{"id":34172,"date":"2021-05-27T13:00:10","date_gmt":"2021-05-27T13:00:10","guid":{"rendered":"https:\/\/toposuranos.com\/material\/?p=34172"},"modified":"2025-08-16T11:05:48","modified_gmt":"2025-08-16T11:05:48","slug":"processus-poissonianus-appropinquatio-processus-binomialis","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/la\/processus-poissonianus-appropinquatio-processus-binomialis\/","title":{"rendered":"Processus Poissonianus: Appropinquatio Processus Binomialis"},"content":{"rendered":"<div style=\"background-color:#F3F3F3; padding:20px;\">\n<center><\/p>\n<h1>Processus Poissonianus: Appropinquatio Processus Binomialis<\/h1>\n<p><\/p>\n<p style=\"text-align:center;\"><strong>Summarium<\/strong><br \/><em>Haec lectio intendit in Processu Poissoniano ut appropinquationem ad Processum Binomialem, incipiens a definitione coefficientium et distributionis Poissonianae, quae derivatur ex eventu Bernoulliano cum magno numero conatuum et probabilitate singulari minutissima. Pars centralis huius lectionis tractat processus appropinquatos Poissonianos, tam spatiales quam temporales, utens exemplis particularum minimarum in liquido et emissione particularum a substantia radioactiva, respective. Denique concluditur cum exemplis practicis applicationis distributionis Poissonianae in variis contextibus, ut cura clientium in macello et densitas incolarum in loco quodam.<\/em><\/p>\n<p><\/center><br \/>\n<\/p>\n<p style=\"text-align:center;\"><strong>OBJECTIVA DISCENDI:<\/strong><br \/>\nAd finem huius lectionis, discipulus poterit:\n<\/p>\n<ol>\n<li><strong>Intelligere<\/strong> definitionem et coefficientes distributionis Poissonianae.<\/li>\n<li><strong>Intelligere<\/strong> processum Poissonianum ut appropinquationem ad processum binomialem.<\/li>\n<li><strong>Intelligere<\/strong> aequivalentiam formalem inter processus spatiales et temporales Poissonianos.<\/li>\n<li><strong>Uti<\/strong> distributione Poissoniana ad quaestiones practicas solvendas.<\/li>\n<\/ol>\n<p><center><br \/>\n<strong><u>INDEX CONTENTORUM<\/u>:<\/strong><br \/>\n<a href=\"#1\">Coefficientes et Distributio Poissoniana<\/a><br \/>\n<a href=\"#2\">Processus appropinquati Poissoniani<\/a><br \/>\n<a href=\"#3\">Processus Spatialis Poissonianus<\/a><br \/>\n<a href=\"#4\">Processus Temporalis Poissonianus<\/a><br \/>\n<a href=\"#5\">Temporalis et Spatialis<\/a><br \/>\n<a href=\"#6\">Exempla practica ubi distributio Poissoniana adhibetur<\/a><br \/>\n<\/center><br \/>\n<center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/mQ0j3FE8p2U\" 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><\/br><\/br><\/p>\n<h2>Coefficientes et Distributio Poissoniana<\/h2>\n<p style=\"text-align: justify; color:\"><a href=\"https:\/\/www.youtube.com\/watch?v=mQ0j3FE8p2U&amp;t=154s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">Nunc consideremus appropinquationem<\/span><\/strong><\/a> ad <a href=\"https:\/\/toposuranos.com\/el-ensayo-de-bernoulli-para-n-intentos-independientes\/\" rel=\"noopener\" target=\"_blank\">distributionem binomialem<\/a>, in qua numerus conatuum <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n<\/span><\/span> magnus habetur et omnes cum probabilitate singulari <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">p<\/span><\/span> minutissima. Cum hoc facimus, a processu binomiali typico ad Processum Poissonianum transimus. Ad hoc illustrandum, finge successionem huius formae <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{Bi(n;k;p_n)\\}_n,<\/span><\/span> ubi <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n\\to\\infty<\/span><\/span> et <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">p_n<\/span><\/span> relationem satisfacit <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">np_n=\\lambda \\gt 0<\/span><\/span>. Ex hoc videbimus quod<\/p>\n<p style=\"text-align: center; color:\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\lim_{n\\to\\infty}P\\left(Bi(n;k;P_n) \\right) = \\frac{\\lambda^k}{k!