{"id":1888,"date":"2019-02-23T14:40:12","date_gmt":"2019-02-23T14:40:12","guid":{"rendered":"http:\/\/lash.utrng.edu.mx\/?p=1888"},"modified":"2019-03-07T14:04:15","modified_gmt":"2019-03-07T14:04:15","slug":"distribucion-binomial","status":"publish","type":"post","link":"https:\/\/lash.utrng.edu.mx\/?p=1888","title":{"rendered":"Distribuci\u00f3n Binomial"},"content":{"rendered":"\n<p>Un experimento sigue el modelo de la&nbsp;<strong>distribuci\u00f3n binomial o de Bernoulli&nbsp;<\/strong>si:<\/p>\n\n\n\n<p><strong>1.&nbsp;<\/strong>En cada prueba del experimento s\u00f3lo son posibles&nbsp;<strong>dos resultados<\/strong>: el suceso A (<strong>\u00e9xito<\/strong>) y su contrario<img decoding=\"async\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2019\/03\/image-1.png\"><\/p>\n\n\n\n<p><strong>2.&nbsp;<\/strong>La&nbsp;<strong>probabilidad del suceso A es constante<\/strong>, es decir, que no var\u00eda de una prueba a otra. Se representa por&nbsp;<strong>p<\/strong>.<\/p>\n\n\n\n<!--more-->\n\n\n\n<p><strong>3.&nbsp;<\/strong>El&nbsp;<strong>resultado<\/strong>&nbsp;obtenido en cada prueba es&nbsp;<strong>independiente<\/strong>&nbsp;de los resultados obtenidos anteriormente.<\/p>\n\n\n\n<p>La&nbsp;<strong>distribuci\u00f3n binomial<\/strong>&nbsp;se suele representar por&nbsp;<strong>B(n, p)<\/strong>.<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li><strong>n es el n\u00famero de pruebas<\/strong>&nbsp;de que consta el experimento.<\/li><li><strong>p es la probabilidad de \u00e9xito<\/strong>.<\/li><\/ul>\n\n\n\n<p>La <strong>probabilidad de<\/strong><img decoding=\"async\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2019\/03\/image-1.png\"><strong>  es 1\u2212 p<\/strong>, y la representamos por <strong>q<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<p class=\"has-medium-font-size\"><strong>Variable aleatoria binomial<\/strong><\/p>\n\n\n\n<p>La&nbsp;<strong>variable aleatoria binomial<\/strong>,&nbsp;<strong>X<\/strong>, expresa el&nbsp;<strong>n\u00famero de \u00e9xitos obtenidos<\/strong>&nbsp;en cada prueba del experimento.<\/p>\n\n\n\n<p>La&nbsp;<strong>variable binomial es una variable aleatoria discreta<\/strong>, s\u00f3lo puede tomar los valores 0, 1, 2, 3, 4, &#8230;, n suponiendo que se han realizado n pruebas.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><a href=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2019\/02\/binom-1.png\"><img loading=\"lazy\" decoding=\"async\" width=\"559\" height=\"64\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2019\/02\/binom-1.png\" alt=\"\" class=\"wp-image-1891\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2019\/02\/binom-1.png 559w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2019\/02\/binom-1-300x34.png 300w\" sizes=\"auto, (max-width: 559px) 100vw, 559px\" \/><\/a><\/figure><\/div>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<p style=\"text-align:left\">La&nbsp;<strong>funci\u00f3n de probabilidad de la distribuci\u00f3n binomial<\/strong>, tambi\u00e9n denominada&nbsp;<strong>funci\u00f3n de la distribuci\u00f3n de Bernoulli<\/strong>, es:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/www.vitutor.co.uk\/pro\/3\/images\/24.gif\" alt=\"binomial\"\/><\/figure><\/div>\n\n\n\n<ul class=\"wp-block-list\"><li><strong>n<\/strong>&nbsp;es el n\u00famero de pruebas.<\/li><li><strong>k<\/strong>&nbsp;es el n\u00famero de \u00e9xitos.<\/li><li><strong>p<\/strong>&nbsp;es la probabilidad de \u00e9xito.<\/li><li><strong>q<\/strong>&nbsp;es la probabilidad de fracaso.<\/li><\/ul>\n\n\n\n<p>\n\nEl&nbsp;n\u00famero combinatorio&nbsp;\n\n<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/www.vitutor.co.uk\/pro\/3\/images\/40.gif\" alt=\"n\u00famero combinatorio\"\/><\/figure><\/div>\n\n\n\n<p class=\"has-text-color has-medium-font-size has-vivid-red-color\"><strong>Ejemplo 1<\/strong><\/p>\n\n\n\n<p>La \u00faltima novela de un autor ha tenido un gran \u00e9xito, hasta el punto de que el 80% de los lectores ya la han le\u00eddo. Un grupo de 4 amigos son aficionados a la lectura:<\/p>\n\n\n\n<p><strong>1<\/strong>\u00bfCu\u00e1l es la probabilidad de que en el grupo la hayan le\u00eddo 2 personas?