"\uB2E4\uD56D \uBD84\uD3EC\uB294 \uC5EC\uB7EC \uAC1C\uC758 \uAC12\uC744 \uAC00\uC9C8 \uC218 \uC788\uB294 \uB3C5\uB9BD \uD655\uB960\uBCC0\uC218\uB4E4\uC5D0 \uB300\uD55C \uD655\uB960\uBD84\uD3EC\uB85C, \uC5EC\uB7EC \uBC88\uC758 \uB3C5\uB9BD\uC801 \uC2DC\uD589\uC5D0\uC11C \uAC01\uAC01\uC758 \uAC12\uC774 \uD2B9\uC815 \uD69F\uC218\uAC00 \uB098\uD0C0\uB0A0 \uD655\uB960\uC744 \uC815\uC758\uD55C\uB2E4. \uB2E4\uD56D \uBD84\uD3EC\uC5D0\uC11C \uCC28\uC6D0\uC774 2\uC778 \uACBD\uC6B0 \uC774\uD56D \uBD84\uD3EC\uAC00 \uB41C\uB2E4."@ko . "Die Multinomialverteilung oder Polynomialverteilung ist eine Wahrscheinlichkeitsverteilung in der Stochastik. Sie ist eine diskrete Wahrscheinlichkeitsverteilung und kann als multivariate Verallgemeinerung der Binomialverteilung aufgefasst werden. Sie hat in der Bayesschen Statistik als konjugierte A-priori-Verteilung die Dirichlet-Verteilung."@de . . . "Multinomial distribution"@en . . "\u03A3\u03C4\u03B7 \u03B8\u03B5\u03C9\u03C1\u03AF\u03B1 \u03C0\u03B9\u03B8\u03B1\u03BD\u03BF\u03C4\u03AE\u03C4\u03C9\u03BD, \u03B7 \u03C0\u03BF\u03BB\u03C5\u03C9\u03BD\u03C5\u03BC\u03B9\u03BA\u03AE \u03BA\u03B1\u03C4\u03B1\u03BD\u03BF\u03BC\u03AE \u03B5\u03AF\u03BD\u03B1\u03B9 \u03B7 \u03B3\u03B5\u03BD\u03AF\u03BA\u03B5\u03C5\u03C3\u03B7 \u03C4\u03B7\u03C2 \u03B4\u03B9\u03C9\u03BD\u03C5\u03BC\u03B9\u03BA\u03AE\u03C2 \u03BA\u03B1\u03C4\u03B1\u03BD\u03BF\u03BC\u03AE\u03C2. \u03A7\u03C1\u03B7\u03C3\u03B9\u03BC\u03BF\u03C0\u03BF\u03B9\u03B5\u03AF\u03C4\u03B1\u03B9 \u03C3\u03C4\u03B7\u03BD \u03B5\u03CD\u03C1\u03B5\u03C3\u03B7 \u03C4\u03B7\u03C2 \u03C0\u03B9\u03B8\u03B1\u03BD\u03CC\u03C4\u03B7\u03C4\u03B1\u03C2 \u03BD\u03B1 \u03C0\u03C1\u03BF\u03B2\u03BB\u03B5\u03C6\u03B8\u03B5\u03AF \u03C3\u03C9\u03C3\u03C4\u03AC \u03BC\u03B9\u03B1 \u03C3\u03B5\u03B9\u03C1\u03AC \u03B5\u03C0\u03B1\u03BD\u03B1\u03BB\u03AE\u03C8\u03B5\u03C9\u03BD \u03B1\u03BD\u03B5\u03BE\u03AC\u03C1\u03C4\u03B7\u03C4\u03C9\u03BD \u03C4\u03C5\u03C7\u03B1\u03AF\u03C9\u03BD \u03B5\u03BD\u03B4\u03B5\u03C7\u03BF\u03BC\u03AD\u03BD\u03C9\u03BD, \u03C4\u03BF \u03BA\u03B1\u03B8\u03AD\u03BD\u03B1 \u03B5\u03BA \u03C4\u03C9\u03BD \u03BF\u03C0\u03BF\u03AF\u03C9\u03BD \u03AD\u03C7\u03B5\u03B9 \u03C4\u03B7 \u03B4\u03B9\u03BA\u03AE \u03C4\u03BF\u03C5 \u03B3\u03BD\u03C9\u03C3\u03C4\u03AE \u03C0\u03B9\u03B8\u03B1\u03BD\u03CC\u03C4\u03B7\u03C4\u03B1 \u03BD\u03B1 \u03C3\u03C5\u03BC\u03B2\u03B5\u03AF."@el . . "Distribui\u00E7\u00E3o multinomial"@pt . . . . "\u041F\u043E\u043B\u0456\u043D\u043E\u043C\u0456\u0430\u043B\u044C\u043D\u0438\u0439 \u0440\u043E\u0437\u043F\u043E\u0434\u0456\u043B"@uk . "event probabilities"@en . . "\u03A3\u03C4\u03B7 \u03B8\u03B5\u03C9\u03C1\u03AF\u03B1 \u03C0\u03B9\u03B8\u03B1\u03BD\u03BF\u03C4\u03AE\u03C4\u03C9\u03BD, \u03B7 \u03C0\u03BF\u03BB\u03C5\u03C9\u03BD\u03C5\u03BC\u03B9\u03BA\u03AE \u03BA\u03B1\u03C4\u03B1\u03BD\u03BF\u03BC\u03AE \u03B5\u03AF\u03BD\u03B1\u03B9 \u03B7 \u03B3\u03B5\u03BD\u03AF\u03BA\u03B5\u03C5\u03C3\u03B7 \u03C4\u03B7\u03C2 \u03B4\u03B9\u03C9\u03BD\u03C5\u03BC\u03B9\u03BA\u03AE\u03C2 \u03BA\u03B1\u03C4\u03B1\u03BD\u03BF\u03BC\u03AE\u03C2. \u03A7\u03C1\u03B7\u03C3\u03B9\u03BC\u03BF\u03C0\u03BF\u03B9\u03B5\u03AF\u03C4\u03B1\u03B9 \u03C3\u03C4\u03B7\u03BD \u03B5\u03CD\u03C1\u03B5\u03C3\u03B7 \u03C4\u03B7\u03C2 \u03C0\u03B9\u03B8\u03B1\u03BD\u03CC\u03C4\u03B7\u03C4\u03B1\u03C2 \u03BD\u03B1 \u03C0\u03C1\u03BF\u03B2\u03BB\u03B5\u03C6\u03B8\u03B5\u03AF \u03C3\u03C9\u03C3\u03C4\u03AC \u03BC\u03B9\u03B1 \u03C3\u03B5\u03B9\u03C1\u03AC \u03B5\u03C0\u03B1\u03BD\u03B1\u03BB\u03AE\u03C8\u03B5\u03C9\u03BD \u03B1\u03BD\u03B5\u03BE\u03AC\u03C1\u03C4\u03B7\u03C4\u03C9\u03BD \u03C4\u03C5\u03C7\u03B1\u03AF\u03C9\u03BD \u03B5\u03BD\u03B4\u03B5\u03C7\u03BF\u03BC\u03AD\u03BD\u03C9\u03BD, \u03C4\u03BF \u03BA\u03B1\u03B8\u03AD\u03BD\u03B1 \u03B5\u03BA \u03C4\u03C9\u03BD \u03BF\u03C0\u03BF\u03AF\u03C9\u03BD \u03AD\u03C7\u03B5\u03B9 \u03C4\u03B7 \u03B4\u03B9\u03BA\u03AE \u03C4\u03BF\u03C5 \u03B3\u03BD\u03C9\u03C3\u03C4\u03AE \u03C0\u03B9\u03B8\u03B1\u03BD\u03CC\u03C4\u03B7\u03C4\u03B1 \u03BD\u03B1 \u03C3\u03C5\u03BC\u03B2\u03B5\u03AF."@el . "\uB2E4\uD56D \uBD84\uD3EC\uB294 \uC5EC\uB7EC \uAC1C\uC758 \uAC12\uC744 \uAC00\uC9C8 \uC218 \uC788\uB294 \uB3C5\uB9BD \uD655\uB960\uBCC0\uC218\uB4E4\uC5D0 \uB300\uD55C \uD655\uB960\uBD84\uD3EC\uB85C, \uC5EC\uB7EC \uBC88\uC758 \uB3C5\uB9BD\uC801 \uC2DC\uD589\uC5D0\uC11C \uAC01\uAC01\uC758 \uAC12\uC774 \uD2B9\uC815 \uD69F\uC218\uAC00 \uB098\uD0C0\uB0A0 \uD655\uB960\uC744 \uC815\uC758\uD55C\uB2E4. \uB2E4\uD56D \uBD84\uD3EC\uC5D0\uC11C \uCC28\uC6D0\uC774 2\uC778 \uACBD\uC6B0 \uC774\uD56D \uBD84\uD3EC\uAC00 \uB41C\uB2E4."@ko . . . "En th\u00E9orie des probabilit\u00E9s, les lois multinomiales (aussi appel\u00E9e distributions polynomiales) g\u00E9n\u00E9ralisent les lois binomiales. Ces derni\u00E8res concernent le nombre de succ\u00E8s dans n \u00E9preuves de Bernoulli ind\u00E9pendantes donnant chacune un r\u00E9sultat binaire, comme dans le jeu de pile ou face. Les lois multinomiales, elles, sont applicables par exemple \u00E0 n jets d'un d\u00E9 \u00E0 six faces. Contrairement \u00E0 ces exemples simples, les diff\u00E9rentes possibilit\u00E9s ne sont g\u00E9n\u00E9ralement pas \u00E9quiprobables."@fr . . "En teor\u00EDa de probabilidad, la distribuci\u00F3n multinomial o distribuci\u00F3n multin\u00F3mica es una generalizaci\u00F3n de la distribuci\u00F3n binomial. La distribuci\u00F3n binomial es la probabilidad de un n\u00FAmero de \u00E9xitos en N sucesos de Bernoulli independientes, con la misma probabilidad de \u00E9xito en cada suceso. En una distribuci\u00F3n multinomial, el an\u00E1logo a la distribuci\u00F3n de Bernoulli es la distribuci\u00F3n categ\u00F3rica, donde cada suceso concluye en \u00FAnicamente un resultado de un n\u00FAmero finito K de los posibles, con probabilidades (tal que para i entre 1 y K y ); y con n sucesos independientes. Entonces sea la variable aleatoria , que indica el n\u00FAmero de veces que se ha dado el resultado i sobre los n sucesos. El vector sigue una distribuci\u00F3n multinomial con par\u00E1metros n y p, donde . N\u00F3tese que en algunos campos las distribuciones categ\u00F3rica y multinomial se encuentran unidas, y es com\u00FAn hablar de una distribuci\u00F3n multinomial cuando el t\u00E9rmino m\u00E1s preciso ser\u00EDa una distribuci\u00F3n categ\u00F3rica."@es . . . . "En probabilitat i estad\u00EDstica la distribuci\u00F3 multinomial \u00E9s una extensi\u00F3 de la distribuci\u00F3 binomial quan en un experiment aleatori hi ha m\u00E9s de dos resultats possibles. Concretament, fem repeticions d'un experiment que t\u00E9 resultats diferents possibles i comptem el nombre de vegades que es produeix cadascun dels resultats possibles. Entre les nombroses aplicacions d'aquesta distribuci\u00F3 en Estad\u00EDstica destaca el test de Pearson de la ."