"Probabilitate teorian, konbergentzia estokastikoa zorizko aldagaien segida batek limitean duen joera aztertzen duen arloa da. Konbergentziaren azterketa funtsezkoa inferentzia estatistikoan, lagin handietan zenbatesleek dituzten propietateak aztertzean kasu. Konbergentzia modu asko daude, limiteko joerak nola definitzen diren; horrela, eta bereizten dira, besteak beste. Limitearen teorema zentrala, zenbaki handien legea eta bestelako teoremek ezartzen dituzte konbergentzia estokastikoaren emaitzak, zorizko aldagaiek segidak betetzen dituen baldintzen arabera. Konbergentzia estokastikoaren oinarri teorikoak XIX. mendean eta batez ere XX. mendearen lehenengo zatian garatu ziren, matematika-tresna zorrotzak erabiliz eta Andrei Kolmogoroven eskutik besteak beste."@eu . . "Zbie\u017Cno\u015B\u0107 wed\u0142ug rozk\u0142adu \u2013 jeden z rodzaj\u00F3w zbie\u017Cno\u015Bci wektor\u00F3w losowych, nazywany czasem s\u0142ab\u0105 zbie\u017Cno\u015Bci\u0105."@pl . . . . . "V teorii pravd\u011Bpodobnosti existuje n\u011Bkolik r\u016Fzn\u00FDch pojm\u016F konvergence n\u00E1hodn\u00FDch prom\u011Bnn\u00FDch. Konvergence posloupnosti n\u00E1hodn\u00FDch prom\u011Bnn\u00FDch k n\u011Bjak\u00E9 limitn\u00ED n\u00E1hodn\u00E9 prom\u011Bnn\u00E9 je d\u016Fle\u017Eit\u00FDm konceptem v teorii pravd\u011Bpodobnosti, a v jej\u00EDch aplikac\u00EDch na statistiku a n\u00E1hodn\u00E9 procesy. Stejn\u00E9 koncepty jsou zn\u00E1my v matematice obecn\u011Bji jako stochastick\u00E1 konvergence a formalizuj\u00ED o\u010Dek\u00E1v\u00E1n\u00ED, \u017Ee chov\u00E1n\u00ED posloupnosti v z\u00E1sad\u011B n\u00E1hodn\u00FDch nebo nep\u0159edpov\u011Bditeln\u00FDch ud\u00E1lost\u00ED se n\u011Bkdy m\u016F\u017Ee ust\u00E1lit do formy, kter\u00E1 se v z\u00E1sad\u011B nem\u011Bn\u00ED, kdy\u017E zkoum\u00E1me polo\u017Eky, kter\u00E9 jsou v posloupnosti dostate\u010Dn\u011B daleko. R\u016Fzn\u00E9 typy konvergence se odv\u00EDjej\u00ED od toho, jak lze takov\u00E9 chov\u00E1n\u00ED charakterizovat: dva snadno p\u0159edstaviteln\u00E9 p\u0159\u00EDpady jsou, \u017Ee posloupnost za\u010Dne b\u00FDt od ur\u010Dit\u00E9ho \u010Dlenu konstantn\u00ED, nebo \u017Ee hodnoty posloupnosti se budou d\u00E1le m\u011Bnit, ale bude mo\u017En\u00E9 je popsat n\u011Bjak\u00FDm pevn\u00FDm rozd\u011Blen\u00EDm pravd\u011Bpodobnosti."@cs . "\uD655\uB960\uBCC0\uC218\uC758 \uC218\uB834\uC5D0\uB294 \uC5EC\uB7EC \uAC00\uC9C0\uC758 \uC815\uC758\uAC00 \uC874\uC7AC\uD55C\uB2E4."@ko . . . . . . . "\u0421\u0445\u043E\u0434\u0438\u0301\u043C\u043E\u0441\u0442\u044C \u043F\u043E \u0440\u0430\u0441\u043F\u0440\u0435\u0434\u0435\u043B\u0435\u0301\u043D\u0438\u044E \u0432 \u0442\u0435\u043E\u0440\u0438\u0438 \u0432\u0435\u0440\u043E\u044F\u0442\u043D\u043E\u0441\u0442\u0435\u0439 \u2014 \u0432\u0438\u0434 \u0441\u0445\u043E\u0434\u0438\u043C\u043E\u0441\u0442\u0438 \u0441\u043B\u0443\u0447\u0430\u0439\u043D\u044B\u0445 \u0432\u0435\u043B\u0438\u0447\u0438\u043D."@ru . . . . . . . . . "Example 2"@en . . "V teorii pravd\u011Bpodobnosti existuje n\u011Bkolik r\u016Fzn\u00FDch pojm\u016F konvergence n\u00E1hodn\u00FDch prom\u011Bnn\u00FDch. Konvergence posloupnosti n\u00E1hodn\u00FDch prom\u011Bnn\u00FDch k n\u011Bjak\u00E9 limitn\u00ED n\u00E1hodn\u00E9 prom\u011Bnn\u00E9 je d\u016Fle\u017Eit\u00FDm konceptem v teorii pravd\u011Bpodobnosti, a v jej\u00EDch aplikac\u00EDch na statistiku a n\u00E1hodn\u00E9 procesy. Stejn\u00E9 koncepty jsou zn\u00E1my v matematice obecn\u011Bji jako stochastick\u00E1 konvergence a formalizuj\u00ED o\u010Dek\u00E1v\u00E1n\u00ED, \u017Ee chov\u00E1n\u00ED posloupnosti v z\u00E1sad\u011B n\u00E1hodn\u00FDch nebo nep\u0159edpov\u011Bditeln\u00FDch ud\u00E1lost\u00ED se n\u011Bkdy m\u016F\u017Ee ust\u00E1lit do formy, kter\u00E1 se v z\u00E1sad\u011B nem\u011Bn\u00ED, kdy\u017E zkoum\u00E1me polo\u017Eky, kter\u00E9 jsou v posloupnosti dostate\u010Dn\u011B daleko. R\u016Fzn\u00E9 typy konvergence se odv\u00EDjej\u00ED od toho, jak lze takov\u00E9 chov\u00E1n\u00ED charakterizovat: dva snadno p\u0159edstaviteln\u00E9 p\u0159\u00EDpady jsou, \u017Ee posloupnost za\u010Dne b\u00FDt od ur\u010Dit\u00E9ho \u010Dlenu konstantn\u00ED, nebo \u017Ee hodnoty posloupnosti se budou "@cs . "\u6982\u7387\u8BBA\u4E2D\u6709\u82E5\u5E72\u5173\u4E8E\u968F\u673A\u53D8\u91CF\u6536\u655B\uFF08Convergence of random variables\uFF09\u7684\u5B9A\u4E49\u3002\u7814\u7A76\u4E00\u5217\u968F\u673A\u53D8\u91CF\u662F\u5426\u4F1A\u6536\u655B\u5230\u67D0\u4E2A\u6781\u9650\u968F\u673A\u53D8\u91CF\u662F\u6982\u7387\u8BBA\u4E2D\u7684\u91CD\u8981\u5185\u5BB9\uFF0C\u5728\u7EDF\u8BA1\u6982\u7387\u548C\u968F\u673A\u8FC7\u7A0B\u4E2D\u90FD\u6709\u5E94\u7528\u3002\u5728\u66F4\u5E7F\u6CDB\u7684\u6570\u5B66\u9886\u57DF\u4E2D\uFF0C\u968F\u673A\u53D8\u91CF\u7684\u6536\u655B\u88AB\u79F0\u4E3A\u968F\u673A\u6536\u655B\uFF0C\u8868\u793A\u4E00\u7CFB\u5217\u672C\u8D28\u4E0A\u968F\u673A\u4E0D\u53EF\u9884\u6D4B\u7684\u4E8B\u4EF6\u6240\u53D1\u751F\u7684\u6A21\u5F0F\u53EF\u4EE5\u5728\u6837\u672C\u6570\u91CF\u8DB3\u591F\u5927\u7684\u65F6\u5019\u5F97\u5230\u5408\u7406\u53EF\u9760\u7684\u9884\u6D4B\u3002\u5404\u79CD\u4E0D\u540C\u7684\u6536\u655B\u5B9A\u4E49\u5B9E\u9645\u4E0A\u662F\u8868\u793A\u9884\u6D4B\u65F6\u4E0D\u540C\u7684\u523B\u753B\u65B9\u5F0F\u3002"@zh . . . . "In der Stochastik existieren verschiedene Konzepte eines Grenzwertbegriffs f\u00FCr Zufallsvariablen. Anders als im Fall reeller Zahlenfolgen gibt es keine nat\u00FCrliche Definition f\u00FCr das Grenzverhalten von Zufallsvariablen bei wachsendem Stichprobenumfang, weil das asymptotische Verhalten der Experimente immer von den einzelnen Realisierungen abh\u00E4ngt und wir es also formal mit der Konvergenz von Funktionen zu tun haben. Daher haben sich im Laufe der Zeit unterschiedlich starke Konzepte herausgebildet, die wichtigsten dieser Konvergenzarten werden im Folgenden kurz vorgestellt."@de . 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"text-align: left;"@en . "Graphic example"@en . "\u0417\u0431\u0456\u0436\u043D\u0456\u0441\u0442\u044C \u0432\u0438\u043F\u0430\u0434\u043A\u043E\u0432\u0438\u0445 \u0432\u0435\u043B\u0438\u0447\u0438\u043D"@uk . "En teoria de la probabilitat, l'estudi de la converg\u00E8ncia de variables aleat\u00F2ries \u00E9s fonamental, tant per la seva riquesa matem\u00E0tica (lleis dels grans nombres, teorema del l\u00EDmit central, llei del logaritme iterat, etc.) com per les seves aplicacions a l'Estad\u00EDstica. En aquest article s'estudien les converg\u00E8ncies m\u00E9s habituals: en distribuci\u00F3 o llei, en probabilitat, quasi segura i en mitjana d'ordre . La refer\u00E8ncia general d'aquesta p\u00E0gina \u00E9s Serfling on es troben les demostracions o les refer\u00E8ncies corresponents, i nombrosos exemples i contraexemples."@ca . . "background-color: lightblue; text-align: left; padding-left: 3pt;"@en . "En teor\u00EDa de la probabilidad, existen diferentes nociones de convergencia de variables aleatorias. La convergencia de sucesiones de variables aleatorias a una variable aleatoria l\u00EDmite es un concepto importante en teor\u00EDa de la probabilidad, y en sus aplicaciones a la estad\u00EDstica y los procesos estoc\u00E1sticos."@es . . . . . "In de kansrekening kan convergentie van een rij stochastische variabelen verschillende betekenissen hebben. Anders dan bij rijen getallen is er geen voor de hand liggende definitie voor het asymptotische gedrag bij toenemende omvang van de steekproef. Daardoor zijn er verschillende convergentiebegrippen ontstaan, van verschillende sterkte. De belangrijkste daarvan worden in dit lemma besproken. Het gaat steeds om een rij stochastische variabelen , gedefinieerd op een kansruimte"@nl . "In probability theory, there exist several different notions of convergence of random variables. The convergence of sequences of random variables to some limit random variable is an important concept in probability theory, and its applications to statistics and stochastic processes. The same concepts are known in more general mathematics as stochastic convergence and they formalize the idea that a sequence of essentially random or unpredictable events can sometimes be expected to settle down into a behavior that is essentially unchanging when items far enough into the sequence are studied. The different possible notions of convergence relate to how such a behavior can be characterized: two readily understood behaviors are that the sequence eventually takes a constant value, and that values"@en . . . "Em teoria das probabilidades, existem v\u00E1rias no\u00E7\u00F5es diferentes de converg\u00EAncia de vari\u00E1veis aleat\u00F3rias. A converg\u00EAncia de sequ\u00EAncias de vari\u00E1veis aleat\u00F3rias a alguma vari\u00E1vel aleat\u00F3ria limite \u00E9 um importante conceito em teoria das probabilidades e tem aplica\u00E7\u00F5es na estat\u00EDstica e nos processos estoc\u00E1sticos. Os mesmos conceitos s\u00E3o conhecidos em matem\u00E1tica geral como converg\u00EAncia estoc\u00E1stica e formalizam a ideia de que \u00E9 poss\u00EDvel esperar que uma sequ\u00EAncia de eventos essencialmente aleat\u00F3rios ou imprevis\u00EDveis \u00E0s vezes mantenha um comportamento essencialmente imut\u00E1vel quando itens suficientemente distantes na sequ\u00EAncia s\u00E3o estudados. As poss\u00EDveis no\u00E7\u00F5es diferentes de converg\u00EAncia se relacionam a como tal comportamento pode ser caracterizado: dois comportamentos prontamente entendidos s\u00E3o que a sequ\u00EAncia eventualmente assume um valor constante e que os valores na sequ\u00EAncia continuam mudando, mas podem ser descritos por uma distribui\u00E7\u00E3o de probabilidade imut\u00E1vel."