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Encyclopedia > Expectation

This page deals with the concept of expectation as a thought or belief. For expectation in the context of probability theory and statistics, see expected value. Probability theory is the mathematical study of probability. ... Statistics is a broad mathematical discipline which studies ways to collect, summarize and draw conclusions from data. ... In probability theory (and especially gambling), the expected value (or mathematical expectation) of a random variable is the sum of the probability of each possible outcome of the experiment multiplied by its payoff (value). Thus, it represents the average amount one expects to win per bet if bets with identical...

In the case of uncertainty, expectation is what is considered the most likely to happen. An expectation may or may not be realistic. Uncertainty is an inevitable part of the assertion of knowledge: see Bayesian probability. ...

A less advantageous result gives rise to the emotion of disappointment. If something happens that is not at all expected it is a surprise. See also anticipation, hope. In psychology and common use, emotion is an aspect of a human beings mental state, normally based in or tied to the persons internal (physical) and external (social) sensory feeling. ... This article needs cleanup. ... Anticipation is an emotion involving pleasure in considering some expected or longed-for good event, or irritation at having to wait. ... Hope is a belief that desirable things are obtainable regardless of the remoteness of the probabilities. ...

An expectation about the behavior or performance of another person, expressed to that person, may have the nature of a strong request, or an order.

In mathematics or statistic expectation also stands for the expected value. This is some kind of mean value over a few samples. Mathematics is commonly defined as the study of patterns of structure, change, and space; more informally, one might say it is the study of figures and numbers. Mathematical knowledge is constantly growing, through research and application, but mathematics itself is not usually considered a natural science. ... A statistic (singular) is the result of applying a statistical algorithm to a set of data. ... In probability theory (and especially gambling), the expected value (or mathematical expectation) of a random variable is the sum of the probability of each possible outcome of the experiment multiplied by its payoff (value). Thus, it represents the average amount one expects to win per bet if bets with identical...

Results from FactBites:

 Expectation utilities - Wikipedia, the free encyclopedia (111 words) Expectation utilities are future-regarding, and thus imply desires and beliefs; "natural" utilities are not. Expectation utilities allow for long-term projects, which provide a higher proportion of utility than the natural utilities favored by those agents that can only pursue their immediate interest. The notion of 'expectation utility' must not be mistaken for that of expected utility.
 Pythagorean expectation - Wikipedia, the free encyclopedia (364 words) Pythagorean expectation is a formula invented by Bill James to estimate how many games a baseball team "should" have won based on the number of runs they scored and allowed. The term is derived from the formula's resemblance to Pythagoras' formula to compute the length of the hypotenuse of a triangle from the lengths of its other two sides. Applying the pythagorean expectation to Football: Includes a discussion of how the exponent in the formula should be larger the larger the number of points scored per game becomes.
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