@ca . "En teor\u00EDa de probabilidad, la distribuci\u00F3n multinomial o distribuci\u00F3n multin\u00F3mica es una generalizaci\u00F3n de la distribuci\u00F3n binomial. La distribuci\u00F3n binomial es la probabilidad de un n\u00FAmero de \u00E9xitos en N sucesos de Bernoulli independientes, con la misma probabilidad de \u00E9xito en cada suceso. En una distribuci\u00F3n multinomial, el an\u00E1logo a la distribuci\u00F3n de Bernoulli es la distribuci\u00F3n categ\u00F3rica, donde cada suceso concluye en \u00FAnicamente un resultado de un n\u00FAmero finito K de los posibles, con probabilidades (tal que para i entre 1 y K y ); y con n sucesos independientes."@es . . "In de kansrekening en de statistiek is de multinomiale verdeling een discrete, multivariate kansverdeling die gezien kan worden als de generalisatie van de binomiale verdeling. De binomiale verdeling is de kansverdeling van het aantal successen in onafhankelijke bernoulli-experimenten met gelijke succeskans . Als een experiment met aselecte trekkingen niet slechts twee uitkomsten (bv. succes en mislukking) heeft, maar meer, beschrijft de multinomiale verdeling de kansen op mogelijke aantallen van de verschillende uitkomsten, als zo'n experiment een vast aantal keren herhaald wordt."@nl . . "In teoria delle probabilit\u00E0 la distribuzione multinomiale \u00E8 una distribuzione di probabilit\u00E0 discreta che generalizza la distribuzione binomiale in pi\u00F9 variabili. In altri termini, laddove la distribuzione binomiale descrive il numero di successi in un processo di Bernoulli, per il quale ogni singola prova pu\u00F2 fornire due soli risultati, la distribuzione multinomiale descrive il caso pi\u00F9 generale in cui ogni prova possa fornire un numero finito di risultati, ognuno con la propria probabilit\u00E0."@it . . "mass"@en . . . . . . . "\u041C\u0443\u043B\u044C\u0442\u0438\u043D\u043E\u043C\u0438\u0430\u0301\u043B\u044C\u043D\u043E\u0435 (\u043F\u043E\u043B\u0438\u043D\u043E\u043C\u0438\u0430\u0301\u043B\u044C\u043D\u043E\u0435) \u0440\u0430\u0441\u043F\u0440\u0435\u0434\u0435\u043B\u0435\u0301\u043D\u0438\u0435 \u0432 \u0442\u0435\u043E\u0440\u0438\u0438 \u0432\u0435\u0440\u043E\u044F\u0442\u043D\u043E\u0441\u0442\u0435\u0439 \u2014 \u044D\u0442\u043E \u043E\u0431\u043E\u0431\u0449\u0435\u043D\u0438\u0435 \u0431\u0438\u043D\u043E\u043C\u0438\u0430\u043B\u044C\u043D\u043E\u0433\u043E \u0440\u0430\u0441\u043F\u0440\u0435\u0434\u0435\u043B\u0435\u043D\u0438\u044F \u043D\u0430 \u0441\u043B\u0443\u0447\u0430\u0439 n>1 \u043D\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043C\u044B\u0445 \u0438\u0441\u043F\u044B\u0442\u0430\u043D\u0438\u0439 \u0441\u043B\u0443\u0447\u0430\u0439\u043D\u043E\u0433\u043E \u044D\u043A\u0441\u043F\u0435\u0440\u0438\u043C\u0435\u043D\u0442\u0430 \u0441 k>2 \u0432\u043E\u0437\u043C\u043E\u0436\u043D\u044B\u043C\u0438 \u0438\u0441\u0445\u043E\u0434\u0430\u043C\u0438."