{"id":832,"date":"2023-07-28T14:48:22","date_gmt":"2023-07-28T14:48:22","guid":{"rendered":"https:\/\/statorials.org\/nl\/binominale-distributiepython\/"},"modified":"2023-07-28T14:48:22","modified_gmt":"2023-07-28T14:48:22","slug":"binominale-distributiepython","status":"publish","type":"post","link":"https:\/\/statorials.org\/nl\/binominale-distributiepython\/","title":{"rendered":"Hoe binomiale distributie in python te gebruiken"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">De <a href=\"https:\/\/statorials.org\/nl\/binominale-verdeling-1\/\" target=\"_blank\" rel=\"noopener\">binominale verdeling<\/a> is een van de meest gebruikte verdelingen in de statistiek. Het beschrijft de waarschijnlijkheid van het behalen van <em>k<\/em> successen in <em>n<\/em> binomiale experimenten.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Als een <a href=\"https:\/\/statorials.org\/nl\/willekeurige-variabelen\/\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\"random variable (opens in a new tab)\">willekeurige variabele<\/a> <em>X<\/em> een binominale verdeling volgt, kan de kans dat <em>X<\/em> = <em>k<\/em> succes wordt gevonden met de volgende formule:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>P(X=k) = <sub>n<\/sub> C <sub>k<\/sub> * p <sup>k<\/sup> * (1-p) <sup>nk<\/sup><\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Goud:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>n:<\/strong> aantal pogingen<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>k:<\/strong> aantal successen<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>p:<\/strong> kans op succes bij een bepaalde proef<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong><sub>n<\/sub> C <sub>k<\/sub> :<\/strong> het aantal manieren om <em>k<\/em> successen te behalen in <em>n<\/em> pogingen<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">In deze tutorial wordt uitgelegd hoe u de binomiale distributie in Python gebruikt.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Hoe een binominale verdeling te genereren<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">U kunt een array met waarden genereren die een binominale verdeling volgt met behulp van de functie <a href=\"https:\/\/numpy.org\/doc\/stable\/reference\/random\/generated\/numpy.random.binomial.html\" target=\"_blank\" rel=\"noopener\">random.binomial<\/a> van de numpy-bibliotheek:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #107d3f;\">from<\/span> numpy <span style=\"color: #107d3f;\">import<\/span> random\n\n<span style=\"color: #008080;\">#generate an array of 10 values that follows a binomial distribution<\/span>\nrandom.binomial(n=10, p=.25, size=10)\n\narray([5, 2, 1, 3, 3, 3, 2, 2, 1, 4])\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Elk getal in de resulterende tabel vertegenwoordigt het aantal &#8222;successen&#8220; dat werd ondervonden in de loop van <strong>10<\/strong> pogingen waarbij de kans op succes in een bepaalde poging <strong>0,25<\/strong> was.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Hoe kansen te berekenen met behulp van een binominale verdeling<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">U kunt ook vragen over binomiale waarschijnlijkheid beantwoorden met behulp van de <a href=\"https:\/\/docs.scipy.org\/doc\/scipy\/reference\/generated\/scipy.stats.binom.html\" target=\"_blank\" rel=\"noopener\">binomfunctie<\/a> van de scipy-bibliotheek.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Vraag 1:<\/strong> Nathan maakt 60% van zijn vrije worppogingen. Als hij twaalf vrije worpen maakt, wat is dan de kans dat hij er precies tien maakt?<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #107d3f;\">from<\/span> scipy.stats <span style=\"color: #107d3f;\">import<\/span> binom\n\n<span style=\"color: #008080;\">#calculate binomial probability<\/span>\nbinom.pmf(k= <span style=\"color: #107d3f;\">10<\/span> , n= <span style=\"color: #107d3f;\">12<\/span> , p= <span style=\"color: #107d3f;\">0.6<\/span> )\n\n0.0639\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">De kans dat Nathan precies 10 vrije worpen maakt is <strong>0,0639<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Vraag 2:<\/strong> Marty gooit 5 keer een eerlijke munt op. Wat is de kans dat de munt 2 keer of minder kop krijgt?<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #107d3f;\">from<\/span> scipy.stats <span style=\"color: #107d3f;\">import<\/span> binom\n\n<span style=\"color: #008080;\">#calculate binomial probability<\/span>\nbinom.cdf(k= <span style=\"color: #107d3f;\">2<\/span> , n= <span style=\"color: #107d3f;\">5<\/span> , p= <span style=\"color: #107d3f;\">0.5<\/span> )\n\n0.5\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">De kans dat de munt 2 keer of minder kop oplevert is <strong>0,5<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Vraag 3:<\/strong> We weten dat 70% van de mensen een bepaalde wet steunt. Als er willekeurig 10 individuen worden geselecteerd, wat is dan de kans dat tussen de 4 en 6 van hen de wet steunen?<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #107d3f;\">from<\/span> scipy.stats <span style=\"color: #107d3f;\">import<\/span> binom\n\n<span style=\"color: #008080;\">#calculate binomial probability<\/span>\nbinom.cdf(k= <span style=\"color: #107d3f;\">6<\/span> , n= <span style=\"color: #107d3f;\">10<\/span> , p= <span style=\"color: #107d3f;\">0.7<\/span> ) - binom.cdf(k= <span style=\"color: #107d3f;\">3<\/span> , n= <span style=\"color: #107d3f;\">10<\/span> , p= <span style=\"color: #107d3f;\">0.7<\/span> )\n\n0.3398\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">De kans dat tussen de 4 en 6 willekeurig geselecteerde individuen de wet ondersteunen is <strong>0,3398<\/strong> .