{"id":1915,"date":"2019-03-02T15:31:09","date_gmt":"2019-03-02T15:31:09","guid":{"rendered":"http:\/\/lash.utrng.edu.mx\/?p=1915"},"modified":"2021-02-27T06:18:57","modified_gmt":"2021-02-27T06:18:57","slug":"distribucion-de-poisson","status":"publish","type":"post","link":"https:\/\/lash.utrng.edu.mx\/?p=1915","title":{"rendered":"Distribuci\u00f3n de Poiss\u00f3n"},"content":{"rendered":"\n<p> Es una distribuci\u00f3n de variable discreta, Los sucesos son independientes y ocurren durante <strong>un intervalo de tiempo dado<\/strong> ( segundos , minutos , horas, etc) o en una regi\u00f3n espec\u00edfica<\/p>\n\n\n\n<p><strong>Ejemplos<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>El n\u00famero de coches que pasan a trav\u00e9s de un cierto punto en una carretera<\/li><li>El n\u00famero de errores de ortograf\u00eda que uno comete al escribir en una p\u00e1gina<\/li><li>El n\u00famero de llamadas telef\u00f3nicas en una central telef\u00f3nica por minuto ( d\u00eda , hora, etc)<\/li><li>El n\u00famero de enfermos que llegan por hora (D\u00eda , mes) a un hospital<\/li><li>El n\u00famero de clientes que llegan a una oficina por hora (D\u00eda , semana)<\/li><li>El n\u00famero de defectos por metro cuadrado de tela.<\/li><li>El n\u00famero de estrellas en un determinado volumen de espacio.<\/li><\/ul>\n\n\n\n<div class=\"wp-block-image is-style-default\"><figure class=\"aligncenter size-full\"><a href=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2019\/03\/poisson.png\"><img loading=\"lazy\" decoding=\"async\" width=\"219\" height=\"89\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2019\/03\/poisson.png\" alt=\"\" class=\"wp-image-1916\"\/><\/a><\/figure><\/div>\n\n\n\n<!--more-->\n\n\n\n<p>Su funci\u00f3n de probabilidad viene definida por:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>k \u00a0puede ser 0 ,1,2,3,4\u2026\u2026.. ( es lo que se pregunta)<\/li><li>\u03bb (lambda), es el n\u00famero medio de resultados en el intervalo dado<\/li><\/ul>\n\n\n\n<p class=\"has-vivid-cyan-blue-color has-text-color has-medium-font-size\"><strong>Ejemplo<\/strong><\/p>\n\n\n\n<p>Una compa\u00f1\u00eda telef\u00f3nica recibe llamadas a raz\u00f3n de 4 por minuto. calcular la probabilidad de :<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>a)Recibir 2 llamadas en un minuto<\/li><li>b)No recibir ninguna llamada en un minuto<\/li><li>c)Recibir menos de 3 llamadas en un minuto<\/li><li>d) Recibir m\u00e1s de 3 llamadas en un minuto<\/li><\/ul>\n\n\n\n<p>Tenemos lo siguiente:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>\u03bb = 4 llamadas\/minuto<\/li><\/ul>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><a href=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2019\/03\/poisson.png\"><img loading=\"lazy\" decoding=\"async\" width=\"219\" height=\"89\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2019\/03\/poisson.png\" alt=\"\" class=\"wp-image-1916\"\/><\/a><\/figure><\/div>\n\n\n\n<p>a) soluci\u00f3n<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>X=2<\/li><li>\u03bb=4<\/li><\/ul>\n\n\n\n<figure class=\"wp-block-gallery aligncenter columns-1 wp-block-gallery-1 is-layout-flex wp-block-gallery-is-layout-flex\"><ul class=\"blocks-gallery-grid\"><li class=\"blocks-gallery-item\"><figure><img loading=\"lazy\" decoding=\"async\" width=\"142\" height=\"58\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2019\/03\/e1.png\" alt=\"\" data-id=\"1917\" data-link=\"http:\/\/lash.utrng.edu.mx\/?attachment_id=1917\" class=\"wp-image-1917\"\/><\/figure><\/li><li class=\"blocks-gallery-item\"><figure><img