}e^{-\\lambda}<\/span><\/span><\/p>\n<p style=\"text-align: justify; color:\">Hoc revera non est difficile demonstrare: si probabilitatem eventus Bernoulliani <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">Bi(n;k;p_n)<\/span><\/span> accipimus eamque multiplicamus et dividimus per <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n^k<\/span><\/span>, rationem sequentem obtinemus:<\/p>\n<table style=\"text-align: justify; color:\">\n<tbody>\n<tr>\n<td width=\"80px\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">P(B(n;k;p_n))<\/span><\/span><\/td>\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 style=\"color: #f00000;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\cdot \\displaystyle \\frac{n^k}{n^k}<\/span><\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td width=\"80px\"><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle=\\frac{n!}{(n-k)!k!}p^k(1-p)^{n-k} \\cdot \\frac{n^k}{n^k}<\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td width=\"80px\"><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle=\\frac{n(n-1)\\cdots[n-(k-1)]}{n^k} \\cdot \\frac{(np_n)^k}{k!} (1-p_n)^{-k}(1-p_n)^n<\/span><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify; color:\">Itaque si limitem computamus cum <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n\\to\\infty<\/span><\/span>, habebitur:<\/p>\n<p style=\"text-align: center; color:\"><span dir=\"ltr\"><br \/>\n<span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rl}\n\n\\displaystyle \\lim_{n\\to\\infty} {{n}\\choose{k}}p_n^k(1-p_n)^{n-k} &amp;= \\displaystyle \\lim_{n\\to\\infty} \\underbrace{\\frac{n(n-1)\\cdots[n-(k-1)]}{n^k}}_{\\to 1} \\cdot \\frac{\\overbrace{(np_n)^k}^{\\to\\lambda^k}}{k!} \\overbrace{(1-p_n)^{-k}}^{\\to 1} {(1-p_n)^n} \\\\ \\\\\n\n&amp;\\displaystyle = \\frac{\\lambda^k}{k!} \\lim_{n\\to\\infty}\\left(1 - \\frac{\\lambda}{n} \\right)^n \\\\ \\\\\n\n&amp; \\displaystyle = \\frac{\\lambda^k}{k!}e^{-\\lambda}\n\n\\end{array}\n\n<\/span>\n<\/span><\/p>\n<p style=\"text-align: justify; color:\">Ex hoc definiuntur coefficientes Poissoniani, <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">Po(k;\\lambda)<\/span><\/span>, per<\/p>\n<p style=\"text-align: center; color:\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\displaystyle Po(k;\\lambda) := \\lim_{n\\to\\infty} {{n}\\choose{k}}p^k(1-p_n)^{n-k} = \\frac{\\lambda^k}{k!}e^{-\\lambda} <\/span><\/span><\/p>\n<p style=\"text-align: justify; color:\">Et dicitur variabile aleatorium <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">X<\/span><\/span> distributionem Poissonianam habere, <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">X\\sim Po(k,\\lambda),<\/span><\/span> si hoc verificatur:<\/p>\n<p style=\"text-align: center; color:\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> P(X=k) = Po(k;\\lambda) <\/span><\/span><\/p>\n<p><a name=\"2\"><\/a><\/br><\/br><\/p>\n<h2>Processus appropinquati Poissoniani<\/h2>\n<p><a name=\"3\"><\/a><\/br><\/br><\/p>\n<h3>Processus Spatialis Poissonianus<\/h3>\n<p style=\"text-align: justify; color:\"><a href=\"https:\/\/www.youtube.com\/watch?v=mQ0j3FE8p2U&amp;t=665s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">Supponamus nos habere vas voluminis<\/span><\/strong><\/a> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">V<\/span><\/span> cum liquido in quo inveniuntur <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n<\/span><\/span> particulae minutissimae uniformiter permixtae. Hic assumimus liquorem bene agitari et particulas inter se non interagere, nec se allicere nec se repellere. Haec sunt suppositiones quae formalizari possunt per affirmationes sequentes:<\/p>\n<ul style=\"text-align: justify; color:\">\n<li><strong>Hypothesis Homogeneitatis spatialis:<\/strong> Probabilitas particulam invenire in regione <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">D<\/span><\/span> liquidi tantum a volumine illius regionis pendet.<\/li>\n<li><strong>Non-Interactio:<\/strong> Eventus \u00abparticula j-esima est in regione D\u00bb, cum j=1,2,&#8230;,n omnes sunt n-independentes.<\/li>\n<li><strong>Non-Superpositio:<\/strong> Duae particulae idem locum in spatio occupare non possunt.