@ru . . . . . "\u591A\u9805\u5206\u5E03\uFF08\u305F\u3053\u3046\u3076\u3093\u3077\u3001\u82F1: multinomial distribution\uFF09\u306F\u3001\u78BA\u7387\u8AD6\u306B\u304A\u3044\u3066\u4E8C\u9805\u5206\u5E03\u3092\u4E00\u822C\u5316\u3057\u305F\u78BA\u7387\u5206\u5E03\u3067\u3042\u308B\u3002 \u4E8C\u9805\u5206\u5E03\u306F\u3001n \u500B\u306E\u72EC\u7ACB\u306A\u30D9\u30EB\u30CC\u30FC\u30A4\u8A66\u884C\u306E\u300C\u6210\u529F\u300D\u306E\u6570\u306E\u78BA\u7387\u5206\u5E03\u3067\u3042\u308A\u3001\u5404\u8A66\u884C\u306E\u300C\u6210\u529F\u300D\u78BA\u7387\u306F\u540C\u3058\u3067\u3042\u308B\u3002\u591A\u9805\u5206\u5E03\u3067\u306F\u3001\u5404\u8A66\u884C\u306E\u7D50\u679C\u306F\u56FA\u5B9A\u306E\u6709\u9650\u500B\uFF08k \u500B\uFF09\u306E\u5024\u3092\u3068\u308A\u3001\u305D\u308C\u305E\u308C\u306E\u5024\u3092\u3068\u308B\u78BA\u7387\u306F p1, \u2026, pk\uFF08\u3059\u306A\u308F\u3061\u3001i = 1, \u2026, k \u306B\u3064\u3044\u3066 pi \u2265 0 \u3067\u3042\u308A\u3001 \u304C\u6210\u308A\u7ACB\u3064\uFF09\u3067\u3042\u308A\u3001n \u56DE\u306E\u72EC\u7ACB\u3057\u305F\u8A66\u884C\u304C\u884C\u308F\u308C\u308B\u3002\u78BA\u7387\u5909\u6570 Xi \u306F n \u56DE\u306E\u8A66\u884C\u3067 i \u3068\u3044\u3046\u6570\u304C\u51FA\u308B\u56DE\u6570\u3092\u793A\u3059\u3002X = (X1, \u2026, Xk) \u306F n \u3068 p \u3092\u30D1\u30E9\u30E1\u30FC\u30BF\u3068\u3059\u308B\u591A\u9805\u5206\u5E03\u306B\u5F93\u3046\u3002"@ja . "Loi multinomiale"@fr . . . . "Distribuci\u00F3 multinomial"@ca . "16054"^^ . . . "Die Multinomialverteilung oder Polynomialverteilung ist eine Wahrscheinlichkeitsverteilung in der Stochastik. Sie ist eine diskrete Wahrscheinlichkeitsverteilung und kann als multivariate Verallgemeinerung der Binomialverteilung aufgefasst werden. Sie hat in der Bayesschen Statistik als konjugierte A-priori-Verteilung die Dirichlet-Verteilung."@de . . . . . ""@en . . . . "Em probabilidade e estat\u00EDstica, a distribui\u00E7\u00E3o multinomial \u00E9 uma generaliza\u00E7\u00E3o da distribui\u00E7\u00E3o binomial para casos onde temos mais de dois poss\u00EDveis resultados, sendo assim \u00E9 uma distribui\u00E7\u00E3o de probabilidade discreta e multivariada. Temos um total de objetos/itens separados independentemente em categorias/tipos, um item \u00E9 da categoria com probabilidade n\u00E3o-nula onde , al\u00E9m disso dizemos que \u00E9 a quantidade de itens na categoria onde . Como se trata de um caso multivariado dizemos que o vetor aleat\u00F3rio tem distribui\u00E7\u00E3o multinomial e denotamos onde . Fun\u00E7\u00E3o massa de probabilidade (conjunta) multinomial: Onde as retic\u00EAncias indicam um produt\u00F3rio e ."@pt . . . "Distribuzione multinomiale"@it . "In probability theory, the multinomial distribution is a generalization of the binomial distribution. For example, it models the probability of counts for each side of a k-sided dice rolled n times. For n independent trials each of which leads to a success for exactly one of k categories, with each category having a given fixed success probability, the multinomial distribution gives the probability of any particular combination of numbers of successes for the various categories."