loading=\"lazy\" decoding=\"async\" width=\"166\" height=\"47\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2019\/03\/e1b.png\" alt=\"\" data-id=\"1918\" data-link=\"http:\/\/lash.utrng.edu.mx\/?attachment_id=1918\" class=\"wp-image-1918\"\/><\/figure><\/li><li class=\"blocks-gallery-item\"><figure><img loading=\"lazy\" decoding=\"async\" width=\"220\" height=\"25\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2019\/03\/e1c.png\" alt=\"\" data-id=\"1919\" data-link=\"http:\/\/lash.utrng.edu.mx\/?attachment_id=1919\" class=\"wp-image-1919\"\/><\/figure><\/li><\/ul><\/figure>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<p>b) soluci\u00f3n<\/p>\n\n\n\n<figure class=\"wp-block-gallery aligncenter columns-1 wp-block-gallery-2 is-layout-flex wp-block-gallery-is-layout-flex\"><ul class=\"blocks-gallery-grid\"><li class=\"blocks-gallery-item\"><figure><img loading=\"lazy\" decoding=\"async\" width=\"147\" height=\"51\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2019\/03\/e2.png\" alt=\"\" data-id=\"1920\" data-link=\"http:\/\/lash.utrng.edu.mx\/?attachment_id=1920\" class=\"wp-image-1920\"\/><\/figure><\/li><li class=\"blocks-gallery-item\"><figure><img loading=\"lazy\" decoding=\"async\" width=\"161\" height=\"44\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2019\/03\/e2b-1.png\" alt=\"\" data-id=\"1932\" data-link=\"http:\/\/lash.utrng.edu.mx\/index.php\/2019\/03\/02\/distribucion-de-poisson\/e2b-2\/\" class=\"wp-image-1932\"\/><\/figure><\/li><li class=\"blocks-gallery-item\"><figure><img loading=\"lazy\" decoding=\"async\" width=\"226\" height=\"23\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2019\/03\/e2c-1.png\" alt=\"\" data-id=\"1933\" data-link=\"http:\/\/lash.utrng.edu.mx\/index.php\/2019\/03\/02\/distribucion-de-poisson\/e2c-2\/\" class=\"wp-image-1933\"\/><\/figure><\/li><\/ul><\/figure>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<p>c) soluci\u00f3n<\/p>\n\n\n\n<p>P(X&lt;3), es decir, Calcular cuando hay 0, 1 y 2 llamadas; para 0 y 2 llamadas ya lo calculamos anteriormente, solo faltar\u00eda para 1<\/p>\n\n\n\n<figure class=\"wp-block-gallery aligncenter columns-1 wp-block-gallery-3 is-layout-flex wp-block-gallery-is-layout-flex\"><ul class=\"blocks-gallery-grid\"><li class=\"blocks-gallery-item\"><figure><img loading=\"lazy\" decoding=\"async\" width=\"143\" height=\"51\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2019\/03\/e3.png\" alt=\"\" data-id=\"1923\" data-link=\"http:\/\/lash.utrng.edu.mx\/?attachment_id=1923\" class=\"wp-image-1923\"\/><\/figure><\/li><li class=\"blocks-gallery-item\"><figure><img loading=\"lazy\" decoding=\"async\" width=\"157\" height=\"45\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2019\/03\/e3b.png\" alt=\"\" data-id=\"1924\" data-link=\"http:\/\/lash.utrng.edu.mx\/?attachment_id=1924\" class=\"wp-image-1924\"\/><\/figure><\/li><li class=\"blocks-gallery-item\"><figure><img loading=\"lazy\" decoding=\"async\" width=\"216\" height=\"23\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2019\/03\/e3c.png\" alt=\"\" data-id=\"1925\" data-link=\"http:\/\/lash.utrng.edu.mx\/?attachment_id=1925\" class=\"wp-image-1925\"\/><\/figure><\/li><\/ul><\/figure>\n\n\n\n<p>Entonces tenemos que P(X=0) + P(X=1) + P(X=2)=0.0183+0.0732+0.1465=<strong>0.238 <\/strong><\/p>\n\n\n\n<p>d) soluci\u00f3n<\/p>\n\n\n\n<p>Como es imposible calcular ni saber el m\u00e1ximo de llamadas que se pueden recibir, se usar\u00e1 el Complemento(teor\u00eda de conjuntos), pues ya sabemos las probabilidades, para 0,1,2; y para 3 en seguida se calcula:<\/p>\n\n\n\n<figure class=\"wp-block-gallery aligncenter columns-1 wp-block-gallery-4 is-layout-flex wp-block-gallery-is-layout-flex\"><ul class=\"blocks-gallery-grid\"><li class=\"blocks-gallery-item\"><figure><img