확률론에서, 확률 변수의 기댓값(期待값, 영어: expected value)은 각 사건이 벌어졌을 때의 이득과 그 사건이 벌어질 확률을 곱한 것을 전체 사건에 대해 합한 값이다. 이것은 어떤 확률적 사건에 대한 평균의 의미로 생각할 수 있다.

PropertyValue
dbpedia-owl:abstract
  • 확률론에서, 확률 변수의 기댓값(期待값, 영어: expected value)은 각 사건이 벌어졌을 때의 이득과 그 사건이 벌어질 확률을 곱한 것을 전체 사건에 대해 합한 값이다. 이것은 어떤 확률적 사건에 대한 평균의 의미로 생각할 수 있다.
  • В математиката, и по-точно в теорията на вероятностите и статистиката, математическото очакване представлява характеристична стойност на вероятностното разпределение на една случайна величина. Математическото очакване се базира на теорията на абстрактния интеграл на Лебег. Може да се интерпретира като „средна стойност“ на дадена случайна величина, въпреки че тази стойност може да не бъде възможен неин изход. Математическото очакване не бива да се бърка с „най-вероятен изход“ от случайния експеримент.
  • Beklenen değer bir rassal değişkennin alabileceği bütün değerlerin, olasılıklarıyla çarpılması ve bu işlemin bütün değerler üzerinden toplanmasıyla elde edilen değerdir. Ağırlıklı ortalama olarak da düşünülebilir ki ağırlık katsayıları verilen olasılık kütle fonksiyonu veya olasılık yoğunluk fonksiyonudur.
  • 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.
  • Wartość oczekiwana (wartość średnia, przeciętna, dawniej nadzieja matematyczna) – w rachunku prawdopodobieństwa wartość określająca spodziewany wynik doświadczenia losowego. Wartość oczekiwana to inaczej pierwszy moment zwykły. Estymatorem wartości oczekiwanej rozkładu cechy w populacji jest średnia arytmetyczna.
  • In de kansrekening is de verwachting (of verwachtingswaarde) van een stochastische variabele de waarde die deze stochastische variabele 'gemiddeld genomen' zal aannemen. Dit gemiddelde is het gewogen gemiddelde van alle mogelijke uitkomsten met als gewichtsfactor de kans dat een bepaalde waarde zich voordoet. Pascal en Fermat kwamen in 1654 tot dit begrip bij hun oplossing van het puntenprobleem.De verwachting kan berekend worden door de som (of integraal) te nemen van elke mogelijke uitkomst van de stochastische variabele vermenigvuldigd met de kans op deze uitkomst. De verwachting van de stochastische variabele X wordt genoteerd als E(X) (ook wel als E[X] of EX). De letter E komt van expectation, het Engelse woord voor verwachting.De stochastische variabele hoeft niet noodzakelijkerwijs de verwachte waarde zelf te kunnen aannemen. Stel bijvoorbeeld dat men een worp doet met een zuivere dobbelsteen. Er zijn zes mogelijke uitkomsten, die alle met kans 1/6 optreden. De verwachting van de uitkomst van de worp is dus 1/6 + 2/6 + ... + 6/6 = 7/2, ook al kan de uitkomst van een individuele worp nooit 7/2 zijn.
  • Itxaropen matematikoa, esperantza matematikoa edo itxarondako balioa zorizko aldagai baten batezbesteko balioa da, dagozkion probabilitateen arabera kalkulaturik. Intuitiboki, zorizko saiakuntza behin eta berriz errepikatuz epe luzera suertatuko litzatekeen emaitzen batez besteko balioa da, epe luzera itxaron edo espero daitekeen batez besteko emaitza alegia. Estatistikan maiz erabiltzen den kontzeptua da: probabilitate-banaketa bateko ezaugarri jakingarrienetako bat da, parametro ezezagun gisa hartzen dena eta datuetan baliokide duen batezbesteko aritmetiko sinplearen bitartez zenbatesten dena. Matematikan, neurri-teoriatik formulazio matematiko zorrotza du eta, aldi berean, maiz erabiltzen da problema aplikatuetan, hala nola ekonomia arloko erabakien azterketan. Zorizko jokoetan ere maiz kalkulatzen da, jokalari batek jokaldi bateko batezbesteko emaitza jakiteko. Erabaki eta jokoen eremu horietako paradoxa zenbaitetan ere agertzen da, hala nola San Petersburgo paradoxan eta Allaisen paradoxan. Halaber, baliteke mutur luzeak dituzten probabilitate banakuntzetan ez existitzea.
