{"id":34160,"date":"2021-05-12T13:00:35","date_gmt":"2021-05-12T13:00:35","guid":{"rendered":"https:\/\/toposuranos.com\/material\/?p=34160"},"modified":"2025-08-16T10:55:00","modified_gmt":"2025-08-16T10:55:00","slug":"experimentum-bernoulli-et-distributio-binomialis","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/la\/experimentum-bernoulli-et-distributio-binomialis\/","title":{"rendered":"Experimentum Bernoulli et Distributio Binomialis"},"content":{"rendered":"<div style=\"background-color:#F3F3F3; padding:20px;\">\n<center><\/p>\n<h1>Experimentum Bernoulli et Distributio Binomialis<\/h1>\n<p><\/p>\n<p style=\"text-align:center;\"><strong>Summarium<\/strong><br \/><em>In hac lectione conceptum experimentorum Bernoulli eiusque implicationes in theoria probabilitatum investigabimus. Incipimus cum definitione accurata experimentorum Bernoulli, deinde tractamus notionem independentiae inter eventus. His explanatis, theorema binomiale adhibetur ut intellegamus quomodo repetitio experimenti Bernoulli efficiat eventus cum distributione binomiali. Denique proponuntur exercitationes practicae ad hos conceptus applicandos atque confirmandos.<\/em><\/p>\n<p><\/center><br \/>\n<\/p>\n<p style=\"text-align:center;\"><strong>PROPOSITA DISCENDI:<\/strong><br \/>\nPost hanc lectionem confectam, discipulus poterit:\n<\/p>\n<ol>\n<li><strong>Identificare<\/strong> notas praecipuas experimentorum Bernoulli, inter quas independentiam inter conatus.<\/li>\n<li><strong>Applicare<\/strong> recte notationem pro eventibus binomialibus ex experimentis Bernoulli derivatis.<\/li>\n<li><strong>Distingere<\/strong> inter varias formas independentiae (2-independentia, 3-independentia, n-independentia) earumque relationem atque usum in experimentis Bernoulli comprehendere.<\/li>\n<li><strong>Intellegere<\/strong> relationem inter experimentum Bernoulli et theorema binomiale, atque quomodo haec relatio adhiberi possit ad probabilitatem seriei successuum atque defectuum computandam.<\/li>\n<li><strong>Applicare<\/strong> distributionem binomialem (vel Bernoulli) ad probabilitatem certi numeri successuum in serie conatuum computandam.<\/li>\n<\/ol>\n<p><center><br \/>\n<strong><u>INDEX CONTENTORUM<\/u>:<\/strong><br \/>\n<a href=\"#1\">Experimentum Bernoulli<\/a><br \/>\n<a href=\"#2\">Varie formae independentiae<\/a><br \/>\n<a href=\"#3\">Experimentum Bernoulli et theorema binomiale<\/a><br \/>\n<a href=\"#4\">Distributio binomialis (vel Bernoulli) et distributiones Probabilitatis<\/a><br \/>\n<a href=\"#5\">Exercitationes:<\/a><br \/>\n<\/center><\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/uyljDy0bcvU\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center>\n<\/div>\n<p><a name=\"1\"><\/a><\/p>\n<h2>Experimentum Bernoulli<\/h2>\n<p style=\"text-align: justify; color:\"><a href=\"https:\/\/www.youtube.com\/watch?v=uyljDy0bcvU&amp;t=103s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">Experimentum Bernoulli est experimentum casu<\/span><\/strong><\/a> dichotomicum cum quadam probabilitate successus <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">p.<\/span><\/span> Si experimentum Bernoulli <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n<\/span><\/span> vicibus identice ac independente repetitur, obtinentur <strong>eventus Bernoulli:<\/strong> Certus numerus <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">k<\/span><\/span> successuum inter <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n<\/span><\/span> conatus. Hi etiam appellantur <strong>eventus binomiales<\/strong> eosque repraesentamus per notationem<\/p>\n<p style=\"text-align: center; color:\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Large \\displaystyle Bi(n;k;p)<\/span><\/span><\/p>\n<p style=\"text-align: justify; color:\">Alia nota magni momenti experimentorum Bernoulli est quod omnes conatus inter se independentes sunt.<\/p>\n<p style=\"text-align: justify; color:\"><span style=\"color: #000080;\">EXEMPLUM:<\/span> Alea sex facierum saepius iactatur. Exempla eventuum generis Bernoulli pro hoc experimento sunt:<\/p>\n<ul style=\"text-align: justify; color:\">\n<li><strong>Obtinere 3 unitates inter 5 conatus:<\/strong> repraesentatum per <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">Bi(5;3;1\/6)<\/span><\/span><\/li>\n<li><strong>Obtinere 7 numeros pares inter 12 conatus:<\/strong> repraesentatum per <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">Bi(12;7;1\/3)<\/span><\/span><\/li>\n<\/ul>\n<p><a name=\"2\"><\/a><\/p>\n<h3>Varie formae independentiae<\/h3>\n<p style=\"text-align: justify; color:\"><a href=\"https:\/\/www.youtube.com\/watch?v=uyljDy0bcvU&amp;t=283s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">Independentia inter conatus explicatos<\/span><\/strong><\/a> in experimento Bernoulli non est prorsus eadem independentia quam iam consideravimus, sed agitur de versione multo restrictiore. Ad hanc differentiam explicandam