{"id":2874,"date":"2024-10-24T17:00:03","date_gmt":"2024-10-24T15:00:03","guid":{"rendered":"https:\/\/ellistat.com\/?post_type=ressource-pedagogiqu&#038;p=2874"},"modified":"2024-10-24T17:01:21","modified_gmt":"2024-10-24T15:01:21","slug":"ley-hipergeometrica","status":"publish","type":"ressource-pedagogiqu","link":"https:\/\/ellistat.com\/es\/ressource-pedagogiqu\/loi-hypergeometrique\/","title":{"rendered":"Ley hipergeom\u00e9trica"},"content":{"rendered":"<p>La distribuci\u00f3n hipergeom\u00e9trica es una distribuci\u00f3n de probabilidad discreta que modela el n\u00famero de aciertos en una muestra de tama\u00f1o fijo extra\u00edda sin reemplazamiento de una poblaci\u00f3n finita que contiene un n\u00famero especificado de objetos de aciertos y fallos. Suele utilizarse para modelizar situaciones en las que la selecci\u00f3n no es independiente, ya que cada extracci\u00f3n afecta a la composici\u00f3n de la poblaci\u00f3n.&nbsp;<\/p>\n\n\n\n<p>Estas son las principales caracter\u00edsticas de la ley hipergeom\u00e9trica:&nbsp;<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Poblaci\u00f3n finita<\/strong> La poblaci\u00f3n total contiene un n\u00famero fijo de objetos, por ejemplo, cartas, canicas, monedas, etc.&nbsp;<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Objetos de \u00e9xito y fracaso<\/strong> La poblaci\u00f3n se divide en dos grupos: objetos de \u00e9xito (por ejemplo, cartas marcadas, canicas ganadoras) y objetos de fracaso (por ejemplo, cartas sin marcar, canicas perdedoras).&nbsp;<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Dibujo sin sustituci\u00f3n<\/strong> La muestra se extrae sin devolver los objetos a la poblaci\u00f3n despu\u00e9s de cada extracci\u00f3n. Esto significa que la probabilidad de extraer un objeto cambia despu\u00e9s de cada extracci\u00f3n.&nbsp;<\/li>\n<\/ul>\n\n\n\n<p>La funci\u00f3n de masa de probabilidad (PMF) de la distribuci\u00f3n hipergeom\u00e9trica viene dada por la f\u00f3rmula :&nbsp;<\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\ud835\udc43(\ud835\udc4b=\ud835\udc58)=\ud835\udc36\ud835\udc3e\ud835\udc58\u2217\ud835\udc36\ud835\udc41-\ud835\udc3e\ud835\udc5b-\ud835\udc58\ud835\udc36\ud835\udc41\ud835\udc5bPX=k=CkK\u2217Cn-kN-KCnN<\/span><\/p>\n\n\n\n<p>donde :&nbsp;<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>N es el tama\u00f1o total de la poblaci\u00f3n,\u00a0<\/li>\n\n\n\n<li>K es el n\u00famero de objetos que han tenido \u00e9xito en la poblaci\u00f3n,\u00a0<\/li>\n\n\n\n<li>n es el tama\u00f1o de la muestra,\u00a0<\/li>\n\n\n\n<li>k es el n\u00famero de aciertos de la muestra,\u00a0<\/li>\n<\/ul>\n\n\n\n<p>La media (expectativa) de la distribuci\u00f3n hipergeom\u00e9trica es :<\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\mu=n*\\frac{K}{N}<\/span><\/p>\n\n\n\n<p>La varianza de una distribuci\u00f3n binomial es :<\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\sigma=n<em>\\frac{K<\/em>(N-K)*(N-n)}{N^{2}(N-1)}<\/span><\/p>\n\n\n\n<p>La ley hipergeom\u00e9trica se utiliza en diversos campos, como la estad\u00edstica, la gen\u00e9tica, la econom\u00eda y otros \u00e1mbitos en los que se extraen muestras sin reemplazo de una poblaci\u00f3n finita. Se diferencia de la distribuci\u00f3n binomial en que tiene en cuenta los cambios en la probabilidad de \u00e9xito con cada extracci\u00f3n.&nbsp;<\/p>","protected":false},"featured_media":0,"template":"","meta":{"_acf_changed":false},"menu-ressource-pedagogique":[],"class_list":["post-2874","ressource-pedagogiqu","type-ressource-pedagogiqu","status-publish","hentry"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.5 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Loi Hyperg\u00e9om\u00e9trique - Ellistat<\/title>\n<meta name=\"description\" content=\"La loi hyperg\u00e9om\u00e9trique est souvent utilis\u00e9e pour mod\u00e9liser des situations o\u00f9 la s\u00e9lection n&#039;est pas ind\u00e9pendante.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/ellistat.com\/es\/recurso-educativo\/ley-hipergeometrica\/\" \/>\n<meta property=\"og:locale\" content=\"es_ES\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Loi Hyperg\u00e9om\u00e9trique - 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