<\/li>\n<\/ul>\n<p style=\"text-align: justify; color:\">Si datur regio <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">D<\/span><\/span> cum volumine <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">v<\/span><\/span>, probabilitas eventus \u00abin <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">D<\/span><\/span> sunt <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">k<\/span><\/span> particulae\u00bb pendet tantum ex <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">v<\/span><\/span>; vocemus <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">g_k(v)<\/span><\/span> talem eventum. Sit <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">h(v)<\/span><\/span> probabilitas quod particula sit intra regionem voluminis <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">v.<\/span><\/span> Si <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">D_1<\/span><\/span> et <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">D_2<\/span><\/span> sunt duae regiones disiunctae voluminis <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">v_1<\/span><\/span> et <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">v_2<\/span><\/span> respective, tunc si <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">D=D_1\\cup D_2,<\/span><\/span> volumen habet <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">v,<\/span><\/span> tunc <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">v=v_1+v_2.<\/span><\/span> Et quia <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">D_1<\/span><\/span> et <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">D_2<\/span><\/span> sunt disiunctae (<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">D_1\\cap D_2 = \\emptyset <\/span><\/span>), habebitur<\/p>\n<p style=\"text-align: center; color:\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> h(v) = h(v_1) + h(v_2) <\/span><\/span><\/p>\n<p style=\"text-align: justify; color:\">Si <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">V<\/span><\/span> est volumen totius liquidi, tunc habebitur<\/p>\n<p style=\"text-align: center; color:\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> h(V) = 1 <\/span><\/span><\/p>\n<p style=\"text-align: justify; color:\">Et consequentur:<\/p>\n<p style=\"text-align: center; color:\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> h(v) =\\displaystyle \\frac{v}{V} <\/span><\/span><\/p>\n<p style=\"text-align: justify; color:\">Hinc habemus eventum <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">g_k(v)<\/span><\/span> esse revera eventum Bernoullianum cum <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">p=v\/V<\/span><\/span> et dari per:<\/p>\n<p style=\"text-align: center; color:\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> g_k(v) =B(n;k;p=v\/V) <\/span><\/span><\/p>\n<p style=\"text-align: justify; color:\">Attamen, pleraeque res practicae huius generis implicant magnum numerum particularum <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n<\/span><\/span> et regiones consideratae parvae fiunt respectu magnitudinis systematis, ita ut condiciones adhibendae appropinquationis Poissonianae impleantur et habeatur:<\/p>\n<p style=\"text-align: center; color:\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle P(g_k(v)) = \\lim_{\\begin{matrix}n\\to\\infty\\\\ v\/V=c \\end{matrix}}P(B(n;k;p=v\/V)) =\\displaystyle \\frac{(cv)^k}{k!}e^{-cv}<\/span><\/span><\/p>\n<p><a name=\"4\"><\/a><\/br><\/br><\/p>\n<h3>Processus Temporalis Poissonianus<\/h3>\n<p style=\"text-align: justify; color:\"><a href=\"https:\/\/www.youtube.com\/watch?v=mQ0j3FE8p2U&amp;t=944s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">Supponamus nos registrare quantitatem<\/span><\/strong><\/a> particularum emissarum a substantia radioactiva ab instante t=0 et ex hoc computabimus probabilitatem quod in intervallo [0,t[ exacte k particulae emittantur sub sequentibus suppositionibus:<\/p>\n<ul style=\"text-align: justify; color:\">\n<li><strong>Invariantia:<\/strong> Conditiones experimenti tempore non mutantur.<\/li>\n<li><strong>Non-Memoria:<\/strong> Quod evenit in [0,t[ non afficit id quod fit in [t,t'[.<\/li>\n<li><strong>Eventus Isolati:<\/strong> Particulae singillatim emittuntur.