@en . . . "1045553"^^ . . . "\uB2E4\uD56D \uBD84\uD3EC"@ko . . . . . . . . . . "Multinomial"@en . "En probabilitat i estad\u00EDstica la distribuci\u00F3 multinomial \u00E9s una extensi\u00F3 de la distribuci\u00F3 binomial quan en un experiment aleatori hi ha m\u00E9s de dos resultats possibles. Concretament, fem repeticions d'un experiment que t\u00E9 resultats diferents possibles i comptem el nombre de vegades que es produeix cadascun dels resultats possibles. Entre les nombroses aplicacions d'aquesta distribuci\u00F3 en Estad\u00EDstica destaca el test de Pearson de la ."@ca . . "number of trials"@en . . . "\u041C\u0443\u043B\u044C\u0442\u0438\u043D\u043E\u043C\u0438\u0430\u043B\u044C\u043D\u043E\u0435 \u0440\u0430\u0441\u043F\u0440\u0435\u0434\u0435\u043B\u0435\u043D\u0438\u0435"@ru . . . "1120845934"^^ . "\u0423 \u0442\u0435\u043E\u0440\u0456\u0457 \u0456\u043C\u043E\u0432\u0456\u0440\u043D\u043E\u0441\u0442\u0435\u0439 \u043F\u043E\u043B\u0456\u043D\u043E\u043C\u0456\u0430\u043B\u044C\u043D\u0438\u0439 \u0440\u043E\u0437\u043F\u043E\u0434\u0456\u043B \u0454 \u0443\u0437\u0430\u0433\u0430\u043B\u044C\u043D\u0435\u043D\u043D\u044F\u043C \u0431\u0456\u043D\u043E\u043C\u0456\u0430\u043B\u044C\u043D\u043E\u0433\u043E \u0440\u043E\u0437\u043F\u043E\u0434\u0456\u043B\u0443.\u0411\u0456\u043D\u043E\u043C\u0456\u0430\u043B\u044C\u043D\u0438\u0439 \u0440\u043E\u0437\u043F\u043E\u0434\u0456\u043B \u0454 \u0440\u043E\u0437\u043F\u043E\u0434\u0456\u043B\u043E\u043C \u0439\u043C\u043E\u0432\u0456\u0440\u043D\u043E\u0441\u0442\u0435\u0439 \u0447\u0438\u0441\u043B\u0430 \u0443\u0441\u043F\u0456\u0445\u0456\u0432 \u0443 \u043D\u0435\u0437\u0430\u043B\u0435\u0436\u043D\u0456\u0439 \u0441\u0445\u0435\u043C\u0456 \u0432\u0438\u043F\u0440\u043E\u0431\u0443\u0432\u0430\u043D\u044C \u0411\u0435\u0440\u043D\u0443\u043B\u043B\u0456, \u0437 \u0442\u0456\u0454\u044E \u0436 \u0441\u0430\u043C\u043E\u044E \u0456\u043C\u043E\u0432\u0456\u0440\u043D\u0456\u0441\u0442\u044E \u0443\u0441\u043F\u0456\u0445\u0443 \u0432 \u043A\u043E\u0436\u043D\u043E\u043C\u0443 \u0432\u0438\u043F\u0440\u043E\u0431\u0443\u0432\u0430\u043D\u043D\u0456."@uk . . . . . . "\u0423 \u0442\u0435\u043E\u0440\u0456\u0457 \u0456\u043C\u043E\u0432\u0456\u0440\u043D\u043E\u0441\u0442\u0435\u0439 \u043F\u043E\u043B\u0456\u043D\u043E\u043C\u0456\u0430\u043B\u044C\u043D\u0438\u0439 \u0440\u043E\u0437\u043F\u043E\u0434\u0456\u043B \u0454 \u0443\u0437\u0430\u0433\u0430\u043B\u044C\u043D\u0435\u043D\u043D\u044F\u043C \u0431\u0456\u043D\u043E\u043C\u0456\u0430\u043B\u044C\u043D\u043E\u0433\u043E \u0440\u043E\u0437\u043F\u043E\u0434\u0456\u043B\u0443.\u0411\u0456\u043D\u043E\u043C\u0456\u0430\u043B\u044C\u043D\u0438\u0439 \u0440\u043E\u0437\u043F\u043E\u0434\u0456\u043B \u0454 \u0440\u043E\u0437\u043F\u043E\u0434\u0456\u043B\u043E\u043C \u0439\u043C\u043E\u0432\u0456\u0440\u043D\u043E\u0441\u0442\u0435\u0439 \u0447\u0438\u0441\u043B\u0430 \u0443\u0441\u043F\u0456\u0445\u0456\u0432 \u0443 \u043D\u0435\u0437\u0430\u043B\u0435\u0436\u043D\u0456\u0439 \u0441\u0445\u0435\u043C\u0456 \u0432\u0438\u043F\u0440\u043E\u0431\u0443\u0432\u0430\u043D\u044C \u0411\u0435\u0440\u043D\u0443\u043B\u043B\u0456, \u0437 \u0442\u0456\u0454\u044E \u0436 \u0441\u0430\u043C\u043E\u044E \u0456\u043C\u043E\u0432\u0456\u0440\u043D\u0456\u0441\u0442\u044E \u0443\u0441\u043F\u0456\u0445\u0443 \u0432 \u043A\u043E\u0436\u043D\u043E\u043C\u0443 \u0432\u0438\u043F\u0440\u043E\u0431\u0443\u0432\u0430\u043D\u043D\u0456."