{"id":134,"date":"2016-11-18T23:30:20","date_gmt":"2016-11-19T04:30:20","guid":{"rendered":"http:\/\/blog.espol.edu.ec\/estg1003\/?p=134"},"modified":"2026-04-04T10:49:51","modified_gmt":"2026-04-04T15:49:51","slug":"pmf-poisson","status":"publish","type":"post","link":"https:\/\/blog.espol.edu.ec\/algoritmos101\/stp-u01eva\/pmf-poisson\/","title":{"rendered":"pmf - Poisson"},"content":{"rendered":"\n<p><strong><em>Referencia<\/em><\/strong>: Gubner p.70, Le\u00f3n-Garc\u00eda \/p.116<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Variable aleatoria Poisson<\/h3>\n\n\n\n<p>Una variable aleatoria X se dice que tiene funci\u00f3n de probabilidad de masa pmf con par\u00e1metro \u03bb&gt;0, definida por:<\/p>\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> P_x(k) = \\frac {\\lambda^k e^{-\\lambda}}{k!} <\/span>\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> k=0,1,2,... <\/span>\n\n\n\n<h2 class=\"wp-block-heading\">Ejemplo - visitas de clientes a p\u00e1gina<\/h2>\n\n\n\n<p>El n\u00famero de visitas a un sitio de Internet muy popular en intervalos de 1 minuto se describe con una variable aleatoria tipo Poisson.<\/p>\n\n\n\n<p>Encuentre la probabilidad que se de al menos una visita entre las 3:00 am y 3:01 am si \u03bb=2. Luego encuentre la probabilidad que se realicen al menos 2 visitas durante el mismo intervalo de tiempo.<\/p>\n\n\n\n<p><strong>Soluci\u00f3n<\/strong>: Sea X&nbsp;el n\u00famero de visitas. Entonces:<\/p>\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> P(X\\geq 1) = 1 - P(X=0) <\/span>\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\">= 1-e^{-\\lambda} = 1- e^{-2} \\approx 0.865 <\/span>\n\n\n\n<p>De forma similar:<\/p>\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> P(X\\geq 2) = 1 - P(X=0) - P(X=1) <\/span>\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> = 1-e^{-\\lambda} - \\lambda e^{-\\lambda} <\/span>\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> = 1-e^{-\\lambda}(1+\\lambda) <\/span>\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> = 1-e^{-2}(1+2) = 0.594 <\/span>\n\n\n<div class=\"wp-block-syntaxhighlighter-code alignwide\"><pre class=\"brush: python; title: ; notranslate\" title=\"\">\n# Distribuci\u00f3n Poisson con valor lambda\nimport numpy as np\nimport matplotlib.pyplot as plt\nimport scipy.stats as stats\n\n# INGRESO\nn = 10\nlambd = 2\nmedia = 0\n\n# PROCEDIMIENTO\nk  = np.arange(media-1, n+1)\npx = stats.poisson.pmf(k,lambd)\n\n# SALIDA\nprint('k: ', k)\nprint('p(k):', px)\n\n# grafica\nplt.title('Poisson rango hasta n='+str(n))\nplt.stem(k,px)\nplt.xlabel('k')\nplt.margins(0.1)\nplt.show()\n<\/pre><\/div>\n\n\n<pre class=\"wp-block-code alignwide\"><code>k:    &#091;-1  0  1  2  3  4  5  6  7  8  9 10]\np(k): &#091; 0.0000000e+00   1.3533528e-01   2.7067056e-01\n        2.7067056e-01   1.8044704e-01   9.0223522e-02\n        3.6089408e-02   1.2029803e-02   3.4370865e-03\n        8.5927164e-04   1.9094925e-04   3.8189850e-05]<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"564\" height=\"412\" src=\"http:\/\/blog.espol.edu.ec\/algoritmos101\/files\/2017\/04\/poisson_pmf01.png\" alt=\"poisson pmf 01\" class=\"wp-image-21962\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Referencia: Gubner p.70, Le\u00f3n-Garc\u00eda \/p.116 Variable aleatoria Poisson Una variable aleatoria X se dice que tiene funci\u00f3n de probabilidad de masa pmf con par\u00e1metro \u03bb&gt;0, definida por: Ejemplo - visitas de clientes a p\u00e1gina El n\u00famero de visitas a un sitio de Internet muy popular en intervalos de 1 minuto se describe con una variable [&hellip;]<\/p>\n","protected":false},"author":8043,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"wp-custom-template-entrada-stp-unidades","format":"standard","meta":{"footnotes":""},"categories":[213],"tags":[],"class_list":["post-134","post","type-post","status-publish","format-standard","hentry","category-stp-u01eva"],"_links":{"self":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/134","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/users\/8043"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/comments?post=134"}],"version-history":[{"count":3,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/134\/revisions"}],"predecessor-version":[{"id":23266,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/134\/revisions\/23266"}],"wp:attachment":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/media?parent=134"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/categories?post=134"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/tags?post=134"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}