@pt . . . "\u0641\u064A \u0646\u0638\u0631\u064A\u0629 \u0627\u0644\u0627\u062D\u062A\u0645\u0627\u0644\u0627\u062A\u060C \u062A\u0648\u062C\u062F \u0639\u062F\u0629 \u0645\u0641\u0627\u0647\u064A\u0645 \u0645\u062E\u062A\u0644\u0641\u0629 \u0644\u062A\u0642\u0627\u0631\u0628 \u0627\u0644\u0645\u062A\u063A\u064A\u0631\u0627\u062A \u0627\u0644\u0639\u0634\u0648\u0627\u0626\u064A\u0629. \u064A\u0639\u062F \u062A\u0642\u0627\u0631\u0628 \u062A\u0633\u0644\u0633\u0644 \u0627\u0644\u0645\u062A\u063A\u064A\u0631\u0627\u062A \u0627\u0644\u0639\u0634\u0648\u0627\u0626\u064A\u0629 \u0644\u0628\u0639\u0636 \u0627\u0644\u0645\u062A\u063A\u064A\u0631\u0627\u062A \u0627\u0644\u0639\u0634\u0648\u0627\u0626\u064A\u0629 \u0627\u0644\u062D\u062F \u0645\u0641\u0647\u0648\u0645\u064B\u0627 \u0645\u0647\u0645\u064B\u0627 \u0641\u064A \u0646\u0638\u0631\u064A\u0629 \u0627\u0644\u0627\u062D\u062A\u0645\u0627\u0644\u0627\u062A \u0648\u062A\u0637\u0628\u064A\u0642\u0627\u062A\u0647 \u0639\u0644\u0649 \u0627\u0644\u0625\u062D\u0635\u0627\u0621 \u0648\u0627\u0644\u0639\u0645\u0644\u064A\u0627\u062A \u0627\u0644\u0639\u0634\u0648\u0627\u0626\u064A\u0629. \u062A\u064F\u0639\u0631\u0641 \u0646\u0641\u0633 \u0627\u0644\u0645\u0641\u0627\u0647\u064A\u0645 \u0641\u064A \u0627\u0644\u0631\u064A\u0627\u0636\u064A\u0627\u062A \u0627\u0644\u0623\u0643\u062B\u0631 \u0639\u0645\u0648\u0645\u064A\u0629 \u0628\u0627\u0633\u0645 \u0627\u0644\u062A\u0642\u0627\u0631\u0628 \u0627\u0644\u0639\u0634\u0648\u0627\u0626\u064A \u0648\u062A\u0636\u0641\u064A \u0627\u0644\u0637\u0627\u0628\u0639 \u0627\u0644\u0631\u0633\u0645\u064A \u0639\u0644\u0649 \u0641\u0643\u0631\u0629 \u0623\u0646\u0647 \u064A\u0645\u0643\u0646 \u062A\u0648\u0642\u0639 \u062A\u0633\u0644\u0633\u0644 \u0627\u0644\u0623\u062D\u062F\u0627\u062B \u0627\u0644\u0639\u0634\u0648\u0627\u0626\u064A\u0629 \u0623\u0648 \u063A\u064A\u0631 \u0627\u0644\u0645\u062A\u0648\u0642\u0639\u0629 \u0641\u064A \u0628\u0639\u0636 \u0627\u0644\u0623\u062D\u064A\u0627\u0646 \u0641\u064A \u0633\u0644\u0648\u0643 \u0644\u0627 \u064A\u062A\u063A\u064A\u0631 \u0628\u0634\u0643\u0644 \u0623\u0633\u0627\u0633\u064A \u0639\u0646\u062F \u062F\u0631\u0627\u0633\u0629 \u0627\u0644\u0639\u0646\u0627\u0635\u0631 \u0627\u0644\u0628\u0639\u064A\u062F\u0629 \u0628\u062F\u0631\u062C\u0629 \u0643\u0627\u0641\u064A\u0629 \u0641\u064A \u0627\u0644\u062A\u0633\u0644\u0633\u0644. \u062A\u062A\u0639\u0644\u0642 \u0627\u0644\u0645\u0641\u0627\u0647\u064A\u0645 \u0627\u0644\u0645\u062E\u062A\u0644\u0641\u0629 \u0627\u0644\u0645\u0645\u0643\u0646\u0629 \u0644\u0644\u062A\u0642\u0627\u0631\u0628 \u0628\u0643\u064A\u0641\u064A\u0629 \u0648\u0635\u0641 \u0645\u062B\u0644 \u0647\u0630\u0627 \u0627\u0644\u0633\u0644\u0648\u0643: \u0633\u0644\u0648\u0643\u0627\u0646 \u0645\u0641\u0647\u0645\u0627\u0646 \u0628\u0633\u0647\u0648\u0644\u0629 \u0647\u0645\u0627 \u0623\u0646 \u0627\u0644\u062A\u0633\u0644\u0633\u0644 \u064A\u0623\u062E\u0630 \u0641\u064A \u0646\u0647\u0627\u064A\u0629 \u0627\u0644\u0645\u0637\u0627\u0641 \u0642\u064A\u0645\u0629 \u062B\u0627\u0628\u062A\u0629\u060C \u0648\u0623\u0646 \u0627\u0644\u0642\u064A\u0645 \u0641\u064A \u0627\u0644\u062A\u0633\u0644\u0633\u0644 \u062A\u0633\u062A\u0645\u0631 \u0641\u064A \u0627\u0644\u062A\u063A\u064A\u064A\u0631 \u0648\u0644\u0643\u0646 \u064A\u0645\u0643\u0646 \u0648\u0635\u0641\u0647\u0627 \u0628\u062A\u0648\u0632\u064A\u0639 \u0627\u0644\u0627\u062D\u062A\u0645\u0627\u0644\u0627\u062A \u063A\u064A\u0631 \u0627\u0644\u0645\u062A\u063A\u064A\u0631."@ar . . "\u0423 \u0442\u0435\u043E\u0440\u0456\u0457 \u0439\u043C\u043E\u0432\u0456\u0440\u043D\u043E\u0441\u0442\u0435\u0439 \u0456\u0441\u043D\u0443\u0454 \u0434\u0435\u043A\u0456\u043B\u044C\u043A\u0430 \u0432\u0438\u0434\u0456\u0432 \u0437\u0431\u0456\u0436\u043D\u043E\u0441\u0442\u0456 \u0432\u0438\u043F\u0430\u0434\u043A\u043E\u0432\u0438\u0445 \u0432\u0435\u043B\u0438\u0447\u0438\u043D. \u0417\u0431\u0456\u0436\u043D\u0456\u0441\u0442\u044C \u043F\u043E\u0441\u043B\u0456\u0434\u043E\u0432\u043D\u043E\u0441\u0442\u0456 \u0432\u0438\u043F\u0430\u0434\u043A\u043E\u0432\u0438\u0445 \u0432\u0435\u043B\u0438\u0447\u0438\u043D \u0434\u043E \u0434\u0435\u044F\u043A\u043E\u0457 \u0433\u0440\u0430\u043D\u0438\u0447\u043D\u043E\u0457 \u0432\u0438\u043F\u0430\u0434\u043A\u043E\u0432\u043E\u0457 \u0432\u0435\u043B\u0438\u0447\u0438\u043D\u0438 \u043C\u0430\u0454 \u0448\u0438\u0440\u043E\u043A\u0435 \u0437\u0430\u0441\u0442\u043E\u0441\u0443\u0432\u0430\u043D\u043D\u044F \u0443 \u0441\u0442\u0430\u0442\u0438\u0441\u0442\u0438\u0446\u0456 \u0442\u0430 \u0442\u0435\u043E\u0440\u0456\u0457 \u0432\u0438\u043F\u0430\u0434\u043A\u043E\u0432\u0438\u0445 \u043F\u0440\u043E\u0446\u0435\u0441\u0456\u0432."@uk . . . "\u0421\u0445\u043E\u0434\u0438\u0301\u043C\u043E\u0441\u0442\u044C \u043F\u043E \u0440\u0430\u0441\u043F\u0440\u0435\u0434\u0435\u043B\u0435\u0301\u043D\u0438\u044E \u0432 \u0442\u0435\u043E\u0440\u0438\u0438 \u0432\u0435\u0440\u043E\u044F\u0442\u043D\u043E\u0441\u0442\u0435\u0439 \u2014 \u0432\u0438\u0434 \u0441\u0445\u043E\u0434\u0438\u043C\u043E\u0441\u0442\u0438 \u0441\u043B\u0443\u0447\u0430\u0439\u043D\u044B\u0445 \u0432\u0435\u043B\u0438\u0447\u0438\u043D."