<\/li>\n<\/ul>\n<p style=\"text-align: justify; color:\">Si comparaverimus suppositiones processus temporalis cum processu spatiali, animadvertimus eas formaliter aequivalere. Quemadmodum probabilitas particulam invenire in regione non pendet ex loco unde regio eligitur, sed tantum ex magnitudine, ita probabilitas emissionem particulae observandi non pendet ex momento eligendo ad metiendum, sed solum ex intervallo observationis. Non-memoria est analoga non-interactioni processuum spatialium: quod accidit alio tempore non afficit quod in ceteris momentis fit. Et denique, eventus isolati implicant quod in uno momento temporis tantum una particula emittere potest, analogum ad modum quo locus in spatio uno corpore tantum occupari potest.<\/p>\n<p style=\"text-align: justify; color:\">Ita, si definimus eventum \u00abk particulae emittuntur in intervallo temporis <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">t<\/span><\/span>,\u00bb eius probabilitas erit eventus formae <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">g_k(t)<\/span><\/span>, id est:<\/p>\n<p style=\"text-align: center; color:\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">P(g_k(t)) =\\displaystyle \\frac{(ct)^k}{k!} e^{-ct}<\/span><\/span><\/p>\n<p><a name=\"5\"><\/a><\/br><\/br><\/p>\n<h3>Temporalis et Spatialis<\/h3>\n<p style=\"text-align: justify; color:\"><a href=\"https:\/\/www.youtube.com\/watch?v=mQ0j3FE8p2U&amp;t=1102s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">Uterque processus, spatialis et temporalis, formaliter aequivalet.<\/span><\/strong><\/a> Tantum variantur in modo quo ad usus practicos interpretantur. Via celeris ad clarius faciendam distinctionem est observando munus quod implet constans \u00abc\u00bb quae in utroque casu apparet. Ut functio exponentialis bene definiatur, necesse est ut argumentum eius sit sine dimensione; tamen, haec in suo contentu habet unitates temporis vel spatii secundum utrum de processibus temporalibus an spatialibus agatur. Hoc problema apte componit ipsa constans c. Habemus:<\/p>\n<p style=\"text-align: center; color:\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">Po(k;\\lambda)=\\displaystyle \\frac{\\lambda^k}{k!}e^{-\\lambda}=\\left\\{\\begin{matrix} {Sumendo\\,\\lambda = \\rho v } &amp; \\longmapsto &amp;\\displaystyle \\frac{(\\rho v)^k}{k!}e^{-\\rho v} &amp; {Processus\\,Spatialis} \\\\ {Sumendo\\,\\lambda = \\nu t } &amp; \\longmapsto &amp;\\displaystyle \\frac{(\\nu t)^k}{k!}e^{-\\nu t} &amp; {Processus\\,Temporalis} \\end{matrix} \\right.<\/span><\/span><\/p>\n<ul style=\"text-align: justify; color:\">\n<li>Si <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">c=\\rho<\/span><\/span>, agitur de densitate spaziali (numerus rerum per unitatem spatii), ideo definit processum spatialem Poissonianum.<\/li>\n<li>Si <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">c=\\nu<\/span><\/span>, agitur de densitate temporali (vel frequentia, numerus eventuum per unitatem temporis), ideo definit processum temporalem Poissonianum.<\/li>\n<\/ul>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/8qvHRoEckSc\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center><br \/>\n<a name=\"6\"><\/a><\/br><\/br><\/p>\n<h2>Exempla practica ubi distributio Poissoniana adhibetur<\/h2>\n<ol style=\"text-align: justify; color:\">\n<li>Capsa mercatus mediocriter 2 clientes singulis 9 minutis curat. Elabora tabulam quae probabilitates ostendat quod inter 1, 2, 3, et sic deinceps, usque ad 5 homines in tempore 5 minutorum curentur.<\/li>\n<li>Clinica veterinaria capacitatem habet ad curandos ad summum 12 clientes in die. Si mediocriter accipiunt 9 clientes singulis diebus, quae est probabilitas quod quolibet die capacitas curationis clinicae superetur?<\/li>\n<li>Quaelibet regio densitatem habet 10 hominum pro singulis 1000 metris quadratis. Quae est probabilitas quod in loco 60 metrorum quadratorum minus quam 15 homines inveniamus?<\/li>\n<li>Gallina vult viam transire. Recta linea ambulando, 58 secundis eam percurrit. Si via habet cursum vehiculorum 3 vehicula per minutum, et si vehiculum transit dum gallina conatur transire, pro certo opprimetur exitio mortali. Quae est probabilitas quod gallina viva ad aliam partem perveniat?