Bernoulli trial. When an experiment is conducted, one (and only one) outcome results— although this outcome may be included in any number of events, all of which would be said to have occurred on that trial. After conducting many trials of the same experiment and pooling the results, an experimenter can begin to assess the empirical probabilities of the various outcomes and events that can occur in the experiment and apply the methods of statistical analysis. Experiments and trials Random experiments are often conducted repeatedly, so that the collective results may be sub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ian Hacking
Ian MacDougall Hacking (February 18, 1936 – May 10, 2023) was a Canadian philosopher specializing in the philosophy of science. Throughout his career, he won numerous awards, such as the Killam Prize for the Humanities and the Balzan Prize, and was a member of many prestigious groups, including the Order of Canada, the Royal Society of Canada and the British Academy. Life and career Born in Vancouver, British Columbia, he earned undergraduate degrees from the University of British Columbia (1956) and the University of Cambridge (1958), where he was a student at Trinity College, Cambridge, Trinity College. Hacking also earned his PhD at Cambridge (1962) under the direction of Casimir Lewy, a former student of G. E. Moore. Hacking started his teaching career as an instructor at Princeton University in 1960 but, after just one year, moved to the University of Virginia as an assistant professor. After working as a research fellow at Peterhouse, Cambridge from 1962 to 1964, he ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Inference
Statistical inference is the process of using data analysis to infer properties of an underlying probability distribution.Upton, G., Cook, I. (2008) ''Oxford Dictionary of Statistics'', OUP. . Inferential statistical analysis infers properties of a population, for example by testing hypotheses and deriving estimates. It is assumed that the observed data set is sampled from a larger population. Inferential statistics can be contrasted with descriptive statistics. Descriptive statistics is solely concerned with properties of the observed data, and it does not rest on the assumption that the data come from a larger population. In machine learning, the term ''inference'' is sometimes used instead to mean "make a prediction, by evaluating an already trained model"; in this context inferring properties of the model is referred to as ''training'' or ''learning'' (rather than ''inference''), and using a model for prediction is referred to as ''inference'' (instead of ''prediction''); se ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inductive Reasoning
Inductive reasoning refers to a variety of method of reasoning, methods of reasoning in which the conclusion of an argument is supported not with deductive certainty, but with some degree of probability. Unlike Deductive reasoning, ''deductive'' reasoning (such as mathematical induction), where the conclusion is ''certain'', given the premises are correct, inductive reasoning produces conclusions that are at best ''probable'', given the evidence provided. Types The types of inductive reasoning include generalization, prediction, statistical syllogism, argument from analogy, and causal inference. There are also differences in how their results are regarded. Inductive generalization A generalization (more accurately, an ''inductive generalization'') proceeds from premises about a Sample (statistics), sample to a conclusion about the statistical population, population. The observation obtained from this sample is projected onto the broader population. : The proportion Q of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Empirical Evidence
Empirical evidence is evidence obtained through sense experience or experimental procedure. It is of central importance to the sciences and plays a role in various other fields, like epistemology and law. There is no general agreement on how the terms ''evidence'' and ''empirical'' are to be defined. Often different fields work with quite different conceptions. In epistemology, evidence is what Justification (epistemology), justifies beliefs or what determines whether holding a certain belief is rational. This is only possible if the evidence is possessed by the person, which has prompted various epistemologists to conceive evidence as private mental states like experiences or other beliefs. In philosophy of science, on the other hand, evidence is understood as that which ''Scientific method#Confirmation, confirms'' or ''disconfirms'' Hypothesis#Scientific hypothesis, scientific hypotheses and arbitrates between competing theories. For this role, evidence must be public and uncont ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nobility
Nobility is a social class found in many societies that have an aristocracy. It is normally appointed by and ranked immediately below royalty. Nobility has often been an estate of the realm with many exclusive functions and characteristics. The characteristics associated with nobility may constitute substantial advantages over or relative to non-nobles or simply formal functions (e.g., precedence), and vary by country and by era. Membership in the nobility, including rights and responsibilities, is typically hereditary and patrilineal. Membership in the nobility has historically been granted by a monarch or government, and acquisition of sufficient power, wealth, ownerships, or royal favour has occasionally enabled commoners to ascend into the nobility. There are often a variety of ranks within the noble class. Legal recognition of nobility has been much more common in monarchies, but nobility also existed in such regimes as the Dutch Republic (1581–1795), the Republic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Legal Case
Legal proceeding is an activity that seeks to invoke the power of a tribunal in order to enforce a law. Although the term may be defined more broadly or more narrowly as circumstances require, it has been noted that " e term ''legal proceedings'' includes proceedings brought by or at the instigation of a public authority, and an appeal against the decision of a court or tribunal". Legal proceedings are generally characterized by an orderly process in which participants or their representatives are able to present evidence in support of their claims, and to argue in favor of particular interpretations of the law, after which a judge, jury, or other trier of fact makes a determination of the factual and legal issues. * Activities needed to have a court deem legal process to have been provided, such as through service of process. * Conduct of a trial, whether a lawsuit or civil trial, or a criminal trial. * Issuance and enforcement of court orders, including those imposing forecl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Witness
In law, a witness is someone who, either voluntarily or under compulsion, provides testimonial evidence, either oral or written, of what they know or claim to know. A witness might be compelled to provide testimony in court, before a grand jury, before an administrative tribunal, before a deposition officer, or in a variety of other legal proceedings. A subpoena is a legal document that commands a person to appear at a proceeding. It is used to compel the testimony of a witness in a trial (law), trial. Usually, it can be issued by a judge or by the lawyer representing the plaintiff or the defendant in a civil trial or by the prosecutor or the defense attorney in a Criminal procedure, criminal proceeding, or by a government agency. In many jurisdictions, it is compulsory to comply with the subpoena and either take an oath or solemnly Affirmation in law, affirm to testify truthfully under penalty of perjury. Although informally a witness includes whoever perceived the event, in l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Authority
Authority is commonly understood as the legitimate power of a person or group of other people. In a civil state, ''authority'' may be practiced by legislative, executive, and judicial branches of government,''The New Fontana Dictionary of Modern Thought'' Third Edition, Allan Bullock and Stephen Trombley, Eds. p. 115. each of which has authority and is an authority. The term "authority" has multiple nuances and distinctions within various academic fields ranging from sociology to political science. In the exercise of governance, the terms ''authority'' and ''power'' are inaccurate synonyms. The term ''authority'' identifies the political legitimacy, which grants and justifies rulers' right to exercise the power of government; and the term ''power'' identifies the ability to accomplish an authorized goal, either by compliance or by obedience; hence, ''authority'' is the ''power'' to make decisions and the legitimacy to make such legal decisions and order their execution. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