@ru . "Convergence de variables al\u00E9atoires"@fr . . "\uD655\uB960\uBCC0\uC218\uC758 \uC218\uB834\uC5D0\uB294 \uC5EC\uB7EC \uAC00\uC9C0\uC758 \uC815\uC758\uAC00 \uC874\uC7AC\uD55C\uB2E4."@ko . . . "50723"^^ . . . . . "\u6982\u7387\u8BBA\u4E2D\u6709\u82E5\u5E72\u5173\u4E8E\u968F\u673A\u53D8\u91CF\u6536\u655B\uFF08Convergence of random variables\uFF09\u7684\u5B9A\u4E49\u3002\u7814\u7A76\u4E00\u5217\u968F\u673A\u53D8\u91CF\u662F\u5426\u4F1A\u6536\u655B\u5230\u67D0\u4E2A\u6781\u9650\u968F\u673A\u53D8\u91CF\u662F\u6982\u7387\u8BBA\u4E2D\u7684\u91CD\u8981\u5185\u5BB9\uFF0C\u5728\u7EDF\u8BA1\u6982\u7387\u548C\u968F\u673A\u8FC7\u7A0B\u4E2D\u90FD\u6709\u5E94\u7528\u3002\u5728\u66F4\u5E7F\u6CDB\u7684\u6570\u5B66\u9886\u57DF\u4E2D\uFF0C\u968F\u673A\u53D8\u91CF\u7684\u6536\u655B\u88AB\u79F0\u4E3A\u968F\u673A\u6536\u655B\uFF0C\u8868\u793A\u4E00\u7CFB\u5217\u672C\u8D28\u4E0A\u968F\u673A\u4E0D\u53EF\u9884\u6D4B\u7684\u4E8B\u4EF6\u6240\u53D1\u751F\u7684\u6A21\u5F0F\u53EF\u4EE5\u5728\u6837\u672C\u6570\u91CF\u8DB3\u591F\u5927\u7684\u65F6\u5019\u5F97\u5230\u5408\u7406\u53EF\u9760\u7684\u9884\u6D4B\u3002\u5404\u79CD\u4E0D\u540C\u7684\u6536\u655B\u5B9A\u4E49\u5B9E\u9645\u4E0A\u662F\u8868\u793A\u9884\u6D4B\u65F6\u4E0D\u540C\u7684\u523B\u753B\u65B9\u5F0F\u3002"@zh . . . . "In der Stochastik existieren verschiedene Konzepte eines Grenzwertbegriffs f\u00FCr Zufallsvariablen. Anders als im Fall reeller Zahlenfolgen gibt es keine nat\u00FCrliche Definition f\u00FCr das Grenzverhalten von Zufallsvariablen bei wachsendem Stichprobenumfang, weil das asymptotische Verhalten der Experimente immer von den einzelnen Realisierungen abh\u00E4ngt und wir es also formal mit der Konvergenz von Funktionen zu tun haben. Daher haben sich im Laufe der Zeit unterschiedlich starke Konzepte herausgebildet, die wichtigsten dieser Konvergenzarten werden im Folgenden kurz vorgestellt."@de . "Konvergence n\u00E1hodn\u00FDch prom\u011Bnn\u00FDch"@cs . "En teor\u00EDa de la probabilidad, existen diferentes nociones de convergencia de variables aleatorias. La convergencia de sucesiones de variables aleatorias a una variable aleatoria l\u00EDmite es un concepto importante en teor\u00EDa de la probabilidad, y en sus aplicaciones a la estad\u00EDstica y los procesos estoc\u00E1sticos."@es . . "\u6570\u5B66\u306E\u78BA\u7387\u8AD6\u306E\u5206\u91CE\u306B\u304A\u3044\u3066\u3001\u78BA\u7387\u5909\u6570\u306E\u53CE\u675F\uFF08\u304B\u304F\u308A\u3064\u3078\u3093\u3059\u3046\u306E\u3057\u3085\u3046\u305D\u304F\u3001\u82F1: convergence of random variables\uFF09\u306B\u95A2\u3057\u3066\u306F\u3001\u3044\u304F\u3064\u304B\u306E\u7570\u306A\u308B\u6982\u5FF5\u304C\u3042\u308B\u3002\u78BA\u7387\u5909\u6570\u5217\u306E\u3042\u308B\u6975\u9650\u3078\u306E\u53CE\u675F\u306F\u3001\u78BA\u7387\u8AD6\u3084\u3001\u305D\u306E\u5FDC\u7528\u3068\u3057\u3066\u306E\u7D71\u8A08\u5B66\u3084\u78BA\u7387\u904E\u7A0B\u306E\u7814\u7A76\u306B\u304A\u3051\u308B\u91CD\u8981\u306A\u6982\u5FF5\u306E\u4E00\u3064\u3067\u3042\u308B\u3002\u3088\u308A\u4E00\u822C\u7684\u306A\u6570\u5B66\u306B\u304A\u3044\u3066\u540C\u69D8\u306E\u6982\u5FF5\u306F\u78BA\u7387\u53CE\u675F (stochastic convergence) \u3068\u3057\u3066\u77E5\u3089\u308C\u3001\u305D\u306E\u6982\u5FF5\u306F\u3001\u672C\u8CEA\u7684\u306B\u30E9\u30F3\u30C0\u30E0\u3042\u308B\u3044\u306F\u4E88\u6E2C\u4E0D\u53EF\u80FD\u306A\u4E8B\u8C61\u306E\u5217\u306F\u3001\u305D\u306E\u5217\u304B\u3089\u5341\u5206\u96E2\u308C\u3066\u3044\u308B\u30A2\u30A4\u30C6\u30E0\u3092\u7814\u7A76\u3059\u308B\u5834\u5408\u306B\u304A\u3044\u3066\u3001\u3057\u3070\u3057\u3070\u3001\u672C\u8CEA\u7684\u306B\u4E0D\u5909\u306A\u6319\u52D5\u3078\u3068\u843D\u3061\u7740\u304F\u3053\u3068\u304C\u4E88\u60F3\u3055\u308C\u308B\u3053\u3068\u304C\u3042\u308B\u3001\u3068\u3044\u3046\u8003\u3048\u3092\u5B9A\u5F0F\u5316\u3059\u308B\u3082\u306E\u3067\u3042\u308B\u3002\u7570\u306A\u308B\u53CE\u675F\u306E\u6982\u5FF5\u3068\u306F\u3001\u305D\u306E\u3088\u3046\u306A\u6319\u52D5\u306E\u7279\u5FB4\u3065\u3051\u306B\u95A2\u9023\u3059\u308B\u3082\u306E\u3067\u3042\u308B\uFF1A\u3059\u3050\u306B\u5206\u304B\u308B\u4E8C\u3064\u306E\u6319\u52D5\u3068\u306F\u3001\u305D\u306E\u5217\u304C\u6700\u7D42\u7684\u306B\u5B9A\u6570\u3068\u306A\u308B\u304B\u3001\u3042\u308B\u3044\u306F\u305D\u306E\u5217\u306B\u542B\u307E\u308C\u308B\u5024\u306F\u5909\u52D5\u3092\u7D9A\u3051\u308B\u304C\u3042\u308B\u4E0D\u5909\u306A\u78BA\u7387\u5206\u5E03\u306B\u3088\u3063\u3066\u305D\u306E\u5909\u52D5\u304C\u8868\u73FE\u3055\u308C\u308B\u3001\u3068\u3044\u3046\u3088\u3046\u306A\u3082\u306E\u3067\u3042\u308B\u3002"@ja . . . . . "width: 28em;"@en . . . . . "Converg\u00E8ncia de variables aleat\u00F2ries"@ca . "\u0421\u0445\u043E\u0434\u0438\u043C\u043E\u0441\u0442\u044C \u043F\u043E \u0440\u0430\u0441\u043F\u0440\u0435\u0434\u0435\u043B\u0435\u043D\u0438\u044E"@ru . "Examples of convergence in probability"@en . . "Height of a person"@en . "background-color: lightblue; text-align:left;"@en . "Tossing coins"@en . . . . . . "Convergence of random variables"@en . . . . . . "\u0423 \u0442\u0435\u043E\u0440\u0456\u0457 \u0439\u043C\u043E\u0432\u0456\u0440\u043D\u043E\u0441\u0442\u0435\u0439 \u0456\u0441\u043D\u0443\u0454 \u0434\u0435\u043A\u0456\u043B\u044C\u043A\u0430 \u0432\u0438\u0434\u0456\u0432 \u0437\u0431\u0456\u0436\u043D\u043E\u0441\u0442\u0456 \u0432\u0438\u043F\u0430\u0434\u043A\u043E\u0432\u0438\u0445 \u0432\u0435\u043B\u0438\u0447\u0438\u043D. \u0417\u0431\u0456\u0436\u043D\u0456\u0441\u0442\u044C \u043F\u043E\u0441\u043B\u0456\u0434\u043E\u0432\u043D\u043E\u0441\u0442\u0456 \u0432\u0438\u043F\u0430\u0434\u043A\u043E\u0432\u0438\u0445 \u0432\u0435\u043B\u0438\u0447\u0438\u043D \u0434\u043E \u0434\u0435\u044F\u043A\u043E\u0457 \u0433\u0440\u0430\u043D\u0438\u0447\u043D\u043E\u0457 \u0432\u0438\u043F\u0430\u0434\u043A\u043E\u0432\u043E\u0457 \u0432\u0435\u043B\u0438\u0447\u0438\u043D\u0438 \u043C\u0430\u0454 \u0448\u0438\u0440\u043E\u043A\u0435 \u0437\u0430\u0441\u0442\u043E\u0441\u0443\u0432\u0430\u043D\u043D\u044F \u0443 \u0441\u0442\u0430\u0442\u0438\u0441\u0442\u0438\u0446\u0456 \u0442\u0430 \u0442\u0435\u043E\u0440\u0456\u0457 \u0432\u0438\u043F\u0430\u0434\u043A\u043E\u0432\u0438\u0445 \u043F\u0440\u043E\u0446\u0435\u0441\u0456\u0432."@uk . . . . "We may be almost sure that one day this amount will be zero, and stay zero forever after that."@en . "Suppose that a random number generator generates a pseudorandom floating point number between 0 and 1. Let random variable represent the distribution of possible outputs by the algorithm. Because the pseudorandom number is generated deterministically, its next value is not truly random. Suppose that as you observe a sequence of randomly generated numbers, you can deduce a pattern and make increasingly accurate predictions as to what the next randomly generated number will be. Let be your guess of the value of the next random number after observing the first random numbers. As you learn the pattern and your guesses become more accurate, not only will the distribution of converge to the distribution of , but the outcomes of will converge to the outcomes of ."@en . . "\u78BA\u7387\u5909\u6570\u306E\u53CE\u675F"@ja . . . . . "Dans la th\u00E9orie des probabilit\u00E9s, il existe diff\u00E9rentes notions de convergence de variables al\u00E9atoires. La convergence (dans un des sens d\u00E9crits ci-dessous) de suites de variables al\u00E9atoires est un concept important de la th\u00E9orie des probabilit\u00E9s utilis\u00E9 notamment en statistique et dans l'\u00E9tude des processus stochastiques. Par exemple, la moyenne de n variables al\u00E9atoires ind\u00E9pendantes et identiquement distribu\u00E9es converge presque s\u00FBrement vers l'esp\u00E9rance commune de ces variables al\u00E9atoires (si celle-ci existe).Ce r\u00E9sultat est connu sous le nom de loi forte des grands nombres."@fr . "Suppose is an iid sequence of uniform random variables. Let be their sums. Then according to the central limit theorem, the distribution of approaches the normal distribution. This convergence is shown in the picture: as grows larger, the shape of the probability density function gets closer and closer to the Gaussian curve.\ncenter|200px"@en . "Convergenza di variabili casuali"@it . . "Em teoria das probabilidades, existem v\u00E1rias no\u00E7\u00F5es diferentes de converg\u00EAncia de vari\u00E1veis aleat\u00F3rias. A converg\u00EAncia de sequ\u00EAncias de vari\u00E1veis aleat\u00F3rias a alguma vari\u00E1vel aleat\u00F3ria limite \u00E9 um importante conceito em teoria das probabilidades e tem aplica\u00E7\u00F5es na estat\u00EDstica e nos processos estoc\u00E1sticos. Os mesmos conceitos s\u00E3o conhecidos em matem\u00E1tica geral como converg\u00EAncia estoc\u00E1stica e formalizam a ideia de que \u00E9 poss\u00EDvel esperar que uma sequ\u00EAncia de eventos essencialmente aleat\u00F3rios ou imprevis\u00EDveis \u00E0s vezes mantenha um comportamento essencialmente imut\u00E1vel quando itens suficientemente distantes na sequ\u00EAncia s\u00E3o estudados. As poss\u00EDveis no\u00E7\u00F5es diferentes de converg\u00EAncia se relacionam a como tal comportamento pode ser caracterizado: dois comportamentos prontamente entendidos s\u00E3o que a"@pt . . . . . . . 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"Examples of almost sure convergence"@en . "\u03A3\u03CD\u03B3\u03BA\u03BB\u03B9\u03C3\u03B7 \u03C4\u03C5\u03C7\u03B1\u03AF\u03C9\u03BD \u03BC\u03B5\u03C4\u03B1\u03B2\u03BB\u03B7\u03C4\u03CE\u03BD"@el . "\u03A3\u03C4\u03B7 \u03B8\u03B5\u03C9\u03C1\u03AF\u03B1 \u03C0\u03B9\u03B8\u03B1\u03BD\u03BF\u03C4\u03AE\u03C4\u03C9\u03BD, \u03C5\u03C0\u03AC\u03C1\u03C7\u03BF\u03C5\u03BD \u03C0\u03BF\u03BB\u03BB\u03AD\u03C2 \u03B4\u03B9\u03B1\u03C6\u03BF\u03C1\u03B5\u03C4\u03B9\u03BA\u03AD\u03C2 \u03AD\u03BD\u03BD\u03BF\u03B9\u03B5\u03C2 \u03C4\u03B7\u03C2 \u03C3\u03CD\u03B3\u03BA\u03BB\u03B9\u03C3\u03B7\u03C2 \u03C4\u03C9\u03BD \u03C4\u03C5\u03C7\u03B1\u03AF\u03C9\u03BD \u03BC\u03B5\u03C4\u03B1\u03B2\u03BB\u03B7\u03C4\u03CE\u03BD. \u0397 \u03C3\u03CD\u03B3\u03BA\u03BB\u03B9\u03C3\u03B7 \u03B1\u03BA\u03BF\u03BB\u03BF\u03C5\u03B8\u03B9\u03CE\u03BD \u03C4\u03C5\u03C7\u03B1\u03AF\u03C9\u03BD \u03BC\u03B5\u03C4\u03B1\u03B2\u03BB\u03B7\u03C4\u03CE\u03BD \u03C3\u03B5 \u03BA\u03AC\u03C0\u03BF\u03B9\u03BF \u03CC\u03C1\u03B9\u03BF \u03C4\u03C5\u03C7\u03B1\u03AF\u03B1\u03C2 \u03BC\u03B5\u03C4\u03B1\u03B2\u03BB\u03B7\u03C4\u03AE\u03C2 \u03B5\u03AF\u03BD\u03B1\u03B9 \u03BC\u03B9\u03B1 \u03C3\u03B7\u03BC\u03B1\u03BD\u03C4\u03B9\u03BA\u03AE \u03AD\u03BD\u03BD\u03BF\u03B9\u03B1 \u03C3\u03C4\u03B7 \u03B8\u03B5\u03C9\u03C1\u03AF\u03B1 \u03C0\u03B9\u03B8\u03B1\u03BD\u03BF\u03C4\u03AE\u03C4\u03C9\u03BD \u03BA\u03B1\u03B9 \u03C4\u03B9\u03C2 \u03B5\u03C6\u03B1\u03C1\u03BC\u03BF\u03B3\u03AD\u03C2 \u03C4\u03B7\u03C2 \u03C3\u03B5 \u03C3\u03C4\u03B1\u03C4\u03B9\u03C3\u03C4\u03B9\u03BA\u03AD\u03C2 \u03BA\u03B1\u03B9 \u03C3\u03C4\u03BF\u03C7\u03B1\u03C3\u03C4\u03B9\u03BA\u03AD\u03C2 \u03B4\u03B9\u03B1\u03B4\u03B9\u03BA\u03B1\u03C3\u03AF\u03B5\u03C2. \u039F\u03B9 \u03AF\u03B4\u03B9\u03B5\u03C2 \u03AD\u03BD\u03BD\u03BF\u03B9\u03B5\u03C2 \u03B5\u03AF\u03BD\u03B1\u03B9 \u03B3\u03BD\u03C9\u03C3\u03C4\u03AD\u03C2 \u03C3\u03C4\u03B1 \u03B3\u03B5\u03BD\u03B9\u03BA\u03CC\u03C4\u03B5\u03C1\u03B1 \u03BC\u03B1\u03B8\u03B7\u03BC\u03B1\u03C4\u03B9\u03BA\u03AC, \u03CC\u03C0\u03C9\u03C2 \u03B7 \u03C3\u03CD\u03B3\u03BA\u03BB\u03B9\u03C3\u03B7 \u03C3\u03C4\u03BF\u03C7\u03B1\u03C3\u03C4\u03B9\u03BA\u03CE\u03BD \u03BA\u03B1\u03B9 \u03BD\u03B1 \u03B5\u03C0\u03B9\u03C3\u03B7\u03BC\u03BF\u03C0\u03BF\u03B9\u03AE\u03C3\u03B5\u03B9 \u03C4\u03B7\u03BD \u03B9\u03B4\u03AD\u03B1 \u03CC\u03C4\u03B9 \u03BC\u03B9\u03B1 \u03C3\u03B5\u03B9\u03C1\u03AC \u03B1\u03C0\u03CC \u03BF\u03C5\u03C3\u03B9\u03B1\u03C3\u03C4\u03B9\u03BA\u03AC \u03C4\u03C5\u03C7\u03B1\u03AF\u03B1 \u03AE \u03B1\u03C0\u03C1\u03CC\u03B2\u03BB\u03B5\u03C0\u03C4\u03B1 \u03B3\u03B5\u03B3\u03BF\u03BD\u03CC\u03C4\u03B1 \u03BC\u03C0\u03BF\u03C1\u03BF\u03CD\u03BD \u03BC\u03B5\u03C1\u03B9\u03BA\u03AD\u03C2 \u03C6\u03BF\u03C1\u03AD\u03C2 \u03BD\u03B1 \u03B5\u03B3\u03BA\u03B1\u03C4\u03B1\u03C3\u03C4\u03B1\u03B8\u03BF\u03CD\u03BD \u03C3\u03B5 \u03BC\u03B9\u03B1 \u03C3\u03C5\u03BC\u03C0\u03B5\u03C1\u03B9\u03C6\u03BF\u03C1\u03AC \u03C0\u03BF\u03C5 \u03B5\u03AF\u03BD\u03B1\u03B9 \u03BF\u03C5\u03C3\u03B9\u03B1\u03C3\u03C4\u03B9\u03BA\u03AC \u03B1\u03BC\u03B5\u03C4\u03AC\u03B2\u03BB\u03B7\u03C4\u03B7 \u03CC\u03C4\u03B1\u03BD \u03C4\u03B1 \u03B1\u03C1\u03BA\u03B5\u03C4\u03AC \u03C3\u03C4\u03BF\u03B9\u03C7\u03B5\u03AF\u03B1 \u03BC\u03AD\u03C3\u03B1 \u03C3\u03C4\u03B7\u03BD \u03B1\u03BA\u03BF\u03BB\u03BF\u03C5\u03B8\u03AF\u03B1 \u03BC\u03B5\u03BB\u03B5\u03C4\u03CE\u03BD\u03C4\u03B1\u03B9. \u039F\u03B9 \u03B4\u03B9\u03AC\u03C6\u03BF\u03C1\u03B5\u03C2 \u03C0\u03B9\u03B8\u03B1\u03BD\u03AD\u03C2 \u03AD\u03BD\u03BD\u03BF\u03B9\u03B5\u03C2 \u03C4\u03B7\u03C2 \u03C3\u03CD\u03B3\u03BA\u03BB\u03B9\u03C3\u03B7\u03C2 \u03C3\u03C7\u03B5\u03C4\u03AF\u03B6\u03BF\u03BD\u03C4\u03B1\u03B9 \u03BC\u03B5 \u03C4\u03BF \u03C0\u03CE\u03C2 \u03BC\u03C0\u03BF\u03C1\u03B5\u03AF \u03BD\u03B1 \u03C7\u03B1\u03C1\u03B1\u03BA\u03C4\u03B7\u03C1\u03B9\u03C3\u03C4\u03B5\u03AF \u03BC\u03B9\u03B1 \u03C4\u03AD\u03C4\u03BF\u03B9\u03B1 \u03C3\u03C5\u03BC\u03C0\u03B5\u03C1\u03B9\u03C6\u03BF\u03C1\u03AC: \u03B4\u03CD\u03BF \u03B5\u03CD\u03BA\u03BF\u03BB\u03B1 \u03BA\u03B1\u03C4\u03B1\u03BD\u03BF\u03B7\u03C4\u03AD\u03C2 \u03C3\u03C5\u03BC\u03C0\u03B5\u03C1\u03B9\u03C6\u03BF\u03C1\u03AD\u03C2 \u03B5\u03AF\u03BD\u03B1\u03B9 \u03CC\u03C4\u03B9 \u03B7 \u03B1\u03BB\u03BB\u03B7\u03BB\u03BF\u03C5\u03C7\u03AF\u03B1 \u03C0\u03B1\u03AF\u03C1\u03BD\u03B5\u03B9 \u03C4\u03B5\u03BB\u03B9\u03BA\u03AC \u03BC\u03B9\u03B1 \u03C3\u03C4\u03B1\u03B8\u03B5\u03C1\u03AE \u03C4\u03B9\u03BC\u03AE, \u03BA\u03B1\u03B9 \u03CC\u03C4\u03B9 \u03BF\u03B9 \u03C4\u03B9\u03BC\u03AD\u03C2 \u03C3\u03C4\u03B7\u03BD \u03B1\u03BB\u03BB\u03B7\u03BB\u03BF\u03C5\u03C7\u03AF\u03B1 \u03C3\u03C5\u03BD\u03B5\u03C7\u03AF\u03B6\u03BF\u03C5\u03BD \u03BD\u03B1 \u03B1\u03BB\u03BB\u03AC\u03B6\u03BF\u03C5\u03BD, \u03B1\u03BB\u03BB\u03AC \u03BC\u03C0\u03BF\u03C1\u03B5\u03AF \u03BD\u03B1 \u03C0\u03B5\u03C1\u03B9\u03B3\u03C1\u03B1\u03C6\u03B5\u03AF \u03BC\u03B5 \u03BC\u03B9\u03B1 \u03B1\u03BC\u03B5\u03C4\u03AC\u03B2\u03BB\u03B7\u03C4\u03B7 \u03BA\u03B1\u03C4\u03B1\u03BD\u03BF\u03BC\u03AE \u03C0\u03B9\u03B8\u03B1\u03BD\u03CC\u03C4\u03B7\u03C4\u03B1\u03C2."@el . . . "Convergencia de variables aleatorias"@es . . . . . . . "Let be the fraction of heads after tossing up an unbiased coin times. Then has the Bernoulli distribution with expected value and variance . The subsequent random variables will all be distributed binomially."@en . "Consider a man who tosses seven coins every morning. Each afternoon, he donates one pound to a charity for each head that appeared. The first time the result is all tails, however, he will stop permanently."@en . . . "Zbie\u017Cno\u015B\u0107 wed\u0142ug rozk\u0142adu \u2013 jeden z rodzaj\u00F3w zbie\u017Cno\u015Bci wektor\u00F3w losowych, nazywany czasem s\u0142ab\u0105 zbie\u017Cno\u015Bci\u0105."