species independentiae inter eventus inspiciamus<\/p>\n<h4>2-independentia<\/h4>\n<p style=\"text-align: justify; color:\"><a href=\"https:\/\/toposuranos.com\/probabilidad-condicional-e-independencia-entre-eventos\/\" rel=\"noopener\" target=\"_blank\">Independentia quam iam novimus<\/a> est ea quae inter duos eventus datur. Hanc appellamus \u00ab2-independentiam\u00bb. His verbis dicimus eventus <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">A<\/span><\/span> et <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">B<\/span><\/span> esse 2-independentes si<\/p>\n<p style=\"text-align: center; color:\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">P(A\\cap B) = P(A)P(B)<\/span><\/span><\/p>\n<h4>3-independentia<\/h4>\n<p style=\"text-align: justify; color:\">Similiter, 3-independentia inter tres eventus <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">A,<\/span><\/span> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">B<\/span><\/span> et <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">C<\/span><\/span> definita est per relationem<\/p>\n<p style=\"text-align: center; color:\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">P(A\\cap B\\cap C) = P(A)P(B)P(C)<\/span><\/span><\/p>\n<p style=\"text-align: justify; color:\">Notandum est 2-independentiam inter <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">A,<\/span><\/span> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">B<\/span><\/span> et <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">C<\/span><\/span> non necessario implicare 3-independentiam, quamquam in casu contrario implicatio vera est.<\/p>\n<h4>n-independentia inter experimenta Bernoulli<\/h4>\n<p style=\"text-align: justify; color:\">Similiter ac definitionibus prioribus, n-independentia inter collectionem eventuum <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">A_1, \\cdots, A_n<\/span><\/span> definita est per relationem<\/p>\n<p style=\"text-align: center; color:\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Large \\displaystyle P\\left(\\bigcap_{i=1}^n A_i\\right) = \\prod_{i=1}^n P(A_i) <\/span><\/span><\/p>\n<p style=\"text-align: justify; color:\">Et similiter habetur quod:<\/p>\n<table style=\"color:\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(n-1)<\/span><\/span>-independentia non necessario implicat <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n<\/span><\/span>-independentiam<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n<\/span><\/span>-independentia <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Longrightarrow<\/span> <span class=\"katex-eq\" data-katex-display=\"false\">(n-1)<\/span><\/span>-independentia<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify; color:\">Repetitiones <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n<\/span><\/span> factae in experimento Bernoulli sunt <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n<\/span><\/span>-independentes.<\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h2>Experimentum Bernoulli et theorema binomiale<\/h2>\n<p style=\"text-align: justify; color:\"><a href=\"https:\/\/www.youtube.com\/watch?v=uyljDy0bcvU&amp;t=478s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">Consideremus experimentum successus et defectus<\/span><\/strong><\/a> cum probabilitate successus <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">p<\/span><\/span>; in unoquoque conatu erit, proinde, probabilitas <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">1-p<\/span><\/span> defectus. Manifestum est probabilitatem ut successus aut defectus in unoquoque conatu accidat esse 1; et quoniam omnes conatus independentes sunt, probabilitas ut successus aut defectus in <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n<\/span><\/span> conatibus accidat erit <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">1^n.<\/span><\/span> Ex hoc consequitur:<\/p>\n<p style=\"text-align: center; color:\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Large \\displaystyle 1 = 1^n = [p + (1-p)]^n = \\sum_{k=0}^n {{n}\\choose{k}} p^k(1-p)^{n-k} <\/span><\/span><\/p>\n<p style=\"text-align: justify; color:\">In ultima aequalitate adhibitum est <a href=\"https:\/\/toposuranos.com\/ejercicios-de-induccion-matematica-teorema-del-binomio-de-newton\/\" rel=\"noopener\" target=\"_blank\">Theorema Binomiale Newtoni,<\/a> et termini intra summationem hoc modo interpretari possunt:<\/p>\n<ul style=\"text-align: justify; color:\">\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle {{n}\\choose{k}}<\/span><\/span>: numerus modorum quibus <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">k<\/span><\/span> successus fieri possunt dum <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n<\/span><\/span> conatus fiunt<\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">p^k<\/span><\/span>: probabilitas ut <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">k<\/span><\/span> successus