{"id":301,"date":"2014-10-11T14:08:24","date_gmt":"2014-10-11T12:08:24","guid":{"rendered":"http:\/\/wordpress.callac.online\/index.php\/le-lancer-dun-de-equilibre-avec-r\/"},"modified":"2023-10-14T20:14:28","modified_gmt":"2023-10-14T18:14:28","slug":"le-lancer-dun-de-equilibre-avec-r","status":"publish","type":"page","link":"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/le-logiciel-r\/les-tirages-avec-r\/le-lancer-dun-de-equilibre-avec-r\/","title":{"rendered":"Le lancer d&rsquo;un d\u00e9 \u00e9quilibr\u00e9 avec R"},"content":{"rendered":"<h2>Pr\u00e9sentation<\/h2>\n<p>On souhaite simuler le lancer d&rsquo;un d\u00e9 \u00e9quilibr\u00e9.<\/p>\n<h2>Obtenir un \u00e9chantillon<\/h2>\n<p>Cr\u00e9ons la liste des faces :<\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\">faces&lt;-1:6 \nfaces<\/pre>\n<p><code><br \/>\n[1] 1 2 3 4 5 6<br \/>\n<\/code><\/p>\n<p>Choisissons une taille d&rsquo;\u00e9chantillon :<\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\">tailleEchantillon&lt;-10000 \ntaillEchantillon<\/pre>\n<p><code><br \/>\n[1] 10000<br \/>\n<\/code><\/p>\n<p>Construisons cet \u00e9chantillon avec la fonction <em>sample<\/em> :<\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\">echantillon&lt;-sample(faces,tailleEchantillon,replace=TRUE)<\/pre>\n<p>Voici ces 100 premi\u00e8res valeurs :<\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\">head(echantillon,100)<\/pre>\n<p><code><br \/>\n[1] 3 2 2 5 3 1 2 3 3 1 1 1 1 3 5 1 1 5 6 2 5 1 1 1 5 3 4 5 1 6 1 6 1 2 3 2 5 4 1 3 5 1 2 6 3<br \/>\n[46] 1 6 6 5 5 1 2 1 3 5 4 2 4 1 5 1 3 1 5 6 4 4 6 6 6 1 1 5 6 5 4 1 1 2 2 4 5 5 1 1 6 2 1 6 5<br \/>\n[91] 1 2 3 5 4 3 1 5 4 3<br \/>\n<\/code><\/p>\n<h2>Analyse de l&rsquo;\u00e9chantillon<\/h2>\n<p>Pour obtenir le tableau des effectifs :<\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\">tabEffectifs&lt;-table(echantillon) \ntabEffectifs<\/pre>\n<p><code><br \/>\nechantillon<br \/>\n1    2    3    4    5    6<br \/>\n1687 1684 1651 1693 1672 1613<br \/>\n<\/code><\/p>\n<p>Pour obtenir la tableau des fr\u00e9quences :<\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\">tabFrequences&lt;-prop.table(tabEffectifs)<\/pre>\n<p><code><br \/>\nechantillon<br \/>\n1      2      3      4      5      6<br \/>\n0.1687 0.1684 0.1651 0.1693 0.1672 0.1613<br \/>\n<\/code><\/p>\n<p>On peut alors les repr\u00e9senter par un diagramme en b\u00e2tons.<\/p>\n<p>Le diagramme basique est le suivant :<\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\">barplot(tabEffectifs)<\/pre>\n<p><img loading=\"lazy\" decoding=\"async\" class=\" aligncenter size-full wp-image-914\" src=\"http:\/\/wordpress.callac.online\/wp-content\/uploads\/2014\/10\/png_lancer_un_de_01.png\" alt=\"lancer_un_de_01.png\" width=\"579\" height=\"360\" align=\"center\" srcset=\"https:\/\/wordpress.callac.online\/wp-content\/uploads\/2014\/10\/png_lancer_un_de_01.png 579w, https:\/\/wordpress.callac.online\/wp-content\/uploads\/2014\/10\/png_lancer_un_de_01-300x187.png 300w\" sizes=\"auto, (max-width: 579px) 100vw, 579px\" \/><\/p>\n<h2>Utilisation d&rsquo;un script<\/h2>\n<p>Pour plus de facilit\u00e9, il suffit de sauvegarder le code suivant dans un fichier script et de le lancer. On pourra si besoin changer la valeur de la taille de l&rsquo;\u00e9chantillon.<\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\">###################################################################################\n###################################################################################\n# Simulation du lancer d'un d\u00e9 \u00e9quilibr\u00e9\n###################################################################################\n###################################################################################\n\n\n# Liste des faces\nfaces&lt;-1:6\nprint(\"Liste des faces :\")\nprint(faces)\n\n# Taille de l'\u00e9chantillon\ntailleEchantillon&lt;-1000   #-----------------------------------A modidier\nprint(\"Taille