  • 確率論において、期待値(きたいち)とは、確率変数の実現値を, 確率の重みで平均した値である。例えば、ギャンブルでは、掛け金に対して戻ってくる「見込み」の金額をあらわしたものである。ただし、期待値ぴったりに掛け金が戻ることを意味するのではなく、各試行で期待値に等しい掛け金が戻るわけではない。類義語に平均がある。期待値と同義で使われることもあるが、標本平均を意味する場合もある。
  • Em Estatística, em teoria das probabilidades, o valor esperado, também chamado esperança matemática ou expectância, de uma variável aleatória é a soma das probabilidades de cada possibilidade de saída da experiência multiplicada pelo seu valor. Isto é, representa o valor médio "esperado" de uma experiência se ela for repetida muitas vezes. Note-se que o valor em si pode não ser esperado no sentido geral; pode ser improvável ou impossível. Se todos os eventos tiverem igual probabilidade o valor esperado é a média aritmética.
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  • 확률론에서, 확률 변수의 기댓값(期待값, 영어: expected value)은 각 사건이 벌어졌을 때의 이득과 그 사건이 벌어질 확률을 곱한 것을 전체 사건에 대해 합한 값이다. 이것은 어떤 확률적 사건에 대한 평균의 의미로 생각할 수 있다.
  • Beklenen değer bir rassal değişkennin alabileceği bütün değerlerin, olasılıklarıyla çarpılması ve bu işlemin bütün değerler üzerinden toplanmasıyla elde edilen değerdir. Ağırlıklı ortalama olarak da düşünülebilir ki ağırlık katsayıları verilen olasılık kütle fonksiyonu veya olasılık yoğunluk fonksiyonudur.
  • Wartość oczekiwana (wartość średnia, przeciętna, dawniej nadzieja matematyczna) – w rachunku prawdopodobieństwa wartość określająca spodziewany wynik doświadczenia losowego. Wartość oczekiwana to inaczej pierwszy moment zwykły. Estymatorem wartości oczekiwanej rozkładu cechy w populacji jest średnia arytmetyczna.
  • 確率論において、期待値(きたいち)とは、確率変数の実現値を, 確率の重みで平均した値である。例えば、ギャンブルでは、掛け金に対して戻ってくる「見込み」の金額をあらわしたものである。ただし、期待値ぴったりに掛け金が戻ることを意味するのではなく、各試行で期待値に等しい掛け金が戻るわけではない。類義語に平均がある。期待値と同義で使われることもあるが、標本平均を意味する場合もある。
  • Em Estatística, em teoria das probabilidades, o valor esperado, também chamado esperança matemática ou expectância, de uma variável aleatória é a soma das probabilidades de cada possibilidade de saída da experiência multiplicada pelo seu valor. Isto é, representa o valor médio "esperado" de uma experiência se ela for repetida muitas vezes. Note-se que o valor em si pode não ser esperado no sentido geral; pode ser improvável ou impossível.
  • In de kansrekening is de verwachting (of verwachtingswaarde) van een stochastische variabele de waarde die deze stochastische variabele 'gemiddeld genomen' zal aannemen. Dit gemiddelde is het gewogen gemiddelde van alle mogelijke uitkomsten met als gewichtsfactor de kans dat een bepaalde waarde zich voordoet.
  • В математиката, и по-точно в теорията на вероятностите и статистиката, математическото очакване представлява характеристична стойност на вероятностното разпределение на една случайна величина. Математическото очакване се базира на теорията на абстрактния интеграл на Лебег. Може да се интерпретира като „средна стойност“ на дадена случайна величина, въпреки че тази стойност може да не бъде възможен неин изход.
  • 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.
  • Itxaropen matematikoa, esperantza matematikoa edo itxarondako balioa zorizko aldagai baten batezbesteko balioa da, dagozkion probabilitateen arabera kalkulaturik. Intuitiboki, zorizko saiakuntza behin eta berriz errepikatuz epe luzera suertatuko litzatekeen emaitzen batez besteko balioa da, epe luzera itxaron edo espero daitekeen batez besteko emaitza alegia.
rdfs:label
  • Espérance mathématique
  • Beklenen değer
  • Erwartungswert
  • Esperanza matemática
  • Esperança matemàtica
  • Expected value
  • Itxaropen matematiko
  • Střední hodnota
  • Valor esperado
  • Valore atteso
  • Verwachting (wiskunde)
  • Várható érték
  • Wartość oczekiwana
  • Математическо очакване
  • Математическое ожидание
  • 期待値
  • 기댓값
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