@uk . . . . "En th\u00E9orie des probabilit\u00E9s, les lois multinomiales (aussi appel\u00E9e distributions polynomiales) g\u00E9n\u00E9ralisent les lois binomiales. Ces derni\u00E8res concernent le nombre de succ\u00E8s dans n \u00E9preuves de Bernoulli ind\u00E9pendantes donnant chacune un r\u00E9sultat binaire, comme dans le jeu de pile ou face. Les lois multinomiales, elles, sont applicables par exemple \u00E0 n jets d'un d\u00E9 \u00E0 six faces. Contrairement \u00E0 ces exemples simples, les diff\u00E9rentes possibilit\u00E9s ne sont g\u00E9n\u00E9ralement pas \u00E9quiprobables."@fr . . "In teoria delle probabilit\u00E0 la distribuzione multinomiale \u00E8 una distribuzione di probabilit\u00E0 discreta che generalizza la distribuzione binomiale in pi\u00F9 variabili. In altri termini, laddove la distribuzione binomiale descrive il numero di successi in un processo di Bernoulli, per il quale ogni singola prova pu\u00F2 fornire due soli risultati, la distribuzione multinomiale descrive il caso pi\u00F9 generale in cui ogni prova possa fornire un numero finito di risultati, ognuno con la propria probabilit\u00E0. Un esempio di distribuzione multinomiale \u00E8 dato dal numero di occorrenze di ogni faccia per alcuni lanci successivi di un dado a 6 facce."@it . . . . . "In de kansrekening en de statistiek is de multinomiale verdeling een discrete, multivariate kansverdeling die gezien kan worden als de generalisatie van de binomiale verdeling. De binomiale verdeling is de kansverdeling van het aantal successen in onafhankelijke bernoulli-experimenten met gelijke succeskans . Als een experiment met aselecte trekkingen niet slechts twee uitkomsten (bv. succes en mislukking) heeft, maar meer, beschrijft de multinomiale verdeling de kansen op mogelijke aantallen van de verschillende uitkomsten, als zo'n experiment een vast aantal keren herhaald wordt. Als voorbeeld kan men denken aan het trekken van een kaart uit een goed geschud pak speelkaarten. De getrokken kaart wordt teruggelegd en na goed schudden wordt het experiment herhaald. Als uitkomst noteert men de kleur van de getrokken kaart. Er zijn vier mogelijkheden: schoppen (\u2660), harten (\u2665), ruiten (\u2666) en klaveren (\u2663). Bij elke trekking is de kans 1/4 op elk van deze kleuren. De kansverdeling van het aantal getrokken kaarten van de vier kleuren bij 10 keer trekken is een multinomiale verdeling. De kans op bijvoorbeeld de gebeurtenis 1\u2660, 2\u2665, 3\u2666 en 4\u2663 bepaalt men door te bedenken dat de mogelijkheid dat de kaarten in de aangegeven volgorde getrokken zijn een kans heeft van: De kaarten kunnen echter ook in een andere volgorde getrokken zijn met dezelfde kans. Het aantal mogelijke volgordes is: De kans op de genoemde gebeurtenis is dus:"@nl . . "\u03A0\u03BF\u03BB\u03C5\u03C9\u03BD\u03C5\u03BC\u03B9\u03BA\u03AE \u03BA\u03B1\u03C4\u03B1\u03BD\u03BF\u03BC\u03AE"@el . . . . . . "\u041C\u0443\u043B\u044C\u0442\u0438\u043D\u043E\u043C\u0438\u0430\u0301\u043B\u044C\u043D\u043E\u0435 (\u043F\u043E\u043B\u0438\u043D\u043E\u043C\u0438\u0430\u0301\u043B\u044C\u043D\u043E\u0435) \u0440\u0430\u0441\u043F\u0440\u0435\u0434\u0435\u043B\u0435\u0301\u043D\u0438\u0435 \u0432 \u0442\u0435\u043E\u0440\u0438\u0438 \u0432\u0435\u0440\u043E\u044F\u0442\u043D\u043E\u0441\u0442\u0435\u0439 \u2014 \u044D\u0442\u043E \u043E\u0431\u043E\u0431\u0449\u0435\u043D\u0438\u0435 \u0431\u0438\u043D\u043E\u043C\u0438\u0430\u043B\u044C\u043D\u043E\u0433\u043E \u0440\u0430\u0441\u043F\u0440\u0435\u0434\u0435\u043B\u0435\u043D\u0438\u044F \u043D\u0430 \u0441\u043B\u0443\u0447\u0430\u0439 n>1 \u043D\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043C\u044B\u0445 \u0438\u0441\u043F\u044B\u0442\u0430\u043D\u0438\u0439 \u0441\u043B\u0443\u0447\u0430\u0439\u043D\u043E\u0433\u043E \u044D\u043A\u0441\u043F\u0435\u0440\u0438\u043C\u0435\u043D\u0442\u0430 \u0441 k>2 \u0432\u043E\u0437\u043C\u043E\u0436\u043D\u044B\u043C\u0438 \u0438\u0441\u0445\u043E\u0434\u0430\u043C\u0438."@ru . "Distribuci\u00F3n multinomial"@es . ""@en . . . . . . . . . "In probability theory, the multinomial distribution is a generalization of the binomial distribution. For example, it models the probability of counts for each side of a k-sided dice rolled n times. For n independent trials each of which leads to a success for exactly one of k categories, with each category having a given fixed success probability, the multinomial distribution gives the probability of any particular combination of numbers of successes for the various categories. When k is 2 and n is 1, the multinomial distribution is the Bernoulli distribution. When k is 2 and n is bigger than 1, it is the binomial distribution. When k is bigger than 2 and n is 1, it is the categorical distribution. The term \"multinoulli\" is sometimes used for the categorical distribution to emphasize this four-way relationship (so n determines the prefix, and k the suffix). The Bernoulli distribution models the outcome of a single Bernoulli trial. In other words, it models whether flipping a (possibly biased) coin one time will result in either a success (obtaining a head) or failure (obtaining a tail). The binomial distribution generalizes this to the number of heads from performing n independent flips (Bernoulli trials) of the same coin. The multinomial distribution models the outcome of n experiments, where the outcome of each trial has a categorical distribution, such as rolling a k-sided dice n times. Let k be a fixed finite number. Mathematically, we have k possible mutually exclusive outcomes, with corresponding probabilities p1, ..., pk, and n independent trials. Since the k outcomes are mutually exclusive and one must occur we have pi \u2265 0 for i = 1, ..., k and . Then if the random variables Xi indicate the number of times outcome number i is observed over the n trials, the vector X = (X1, ..., Xk) follows a multinomial distribution with parameters n and p, where p = (p1, ..., pk). While the trials are independent, their outcomes Xi are dependent because they must be summed to n."@en . . . "Multinomialverteilung"@de . . "Em probabilidade e estat\u00EDstica, a distribui\u00E7\u00E3o multinomial \u00E9 uma generaliza\u00E7\u00E3o da distribui\u00E7\u00E3o binomial para casos onde temos mais de dois poss\u00EDveis resultados, sendo assim \u00E9 uma distribui\u00E7\u00E3o de probabilidade discreta e multivariada. Temos um total de objetos/itens separados independentemente em categorias/tipos, um item \u00E9 da categoria com probabilidade n\u00E3o-nula onde , al\u00E9m disso dizemos que \u00E9 a quantidade de itens na categoria onde . Como se trata de um caso multivariado dizemos que o vetor aleat\u00F3rio tem distribui\u00E7\u00E3o multinomial e denotamos onde ."