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- Expected_value abstract "In probability theory, the expected value (or expectation, mathematical expectation, EV, mean, or first moment) refers, intuitively, to the value of a random variable one would "expect" to find if one could repeat the random variable process an infinite number of times and take the average of the values obtained. More formally, the expected value is a weighted average of all possible values. In other words, each possible value that the random variable can assume is multiplied by its assigned weight, and the resulting products are then added together to find the expected value. The weights used in computing this average are the probabilities in the case of a discrete random variable (that is, a random variable that can only take on a finite number of values, such as a roll of a pair of dice), or the values of a probability density function in the case of a continuous random variable (that is, a random variable that can assume a theoretically infinite number of values, such as the height of a person).From a rigorous theoretical standpoint, the expected value of a continuous variable is the integral of the random variable with respect to its probability measure. Since probability can never be negative (although it can be zero), the expected value is proportional to the area under the curve of the graph of the values of a random variable multiplied by the probability of that value. Thus, for a continuous random variable the expected value is the limit of the weighted sum, i.e. the integral.The intuitive explanation of the expected value above is a consequence of the law of large numbers: the expected value, when it exists, is almost surely the limit of the sample mean as the sample size grows to infinity. More informally, it can be interpreted as the long-run average of the results of many independent repetitions of an experiment (e.g. a dice roll). The value may not be expected in the ordinary sense—the "expected value" itself may be unlikely or even impossible (such as having 2.5 children), as is also the case with the sample mean.The expected value does not exist for random variables having some distributions with large "tails", such as the Cauchy distribution. For random variables such as these, the long-tails of the distribution prevent the sum/integral from converging.The expected value is a key aspect of how one characterizes a probability distribution; it is one type of location parameter. By contrast, the variance is a measure of dispersion of the possible values of the random variable around the expected value. The variance itself is defined in terms of two expectations: it is the expected value of the squared deviation of the variable's value from the variable's expected value.The expected value plays important roles in a variety of contexts. In regression analysis, one desires a formula in terms of observed data that will give a "good" estimate of the parameter giving the effect of some explanatory variable upon a dependent variable. The formula will give different estimates using different samples of data, so the estimate it gives is itself a random variable. A formula is typically considered good in this context if it is an unbiased estimator—that is, if the expected value of the estimate (the average value it would give over an arbitrarily large number of separate samples) can be shown to equal the true value of the desired parameter.In decision theory, and in particular in choice under uncertainty, an agent is described as making an optimal choice in the context of incomplete information. For risk neutral agents, the choice involves using the expected values of uncertain quantities, while for risk averse agents it involves maximizing the expected value of some objective function such as a von Neumann-Morgenstern utility function.".
- Expected_value thumbnail Largenumbers.svg?width=300.
- Expected_value wikiPageExternalLink huygens.pdf.
- Expected_value wikiPageID "9653".
- Expected_value wikiPageRevisionID "598065223".
- Expected_value hasPhotoCollection Expected_value.
- Expected_value subject Category:Gambling_terminology.
- Expected_value subject Category:Theory_of_probability_distributions.
- Expected_value comment "In probability theory, the expected value (or expectation, mathematical expectation, EV, mean, or first moment) refers, intuitively, to the value of a random variable one would "expect" to find if one could repeat the random variable process an infinite number of times and take the average of the values obtained. More formally, the expected value is a weighted average of all possible values.".
- Expected_value label "Erwartungswert".
- Expected_value label "Esperanza matemática".
- Expected_value label "Espérance mathématique".
- Expected_value label "Expected value".
- Expected_value label "Valor esperado".
- Expected_value label "Valore atteso".
- Expected_value label "Verwachting (wiskunde)".
- Expected_value label "Wartość oczekiwana".
- Expected_value label "Математическое ожидание".
- Expected_value label "قيمة متوقعة".
- Expected_value label "期待値".
- Expected_value label "期望值".
- Expected_value sameAs Střední_hodnota.
- Expected_value sameAs Erwartungswert.
- Expected_value sameAs Αναμενόμενη_τιμή.
- Expected_value sameAs Esperanza_matemática.
- Expected_value sameAs Itxaropen_matematiko.
- Expected_value sameAs Espérance_mathématique.
- Expected_value sameAs Valore_atteso.
- Expected_value sameAs 期待値.
- Expected_value sameAs 기댓값.
- Expected_value sameAs Verwachting_(wiskunde).
- Expected_value sameAs Wartość_oczekiwana.
- Expected_value sameAs Valor_esperado.
- Expected_value sameAs m.02mnh.
- Expected_value sameAs Q200125.
- Expected_value sameAs Q200125.
- Expected_value wasDerivedFrom Expected_value?oldid=598065223.
- Expected_value depiction Largenumbers.svg.
- Expected_value isPrimaryTopicOf Expected_value.