de l'\u00e9chantillon\")\nprint(tailleEchantillon)\n\n# Cr\u00e9ation de l'\u00e9chantillon\nechantillon&lt;-sample(faces,tailleEchantillon,replace=TRUE)\n\n# Tableau des fr\u00e9quences\ntabEffectifs&lt;-table(echantillon)\nprint(\"Tableau des effectifs\")\nprint(tabEffectifs)\n\n# diagramme en b\u00e2tons des effectifs\nbarplot(tabEffectifs)\n\n\ntabFrequences&lt;-prop.table(tabEffectifs)\nprint(\"Tableau des fr\u00e9quences\")\nprint(tabFrequences)\n\n\ntitreEffectifs&lt;-paste(\"Lancer d'un d\u00e9 \u00e9quilibr\u00e9\",\"\\n\",\n                      \"Taille de l'\u00e9chantillon : \",bquote(.(tailleEchantillon)))\n\nbarplot(tabEffectifs,ylim=c(0,tailleEchantillon\/5),las=1,col=\"blue\"\n        , xlab=\"Faces\",ylab=\"Effectifs\",\n        ,main=titreEffectifs)\n\nabline(a=tailleEchantillon\/6,b=0,lwd=1.5,col=\"grey\",lty=2)\n\n\n# diagramme en b\u00e2tons des fr\u00e9quences\ntitreFrequences&lt;-paste(\"Lancer d'un d\u00e9 \u00e9quilibr\u00e9\",\"\\n\",\n                       \"Taille de l'\u00e9chantillon : \",bquote(.(tailleEchantillon)))\n\nbarplot(tabFrequences,ylim=c(0,0.2),las=1,col=\"brown\"\n        , xlab=\"Faces\",ylab=\"Fr\u00e9quences\",\n        ,main=titreFrequences)\n\nabline(a=1\/6,b=0,lwd=1.5,col=\"grey\",lty=2)<\/pre>\n<p>On obtient dans la console :<\/p>\n<p><code><br \/>\n[1] \"Liste des faces :\"<br \/>\n[1] 1 2 3 4 5 6<br \/>\n[1] \"Taille de l'\u00e9chantillon\"<br \/>\n[1] 1000<br \/>\n[1] \"Tableau des effectifs\"<br \/>\nechantillon<br \/>\n1   2   3   4   5   6<br \/>\n187 153 170 162 144 184<br \/>\n[1] \"Tableau des fr\u00e9quences\"<br \/>\nechantillon<br \/>\n1     2     3     4     5     6<br \/>\n0.187 0.153 0.170 0.162 0.144 0.184<br \/>\n<\/code><\/p>\n<p>On obtient les deux graphiques suivants.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\" aligncenter size-full wp-image-915\" src=\"http:\/\/wordpress.callac.online\/wp-content\/uploads\/2014\/10\/png_lancer_de_equilibre_02.png\" alt=\"lancer_de_equilibre_02.png\" width=\"579\" height=\"360\" align=\"center\" srcset=\"https:\/\/wordpress.callac.online\/wp-content\/uploads\/2014\/10\/png_lancer_de_equilibre_02.png 579w, https:\/\/wordpress.callac.online\/wp-content\/uploads\/2014\/10\/png_lancer_de_equilibre_02-300x187.png 300w\" sizes=\"auto, (max-width: 579px) 100vw, 579px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\" aligncenter size-full wp-image-916\" src=\"http:\/\/wordpress.callac.online\/wp-content\/uploads\/2014\/10\/png_lancer_de_equilibre_03.png\" alt=\"lancer_de_equilibre_03.png\" width=\"579\" height=\"360\" align=\"center\" srcset=\"https:\/\/wordpress.callac.online\/wp-content\/uploads\/2014\/10\/png_lancer_de_equilibre_03.png 579w, https:\/\/wordpress.callac.online\/wp-content\/uploads\/2014\/10\/png_lancer_de_equilibre_03-300x187.png 300w\" sizes=\"auto, (max-width: 579px) 100vw, 579px\" \/><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Pr\u00e9sentation On souhaite simuler le lancer d&rsquo;un d\u00e9 \u00e9quilibr\u00e9. Obtenir un \u00e9chantillon Cr\u00e9ons la liste des faces : faces&lt;-1:6 faces [1] 1 2 3 4 5 6 Choisissons une taille&hellip;<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":2085,"menu_order":1,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-301","page","type-page","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.1.1 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Le lancer d&#039;un d\u00e9 \u00e9quilibr\u00e9 avec R - Maths &amp; Num\u00e9rique<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/le-logiciel-r\/les-tirages-avec-r\/le-lancer-dun-de-equilibre-avec-r\/\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Le lancer d&#039;un d\u00e9 \u00e9quilibr\u00e9 avec R - Maths &amp; Num\u00e9rique\" \/>\n<meta property=\"og:description\" content=\"Pr\u00e9sentation On souhaite simuler le lancer d&rsquo;un d\u00e9 \u00e9quilibr\u00e9. 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