@pt . . "\u591A\u9805\u5206\u5E03\uFF08\u305F\u3053\u3046\u3076\u3093\u3077\u3001\u82F1: multinomial distribution\uFF09\u306F\u3001\u78BA\u7387\u8AD6\u306B\u304A\u3044\u3066\u4E8C\u9805\u5206\u5E03\u3092\u4E00\u822C\u5316\u3057\u305F\u78BA\u7387\u5206\u5E03\u3067\u3042\u308B\u3002 \u4E8C\u9805\u5206\u5E03\u306F\u3001n \u500B\u306E\u72EC\u7ACB\u306A\u30D9\u30EB\u30CC\u30FC\u30A4\u8A66\u884C\u306E\u300C\u6210\u529F\u300D\u306E\u6570\u306E\u78BA\u7387\u5206\u5E03\u3067\u3042\u308A\u3001\u5404\u8A66\u884C\u306E\u300C\u6210\u529F\u300D\u78BA\u7387\u306F\u540C\u3058\u3067\u3042\u308B\u3002\u591A\u9805\u5206\u5E03\u3067\u306F\u3001\u5404\u8A66\u884C\u306E\u7D50\u679C\u306F\u56FA\u5B9A\u306E\u6709\u9650\u500B\uFF08k \u500B\uFF09\u306E\u5024\u3092\u3068\u308A\u3001\u305D\u308C\u305E\u308C\u306E\u5024\u3092\u3068\u308B\u78BA\u7387\u306F p1, \u2026, pk\uFF08\u3059\u306A\u308F\u3061\u3001i = 1, \u2026, k \u306B\u3064\u3044\u3066 pi \u2265 0 \u3067\u3042\u308A\u3001 \u304C\u6210\u308A\u7ACB\u3064\uFF09\u3067\u3042\u308A\u3001n \u56DE\u306E\u72EC\u7ACB\u3057\u305F\u8A66\u884C\u304C\u884C\u308F\u308C\u308B\u3002\u78BA\u7387\u5909\u6570 Xi \u306F n \u56DE\u306E\u8A66\u884C\u3067 i \u3068\u3044\u3046\u6570\u304C\u51FA\u308B\u56DE\u6570\u3092\u793A\u3059\u3002X = (X1, \u2026, Xk) \u306F n \u3068 p \u3092\u30D1\u30E9\u30E1\u30FC\u30BF\u3068\u3059\u308B\u591A\u9805\u5206\u5E03\u306B\u5F93\u3046\u3002"@ja . "\u591A\u9805\u5206\u5E03"@ja . . . "number of mutually exclusive events"@en . "Multinomick\u00E9 rozd\u011Blen\u00ED"@cs . "Multinomick\u00E9 rozd\u011Blen\u00ED popisuje \u010Detnost dvou a v\u00EDce jev\u016F, kter\u00E9 jsou v\u00FDsledkem n\u011Bjak\u00FDch pokus\u016F. Multinomick\u00E9 rozd\u011Blen\u00ED mus\u00ED vyhovovat podm\u00EDnk\u00E1m: 1. \n* Pokusy jsou na sob\u011B nez\u00E1visl\u00E9. 2. \n* Z jev\u016F v\u017Edy mus\u00ED nastat pr\u00E1v\u011B jeden. 3. \n* Pravd\u011Bpodobnosti v\u00FDsledn\u00FDch jev\u016F jsou ve v\u0161ech pokusech stejn\u00E9. P\u0159\u00EDkladem m\u016F\u017Ee b\u00FDt nap\u0159\u00EDklad rozd\u011Blen\u00ED \u010Detnost\u00ED jednotliv\u00FDch hodnot na kostce, se kterou h\u00E1z\u00EDme. Pokud by n\u00E1s zaj\u00EDmala pouze \u010Detnost jedn\u00E9 hodnoty na kostce v n nez\u00E1visl\u00FDch pokusech, pak by se jednalo o binomick\u00E9 rozd\u011Blen\u00ED."@cs . "Multinomiale verdeling"@nl . "Multinomick\u00E9 rozd\u011Blen\u00ED popisuje \u010Detnost dvou a v\u00EDce jev\u016F, kter\u00E9 jsou v\u00FDsledkem n\u011Bjak\u00FDch pokus\u016F. Multinomick\u00E9 rozd\u011Blen\u00ED mus\u00ED vyhovovat podm\u00EDnk\u00E1m: 1. \n* Pokusy jsou na sob\u011B nez\u00E1visl\u00E9. 2. \n* Z jev\u016F v\u017Edy mus\u00ED nastat pr\u00E1v\u011B jeden. 3. \n* Pravd\u011Bpodobnosti v\u00FDsledn\u00FDch jev\u016F jsou ve v\u0161ech pokusech stejn\u00E9. P\u0159\u00EDkladem m\u016F\u017Ee b\u00FDt nap\u0159\u00EDklad rozd\u011Blen\u00ED \u010Detnost\u00ED jednotliv\u00FDch hodnot na kostce, se kterou h\u00E1z\u00EDme. Pokud by n\u00E1s zaj\u00EDmala pouze \u010Detnost jedn\u00E9 hodnoty na kostce v n nez\u00E1visl\u00FDch pokusech, pak by se jednalo o binomick\u00E9 rozd\u011Blen\u00ED."@cs . . "where"@en .