<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Hoe een binominale verdeling te visualiseren<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">U kunt een binominale verdeling in Python visualiseren met behulp van de <strong>seaborn-<\/strong> en <strong>matplotlib-<\/strong> bibliotheken:<\/span> <\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #107d3f;\">from<\/span> numpy <span style=\"color: #107d3f;\">import<\/span> random\n<span style=\"color: #107d3f;\">import<\/span> matplotlib.pyplot <span style=\"color: #107d3f;\">as<\/span> plt\n<span style=\"color: #107d3f;\">import<\/span> seaborn <span style=\"color: #107d3f;\">as<\/span> sns\n\nx = random.binomial(n= <span style=\"color: #107d3f;\">10<\/span> , p= <span style=\"color: #107d3f;\">0.5<\/span> , size= <span style=\"color: #107d3f;\">1000<\/span> )\n\nsns.distplot(x, hist= <span style=\"color: #107d3f;\">True<\/span> , kde= <span style=\"color: #107d3f;\">False<\/span> )\n\nplt.show()\n<\/strong><\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-9215 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/binomepython1.png\" alt=\"Binomiale verdelingsplot in Python\" width=\"396\" height=\"262\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Thee<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>De binominale verdeling is een van de meest gebruikte verdelingen in de statistiek. Het beschrijft de waarschijnlijkheid van het behalen van k successen in n binomiale experimenten. Als een willekeurige variabele X een binominale verdeling volgt, kan de kans dat X = k succes wordt gevonden met de volgende formule: P(X=k) = n C k [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"class_list":["post-832","post","type-post","status-publish","format-standard","hentry","category-gids"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Hoe de binominale verdeling in Python te gebruiken - Statorials<\/title>\n<meta name=\"description\" content=\"Een eenvoudige uitleg over het gebruik van de binomiale verdeling in Python.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/statorials.org\/nl\/binominale-distributiepython\/\" \/>\n<meta property=\"og:locale\" content=\"de_DE\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Hoe de binominale verdeling in Python te gebruiken - Statorials\" \/>\n<meta property=\"og:description\" content=\"Een eenvoudige uitleg over het gebruik van de binomiale verdeling in Python.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/nl\/binominale-distributiepython\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-28T14:48:22+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/binomepython1.png\" \/>\n<meta name=\"author\" content=\"Dr.benjamin anderson\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Verfasst von\" \/>\n\t<meta name=\"twitter:data1\" content=\"Dr.benjamin anderson\" \/>\n\t<meta name=\"twitter:label2\" content=\"Gesch\u00e4tzte Lesezeit\" \/>\n\t<meta name=\"twitter:data2\" content=\"2\u00a0Minuten\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/nl\/binominale-distributiepython\/\",\"url\":\"https:\/\/statorials.org\/nl\/binominale-distributiepython\/\",\"name\":\"Hoe de binominale verdeling in Python te gebruiken - Statorials\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/nl\/#website\"},\"datePublished\":\"2023-07-28T14:48:22+00:00\",\"dateModified\":\"2023-07-28T14:48:22+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/nl\/#\/schema\/person\/d4b8842173cca1bb62cdec41860e4219\"},\"description\":\"Een eenvoudige uitleg over het gebruik van de binomiale verdeling in Python.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/nl\/binominale-distributiepython\/#breadcrumb\"},\"inLanguage\":\"de\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/nl\/binominale-distributiepython\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/nl\/binominale-distributiepython\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Thuis\",\"item\":\"https:\/\/statorials.org\/nl\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Hoe binomiale distributie in python te gebruiken\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/statorials.org\/nl\/#website\",\"url\":\"https:\/\/statorials.org\/nl\/\",\"name\":\"Statorials\",\"description\":\"Uw gids voor statistische competentie\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/statorials.org\/nl\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"de\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/statorials.org\/nl\/#\/schema\/person\/d4b8842173cca1bb62cdec41860e4219\",\"name\":\"Dr.benjamin anderson\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"de\",\"@id\":\"https:\/\/statorials.org\/nl\/#\/schema\/person\/image\/\",\"url\":\"http:\/\/statorials.org\/nl\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"contentUrl\":\"http:\/\/statorials.org\/nl\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"caption\":\"Dr.benjamin anderson\"},\"description\":\"Ik ben Benjamin, een gepensioneerde hoogleraar statistiek die nu een toegewijde Statorials-lesgever is. 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