@pl . . "\u6570\u5B66\u306E\u78BA\u7387\u8AD6\u306E\u5206\u91CE\u306B\u304A\u3044\u3066\u3001\u78BA\u7387\u5909\u6570\u306E\u53CE\u675F\uFF08\u304B\u304F\u308A\u3064\u3078\u3093\u3059\u3046\u306E\u3057\u3085\u3046\u305D\u304F\u3001\u82F1: convergence of random variables\uFF09\u306B\u95A2\u3057\u3066\u306F\u3001\u3044\u304F\u3064\u304B\u306E\u7570\u306A\u308B\u6982\u5FF5\u304C\u3042\u308B\u3002\u78BA\u7387\u5909\u6570\u5217\u306E\u3042\u308B\u6975\u9650\u3078\u306E\u53CE\u675F\u306F\u3001\u78BA\u7387\u8AD6\u3084\u3001\u305D\u306E\u5FDC\u7528\u3068\u3057\u3066\u306E\u7D71\u8A08\u5B66\u3084\u78BA\u7387\u904E\u7A0B\u306E\u7814\u7A76\u306B\u304A\u3051\u308B\u91CD\u8981\u306A\u6982\u5FF5\u306E\u4E00\u3064\u3067\u3042\u308B\u3002\u3088\u308A\u4E00\u822C\u7684\u306A\u6570\u5B66\u306B\u304A\u3044\u3066\u540C\u69D8\u306E\u6982\u5FF5\u306F\u78BA\u7387\u53CE\u675F (stochastic convergence) \u3068\u3057\u3066\u77E5\u3089\u308C\u3001\u305D\u306E\u6982\u5FF5\u306F\u3001\u672C\u8CEA\u7684\u306B\u30E9\u30F3\u30C0\u30E0\u3042\u308B\u3044\u306F\u4E88\u6E2C\u4E0D\u53EF\u80FD\u306A\u4E8B\u8C61\u306E\u5217\u306F\u3001\u305D\u306E\u5217\u304B\u3089\u5341\u5206\u96E2\u308C\u3066\u3044\u308B\u30A2\u30A4\u30C6\u30E0\u3092\u7814\u7A76\u3059\u308B\u5834\u5408\u306B\u304A\u3044\u3066\u3001\u3057\u3070\u3057\u3070\u3001\u672C\u8CEA\u7684\u306B\u4E0D\u5909\u306A\u6319\u52D5\u3078\u3068\u843D\u3061\u7740\u304F\u3053\u3068\u304C\u4E88\u60F3\u3055\u308C\u308B\u3053\u3068\u304C\u3042\u308B\u3001\u3068\u3044\u3046\u8003\u3048\u3092\u5B9A\u5F0F\u5316\u3059\u308B\u3082\u306E\u3067\u3042\u308B\u3002\u7570\u306A\u308B\u53CE\u675F\u306E\u6982\u5FF5\u3068\u306F\u3001\u305D\u306E\u3088\u3046\u306A\u6319\u52D5\u306E\u7279\u5FB4\u3065\u3051\u306B\u95A2\u9023\u3059\u308B\u3082\u306E\u3067\u3042\u308B\uFF1A\u3059\u3050\u306B\u5206\u304B\u308B\u4E8C\u3064\u306E\u6319\u52D5\u3068\u306F\u3001\u305D\u306E\u5217\u304C\u6700\u7D42\u7684\u306B\u5B9A\u6570\u3068\u306A\u308B\u304B\u3001\u3042\u308B\u3044\u306F\u305D\u306E\u5217\u306B\u542B\u307E\u308C\u308B\u5024\u306F\u5909\u52D5\u3092\u7D9A\u3051\u308B\u304C\u3042\u308B\u4E0D\u5909\u306A\u78BA\u7387\u5206\u5E03\u306B\u3088\u3063\u3066\u305D\u306E\u5909\u52D5\u304C\u8868\u73FE\u3055\u308C\u308B\u3001\u3068\u3044\u3046\u3088\u3046\u306A\u3082\u306E\u3067\u3042\u308B\u3002"@ja . . . . . . "1109216539"^^ . . "In teoria della probabilit\u00E0 e statistica \u00E8 molto vivo il problema di studiare fenomeni con comportamento incognito ma, nei grandi numeri, riconducibili a fenomeni noti e ben studiati. A ci\u00F2 vengono in soccorso i vari teoremi di convergenza di variabili casuali, che appunto studiano le condizioni sotto cui certe successioni di variabili casuali di una certa distribuzione tendono ad altre distribuzioni. I pi\u00F9 importanti risultati raggiungibili sotto forma di convergenza di variabili casuali sono il teorema centrale del limite, che afferma che, col crescere della numerosit\u00E0 di un campione, la distribuzione di probabilit\u00E0 della sua media \u00E8 pi\u00F9 o meno come quella di una gaussiana e la legge dei grandi numeri, che giustifica l'utilizzo della media del campione come stima del valore atteso della legge di ogni singola osservazione. Si distinguono pi\u00F9 tipi di convergenza. Ognuna di queste condizioni si esporr\u00E0 qua per variabili casuali reali univariate, ma si generalizza senza troppe difficolt\u00E0 per variabili casuali multivariate."@it . "Consider an animal of some short-lived species. We record the amount of food that this animal consumes per day. This sequence of numbers will be unpredictable, but we may be quite certain that one day the number will become zero, and will stay zero forever after."@en . . . . . . . . "In teoria della probabilit\u00E0 e statistica \u00E8 molto vivo il problema di studiare fenomeni con comportamento incognito ma, nei grandi numeri, riconducibili a fenomeni noti e ben studiati. A ci\u00F2 vengono in soccorso i vari teoremi di convergenza di variabili casuali, che appunto studiano le condizioni sotto cui certe successioni di variabili casuali di una certa distribuzione tendono ad altre distribuzioni."@it . . . . . "\u968F\u673A\u53D8\u91CF\u7684\u6536\u655B"@zh . . . . . "Dans la th\u00E9orie des probabilit\u00E9s, il existe diff\u00E9rentes notions de convergence de variables al\u00E9atoires. La convergence (dans un des sens d\u00E9crits ci-dessous) de suites de variables al\u00E9atoires est un concept important de la th\u00E9orie des probabilit\u00E9s utilis\u00E9 notamment en statistique et dans l'\u00E9tude des processus stochastiques. Par exemple, la moyenne de n variables al\u00E9atoires ind\u00E9pendantes et identiquement distribu\u00E9es converge presque s\u00FBrement vers l'esp\u00E9rance commune de ces variables al\u00E9atoires (si celle-ci existe).Ce r\u00E9sultat est connu sous le nom de loi forte des grands nombres. Dans cet article, on suppose que (Xn) est une suite de variables al\u00E9atoires r\u00E9elles, que X est une variable al\u00E9atoire r\u00E9elle, et que toutes ces variables sont d\u00E9finies sur un m\u00EAme espace probabilis\u00E9 . D'\u00E9ventuelles g\u00E9n\u00E9ralisations seront discut\u00E9es."