<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>n = 4<\/li><li>p = 0.8<\/li><li>q = 0.2<\/li><li>B(4, 0.8)<\/li><\/ul>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img loading=\"lazy\" decoding=\"async\" width=\"280\" height=\"124\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2019\/02\/ejem1.png\" alt=\"\" class=\"wp-image-1899\"\/><\/figure><\/div>\n\n\n\n<p><strong>2<\/strong>\u00bfY c\u00f3mo m\u00e1ximo 2?<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/www.vitutor.co.uk\/pro\/3\/images\/25_1.gif\" alt=\"binomial\"\/><\/figure><\/div>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/www.vitutor.co.uk\/pro\/3\/images\/25_2.gif\" alt=\"binomial\"\/><\/figure><\/div>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<p><strong>Media<\/strong><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/www.vitutor.co.uk\/pro\/3\/images\/26.gif\" alt=\"media\"\/><\/figure><\/div>\n\n\n\n<p><strong>Varianza<\/strong><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/www.vitutor.co.uk\/pro\/3\/images\/27.gif\" alt=\"varianza\"\/><\/figure><\/div>\n\n\n\n<p><strong>Desviaci\u00f3n t\u00edpica<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.vitutor.co.uk\/pro\/3\/images\/28.gif\" alt=\"desviaci\u00f3n t\u00edpica\"\/><\/figure>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<p style=\"color:#15ff00\" class=\"has-text-color has-medium-font-size\"><strong>Ejemplo 2<\/strong><\/p>\n\n\n\n<p>La probabilidad de que un art\u00edculo producido por una fabrica sea defectuoso es 0.02. Se envi\u00f3 un cargamento de 10.000 art\u00edculos a unos almacenes. Hallar el n\u00famero esperado de art\u00edculos defectuosos, la varianza y la desviaci\u00f3n t\u00edpica.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.vitutor.co.uk\/pro\/3\/images\/29.gif\" alt=\"soluci\u00f3n\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.vitutor.co.uk\/pro\/3\/images\/29_1.gif\" alt=\"soluci\u00f3n\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.vitutor.co.uk\/pro\/3\/images\/29_2.gif\" alt=\"soluci\u00f3n\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.vitutor.co.uk\/pro\/3\/images\/28.gif\" alt=\"desviaci\u00f3n t\u00edpica\"\/><\/figure>\n\n\n\n<p style=\"color:#ff0004\" class=\"has-text-color has-medium-font-size\"><strong>E<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Un experimento sigue el modelo de la&nbsp;distribuci\u00f3n binomial o de Bernoulli&nbsp;si: 1.&nbsp;En cada prueba del experimento s\u00f3lo son posibles&nbsp;dos resultados: el suceso A (\u00e9xito) y su contrario 2.&nbsp;La&nbsp;probabilidad del suceso A es constante, es decir, que no var\u00eda de una prueba a otra. Se representa por&nbsp;p.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0,"footnotes":""},"categories":[41],"tags":[],"class_list":["post-1888","post","type-post","status-publish","format-standard","hentry","category-segundoparcialprobabilidadparamed"],"_links":{"self":[{"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/posts\/1888","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1888"}],"version-history":[{"count":11,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/posts\/1888\/revisions"}],"predecessor-version":[{"id":1965,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/posts\/1888\/revisions\/1965"}],"wp:attachment":[{"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1888"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1888"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1888"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}