independentes eveniant<\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(1-p)^{n-k}<\/span><\/span>: probabilitas ut <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n-k<\/span><\/span> defectus independentes eveniant<\/li>\n<\/ul>\n<p style=\"text-align: justify; color:\">His elementis ita ut in summa apparent coniunctis obtinemus: probabilitatem obtinendi <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">k<\/span><\/span> successus inter <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n<\/span><\/span> conatus; vel aequivalenter, probabilitatem obtinendi <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n-k<\/span><\/span> defectus inter <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n<\/span><\/span> conatus.<\/p>\n<p style=\"text-align: justify; color:\">Si unumquodque terminum summae separamus, habemus probabilitates obtinendi:<\/p>\n<table style=\"text-align: justify; color:\">\n<tbody>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle {{n}\\choose{0}} p^0(1-p)^{n-0} = (1-p)^n<\/span><\/span><\/td>\n<td>0 successus inter n conatus<\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle {{n}\\choose{1}} p^1(1-p)^{n-1} = n p(1-p)^{n-1}<\/span><\/span><\/td>\n<td>1 successus inter n conatus<\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle {{n}\\choose{2}} p^2(1-p)^{n-2}<\/span><\/span><\/td>\n<td>2 successus inter n conatus<\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vdots<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vdots<\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle {{n}\\choose{k}} p^k(1-p)^{n-k}<\/span><\/span><\/td>\n<td>k successus inter n conatus<\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vdots<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vdots<\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle {{n}\\choose{n-1}} p^{n-1}(1-p)^{n-(n-1)} = n p^{n-1}(1-p)<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n-1<\/span><\/span> successus inter <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n<\/span><\/span> conatus<\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle {{n}\\choose{n}} p^{n}(1-p)^{0} = p^{n}<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n<\/span><\/span> successus inter <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n<\/span><\/span> conatus<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify; color:\">Et summa horum omnium, ut iam vidimus, est \u00ab1\u00bb. Ostendens omnes possibilitates esse comprehensas.<\/p>\n<p style=\"text-align: justify; color:\">Ex hoc definitur <strong>probabilitas eventus Bernoulli<\/strong>:<\/p>\n<p style=\"text-align: center; color:\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\Large \\color{blue}{P(Bi(n;k;p)) = {{n}\\choose{k}}p^k(1-p)^{n-k}}<\/span><\/span><\/p>\n<p style=\"text-align: justify; color:\">Vel etiam dicimus <strong>numerum successuum <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">X<\/span><\/span> distributionem binomialem habere:<\/strong><\/p>\n<p style=\"text-align: center; color:\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\color{blue}{\\Large \\displaystyle X\\sim Bi(n;p) \\longmapsto P(X=x) = {{n}\\choose{x}}p^x(1-p)^{n-x}}<\/span><\/span><\/p>\n<p><a name=\"4\"><\/a><\/p>\n<h3>Distributio binomialis (vel Bernoulli) et distributiones Probabilitatis<\/h3>\n<p style=\"text-align: justify; color:\"><a href=\"https:\/\/www.youtube.com\/watch?v=uyljDy0bcvU&amp;t=779s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">Per distributionem binomialem<\/span><\/strong><\/a> primum incipimus notiones habere distributionum probabilitatis et variabilis casus. Hoc in casu variabilis casus (discreta) ad numerum successuum refertur, et eius distributio probabilitatis datur per terminos theorematos binomialis<\/p>\n<p style=\"text-align: center; color:\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">{\\Large \\displaystyle P(X=x) = {{n}\\choose{x}}p^x(1-p)^{n-x}}<\/span><\/span><\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/36s4rcfQn7M\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/center><br \/>\n<a name=\"5\"><\/a><\/p>\n<h2>Exercitationes:<\/h2>\n<ol style=\"text-align: justify; color:\">\n<li>Alea aequilibrata sex facierum 5 vicibus iacitur. Computetur probabilitas obtinendi 3 vicibus numerum parem ut eventum.<\/li>\n<li>Nummus 10 vicibus iacitur. Computetur probabilitas obtinendi, ab 0 ad 10 capita, atque efficiatur graphice quae probabilitatem cuiusque eventus ostendat. Quomodo apparebit graphice si numerus iactuum augeatur et probabilitas obtinendi numerum capitum a 0 usque ad illum numerum iactuum consideretur? Folium in Excel hic utile esse potest.