@fr . . "\uD655\uB960 \uBCC0\uC218\uC758 \uC218\uB834"@ko . "As the factory is improved, the dice become less and less loaded, and the outcomes from tossing a newly produced die will follow the uniform distribution more and more closely."@en . "In probability theory, there exist several different notions of convergence of random variables. The convergence of sequences of random variables to some limit random variable is an important concept in probability theory, and its applications to statistics and stochastic processes. The same concepts are known in more general mathematics as stochastic convergence and they formalize the idea that a sequence of essentially random or unpredictable events can sometimes be expected to settle down into a behavior that is essentially unchanging when items far enough into the sequence are studied. The different possible notions of convergence relate to how such a behavior can be characterized: two readily understood behaviors are that the sequence eventually takes a constant value, and that values in the sequence continue to change but can be described by an unchanging probability distribution."@en . "Dice factory"@en . "In de kansrekening kan convergentie van een rij stochastische variabelen verschillende betekenissen hebben. Anders dan bij rijen getallen is er geen voor de hand liggende definitie voor het asymptotische gedrag bij toenemende omvang van de steekproef. Daardoor zijn er verschillende convergentiebegrippen ontstaan, van verschillende sterkte. De belangrijkste daarvan worden in dit lemma besproken. Het gaat steeds om een rij stochastische variabelen , gedefinieerd op een kansruimte"@nl . . . . . "Examples of convergence in distribution"@en . . "Konvergenz (Stochastik)"@de . . . . . "However, when we consider any finite number of days, there is a nonzero probability the terminating condition will not occur."@en . "Example 1"@en . . "Probabilitate teorian, konbergentzia estokastikoa zorizko aldagaien segida batek limitean duen joera aztertzen duen arloa da. Konbergentziaren azterketa funtsezkoa inferentzia estatistikoan, lagin handietan zenbatesleek dituzten propietateak aztertzean kasu. Konbergentzia modu asko daude, limiteko joerak nola definitzen diren; horrela, eta bereizten dira, besteak beste. Limitearen teorema zentrala, zenbaki handien legea eta bestelako teoremek ezartzen dituzte konbergentzia estokastikoaren emaitzak, zorizko aldagaiek segidak betetzen dituen baldintzen arabera. Konbergentzia estokastikoaren oinarri teorikoak XIX. mendean eta batez ere XX. mendearen lehenengo zatian garatu ziren, matematika-tresna zorrotzak erabiliz eta Andrei Kolmogoroven eskutik besteak beste."@eu . . . . "Consider the following experiment. First, pick a random person in the street. Let be their height, which is ex ante a random variable. Then ask other people to estimate this height by eye. Let be the average of the first responses. Then by the law of large numbers, the sequence will converge in probability to the random variable ."@en . "Predicting random number generation"@en . "Convergentie (kansrekening)"@nl . . "En teoria de la probabilitat, l'estudi de la converg\u00E8ncia de variables aleat\u00F2ries \u00E9s fonamental, tant per la seva riquesa matem\u00E0tica (lleis dels grans nombres, teorema del l\u00EDmit central, llei del logaritme iterat, etc.) com per les seves aplicacions a l'Estad\u00EDstica. En aquest article s'estudien les converg\u00E8ncies m\u00E9s habituals: en distribuci\u00F3 o llei, en probabilitat, quasi segura i en mitjana d'ordre . La refer\u00E8ncia general d'aquesta p\u00E0gina \u00E9s Serfling on es troben les demostracions o les refer\u00E8ncies corresponents, i nombrosos exemples i contraexemples."@ca . . . "As grows larger, this distribution will gradually start to take shape more and more similar to the bell curve of the normal distribution. If we shift and rescale appropriately, then will be converging in distribution to the standard normal, the result that follows from the celebrated central limit theorem."@en . "Konbergentzia estokastiko"@eu . "38419"^^ . . . "Let X1, X2, \u2026 be the daily amounts the charity received from him."@en . . . . . "\u062A\u0642\u0627\u0631\u0628 \u0627\u0644\u0645\u062A\u063A\u064A\u0631\u0627\u062A \u0627\u0644\u0639\u0634\u0648\u0627\u0626\u064A\u0629"@ar . "Zbie\u017Cno\u015B\u0107 wed\u0142ug rozk\u0142adu"@pl . . "Converg\u00EAncia de vari\u00E1veis aleat\u00F3rias"@pt . "Suppose a new dice factory has just been built. The first few dice come out quite biased, due to imperfections in the production process. The outcome from tossing any of them will follow a distribution markedly different from the desired uniform distribution."@en .