loading=\"lazy\" decoding=\"async\" width=\"144\" height=\"51\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2019\/03\/e4.png\" alt=\"\" data-id=\"1926\" data-link=\"http:\/\/lash.utrng.edu.mx\/?attachment_id=1926\" class=\"wp-image-1926\"\/><\/figure><\/li><li class=\"blocks-gallery-item\"><figure><img loading=\"lazy\" decoding=\"async\" width=\"169\" height=\"47\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2019\/03\/e4b.png\" alt=\"\" data-id=\"1927\" data-link=\"http:\/\/lash.utrng.edu.mx\/?attachment_id=1927\" class=\"wp-image-1927\"\/><\/figure><\/li><li class=\"blocks-gallery-item\"><figure><img loading=\"lazy\" decoding=\"async\" width=\"251\" height=\"27\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2019\/03\/e4c.png\" alt=\"\" data-id=\"1928\" data-link=\"http:\/\/lash.utrng.edu.mx\/?attachment_id=1928\" class=\"wp-image-1928\"\/><\/figure><\/li><\/ul><\/figure>\n\n\n\n<p>Sumando las probabilidades&#8230;<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><a href=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2019\/03\/e.png\"><img loading=\"lazy\" decoding=\"async\" width=\"334\" height=\"52\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2019\/03\/e.png\" alt=\"\" class=\"wp-image-1929\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2019\/03\/e.png 334w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2019\/03\/e-300x47.png 300w\" sizes=\"auto, (max-width: 334px) 100vw, 334px\" \/><\/a><\/figure><\/div>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><a href=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2019\/03\/complemento1.png\"><img loading=\"lazy\" decoding=\"async\" width=\"315\" height=\"270\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2019\/03\/complemento1.png\" alt=\"\" class=\"wp-image-1935\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2019\/03\/complemento1.png 315w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2019\/03\/complemento1-300x257.png 300w\" sizes=\"auto, (max-width: 315px) 100vw, 315px\" \/><\/a><\/figure><\/div>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><a href=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2019\/03\/e-r.png\"><img loading=\"lazy\" decoding=\"async\" width=\"317\" height=\"97\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2019\/03\/e-r.png\" alt=\"\" class=\"wp-image-1930\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2019\/03\/e-r.png 317w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2019\/03\/e-r-300x92.png 300w\" sizes=\"auto, (max-width: 317px) 100vw, 317px\" \/><\/a><\/figure><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Es una distribuci\u00f3n de variable discreta, Los sucesos son independientes y ocurren durante un intervalo de tiempo dado ( segundos , minutos , horas, etc) o en una regi\u00f3n espec\u00edfica Ejemplos El n\u00famero de coches que pasan a trav\u00e9s de un cierto punto en una carretera El n\u00famero de errores de ortograf\u00eda que uno comete &hellip; <a href=\"https:\/\/lash.utrng.edu.mx\/?p=1915\">Seguir leyendo <span class=\"meta-nav\">&rarr;<\/span><\/a><\/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-1915","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\/1915","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=1915"}],"version-history":[{"count":5,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/posts\/1915\/revisions"}],"predecessor-version":[{"id":3394,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/posts\/1915\/revisions\/3394"}],"wp:attachment":[{"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1915"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1915"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1915"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}