<\/li>\n<li>Habetur urna cum quantitate <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">s<\/span><\/span> pilularum, quarum <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r<\/span><\/span> sunt aureae et reliquae albae. Omnes miscentur et una fortuito extrahitur, vincitur cum aurea exit. Si hoc experimentum identice <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">20<\/span><\/span> vicibus repetitur, aestimetur numerus victoriarum verisimillimus pro quolibet valore possibili <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0\\leq r\\leq s.<\/span><\/span> Folium in Excel hic quoque utile esse potest.<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>Experimentum Bernoulli et Distributio Binomialis SummariumIn hac lectione conceptum experimentorum Bernoulli eiusque implicationes in theoria probabilitatum investigabimus. Incipimus cum definitione accurata experimentorum Bernoulli, deinde tractamus notionem independentiae inter eventus. His explanatis, theorema binomiale adhibetur ut intellegamus quomodo repetitio experimenti Bernoulli efficiat eventus cum distributione binomiali. Denique proponuntur exercitationes practicae ad hos conceptus applicandos atque confirmandos. [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":26419,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":1,"footnotes":""},"categories":[1298,1364],"tags":[],"class_list":["post-34160","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mathematica","category-probabilitates-et-statistica"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Experimentum Bernoulli et Distributio Binomialis - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"Disce repetitionem experimenti Bernoulli eventus efficere cum Distributione Binomiali Probabilitatum.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/toposuranos.com\/material\/la\/experimentum-bernoulli-et-distributio-binomialis\/\" \/>\n<meta property=\"og:locale\" content=\"es_ES\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Experimentum Bernoulli et Distributio Binomialis\" \/>\n<meta property=\"og:description\" content=\"Disce repetitionem experimenti Bernoulli eventus efficere cum Distributione Binomiali Probabilitatum.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/toposuranos.com\/material\/la\/experimentum-bernoulli-et-distributio-binomialis\/\" \/>\n<meta property=\"og:site_name\" content=\"toposuranos.com\/material\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/groups\/toposuranos\" \/>\n<meta property=\"article:published_time\" content=\"2021-05-12T13:00:35+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2025-08-16T10:55:00+00:00\" \/>\n<meta property=\"og:image\" content=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/04\/bernoulli-e1712960368446-1024x285.jpg\" \/>\n<meta name=\"author\" content=\"giorgio.reveco\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:title\" content=\"Experimentum Bernoulli et Distributio Binomialis\" \/>\n<meta name=\"twitter:description\" content=\"Disce repetitionem experimenti Bernoulli eventus efficere cum Distributione Binomiali Probabilitatum.\" \/>\n<meta name=\"twitter:image\" content=\"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/04\/bernoulli-e1712960368446.jpg\" \/>\n<meta name=\"twitter:creator\" content=\"@topuranos\" \/>\n<meta name=\"twitter:site\" content=\"@topuranos\" \/>\n<meta name=\"twitter:label1\" content=\"Escrito por\" \/>\n\t<meta name=\"twitter:data1\" content=\"giorgio.reveco\" \/>\n\t<meta name=\"twitter:label2\" content=\"Tiempo de lectura\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minuto\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/la\\\/experimentum-bernoulli-et-distributio-binomialis\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/la\\\/experimentum-bernoulli-et-distributio-binomialis\\\/\"},\"author\":{\"name\":\"giorgio.reveco\",\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/#\\\/schema\\\/person\\\/e15164361c3f9a2a02cf6c234cf7fdc1\"},\"headline\":\"Experimentum Bernoulli et Distributio Binomialis\",\"datePublished\":\"2021-05-12T13:00:35+00:00\",\"dateModified\":\"2025-08-16T10:55:00+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/la\\\/experimentum-bernoulli-et-distributio-binomialis\\\/\"},\"wordCount\":1006,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/#organization\"},\"image\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/la\\\/experimentum-bernoulli-et-distributio-binomialis\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2024\\\/04\\\/bernoulli-e1712960368446.jpg\",\"articleSection\":[\"Mathematica\",\"Probabilitates et Statistica\"],\"inLanguage\":\"es\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\\\/\\\/toposuranos.com\\\/material\\\/la\\\/experimentum-bernoulli-et-distributio-binomialis\\\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/la\\\/experimentum-bernoulli-et-distributio-binomialis\\\/\",\"url\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/la\\\/experimentum-bernoulli-et-distributio-binomialis\\\/\",\"name\":\"Experimentum Bernoulli et Distributio Binomialis - 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