<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>Processus Poissonianus: Appropinquatio Processus Binomialis SummariumHaec lectio intendit in Processu Poissoniano ut appropinquationem ad Processum Binomialem, incipiens a definitione coefficientium et distributionis Poissonianae, quae derivatur ex eventu Bernoulliano cum magno numero conatuum et probabilitate singulari minutissima. Pars centralis huius lectionis tractat processus appropinquatos Poissonianos, tam spatiales quam temporales, utens exemplis particularum minimarum in liquido et [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":26422,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":16,"footnotes":""},"categories":[1298,1364],"tags":[],"class_list":["post-34172","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 v26.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Processus Poissonianus: Appropinquatio Processus Binomialis - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"Distribuionem Poissonianam intellege ut eventum ex processibus binomialibus ad limitem ductis obtentum.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"http:\/\/toposuranos.com\/material\/la\/processus-poissonianus-appropinquatio-processus-binomialis\/\" \/>\n<meta property=\"og:locale\" content=\"es_ES\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Processus Poissonianus: Appropinquatio Processus Binomialis\" \/>\n<meta property=\"og:description\" content=\"Distribuionem Poissonianam intellege ut eventum ex processibus binomialibus ad limitem ductis obtentum.\" \/>\n<meta property=\"og:url\" content=\"http:\/\/toposuranos.com\/material\/la\/processus-poissonianus-appropinquatio-processus-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=\"2021-05-27T13:00:10+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2025-08-16T11:05:48+00:00\" \/>\n<meta property=\"og:image\" content=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/04\/poisson-e1712962118751-1024x285.jpg\" \/>\n<meta name=\"author\" content=\"giorgio.reveco\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:title\" content=\"Processus Poissonianus: Appropinquatio Processus Binomialis\" \/>\n<meta name=\"twitter:description\" content=\"Distribuionem Poissonianam intellege ut eventum ex processibus binomialibus ad limitem ductis obtentum.\" \/>\n<meta name=\"twitter:image\" content=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/04\/poisson-e1712962118751.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\":\"http:\/\/toposuranos.com\/material\/la\/processus-poissonianus-appropinquatio-processus-binomialis\/#article\",\"isPartOf\":{\"@id\":\"http:\/\/toposuranos.com\/material\/la\/processus-poissonianus-appropinquatio-processus-binomialis\/\"},\"author\":{\"name\":\"giorgio.reveco\",\"@id\":\"http:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1\"},\"headline\":\"Processus Poissonianus: Appropinquatio Processus Binomialis\",\"datePublished\":\"2021-05-27T13:00:10+00:00\",\"dateModified\":\"2025-08-16T11:05:48+00:00\",\"mainEntityOfPage\":{\"@id\":\"http:\/\/toposuranos.com\/material\/la\/processus-poissonianus-appropinquatio-processus-binomialis\/\"},\"wordCount\":1300,\"commentCount\":0,\"publisher\":{\"@id\":\"http:\/\/toposuranos.com\/material\/#organization\"},\"image\":{\"@id\":\"http:\/\/toposuranos.com\/material\/la\/processus-poissonianus-appropinquatio-processus-binomialis\/#primaryimage\"},\"thumbnailUrl\":\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/04\/poisson-e1712962118751.jpg\",\"articleSection\":[\"Mathematica\",\"Probabilitates et Statistica\"],\"inLanguage\":\"es\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"http:\/\/toposuranos.com\/material\/la\/processus-poissonianus-appropinquatio-processus-binomialis\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"http:\/\/toposuranos.com\/material\/la\/processus-poissonianus-appropinquatio-processus-binomialis\/\",\"url\":\"http:\/\/toposuranos.com\/material\/la\/processus-poissonianus-appropinquatio-processus-binomialis\/\",\"name\":\"Processus Poissonianus: Appropinquatio Processus Binomialis - 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