{"id":25385,"date":"2021-03-10T00:00:00","date_gmt":"2021-03-10T00:00:00","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=25385"},"modified":"2024-05-21T09:45:06","modified_gmt":"2024-05-21T09:45:06","slug":"processus-deterministes-et-indeterministes","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/fr\/processus-deterministes-et-indeterministes\/","title":{"rendered":"Processus D\u00e9terministes et Ind\u00e9terministes"},"content":{"rendered":"<div style=\"background-color:#F3F3F3; padding:20px;\">\n<center><\/p>\n<h1>Processus D\u00e9terministes et Ind\u00e9terministes, Probabilit\u00e9s et Hasard<\/h1>\n<p><\/p>\n<p style=\"text-align:center;\"><strong>R\u00e9sum\u00e9<\/strong><br \/><em>Dans cette classe d&#8217;introduction \u00e0 la Th\u00e9orie des Probabilit\u00e9s, nous explorerons la connexion entre les processus d\u00e9terministes et ind\u00e9terministes et leur relation avec les probabilit\u00e9s et le hasard. Nous verrons comment les processus dans la nature sont classifi\u00e9s en deux esp\u00e8ces mutuellement exclusives et comment on essaie de les comprendre \u00e0 travers des mod\u00e8les d\u00e9terministes et ind\u00e9terministes. De plus, nous examinerons comment le manque de contr\u00f4le sur l&#8217;environnement et les conditions initiales m\u00e8ne \u00e0 des processus ind\u00e9terministes et \u00e0 la n\u00e9cessit\u00e9 de traiter avec une multiplicit\u00e9 d&#8217;\u00e9tats possibles. Finalement, nous aborderons le sujet du hasard et des probabilit\u00e9s, en analysant l&#8217;exemple du lancement d&#8217;une pi\u00e8ce de monnaie et comment la compr\u00e9hension de la probabilit\u00e9 est obtenue \u00e0 partir d&#8217;exp\u00e9riences avec des r\u00e9sultats \u00e9quiprobables.<\/em><\/p>\n<p><\/center><br \/>\n<\/p>\n<p style=\"text-align:center;\"><strong>OBJECTIFS D&#8217;APPRENTISSAGE:<\/strong><br \/>\n\u00c0 la fin de cette classe, l&#8217;\u00e9tudiant sera capable de :\n<\/p>\n<ol>\n<li><strong>Comprendre<\/strong> la nature des mod\u00e8les et leur relation avec les processus d\u00e9terministes et ind\u00e9terministes.<\/li>\n<li><strong>Comprendre<\/strong> la relation entre le hasard et les processus ind\u00e9terministes.<\/li>\n<li><strong>Identifier<\/strong> les conditions n\u00e9cessaires pour qu&#8217;un processus soit consid\u00e9r\u00e9 comme al\u00e9atoire.<\/li>\n<li><strong>Identifier<\/strong> les r\u00e9sultats \u00e9quiprobables et comment ils sont utilis\u00e9s pour comprendre la probabilit\u00e9.<\/li>\n<\/ol>\n<p style=\"text-align:center;\"><strong>INDEX DES CONTENUS<\/strong><br \/>\n<a href=\"#1\">ID\u00c9ES DE BASE<\/a><br \/>\n<a href=\"#1\">PROCESSUS D\u00c9TERMINISTES ET IND\u00c9TERMINISTES DANS LA NATURE<\/a><br \/>\n<a href=\"#1\">LES PROBABILIT\u00c9S ET LE HASARD<\/a><\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/DsDU0MjD_XY\" 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>Id\u00e9es de Base<\/h2>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=DsDU0MjD_XY&amp;t=123s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #d00000;\">Pour commencer notre \u00e9tude sur la Th\u00e9orie des Probabilit\u00e9s,<\/span><\/strong><\/a> nous devons d&#8217;abord explorer la connexion qui existe entre les processus d\u00e9terministes et ind\u00e9terministes et leur relation avec les probabilit\u00e9s et le hasard. Les processus qui se produisent dans la nature sont classifi\u00e9s en deux esp\u00e8ces mutuellement exclusives : ou bien ils sont <strong>d\u00e9terministes<\/strong> ou bien <strong>ind\u00e9terministes.<\/strong> Un processus d\u00e9terministe est celui qui, \u00e9tant donn\u00e9es des <strong>conditions initiales,<\/strong> conduit toujours aux m\u00eames r\u00e9sultats. D&#8217;autre part, un processus est ind\u00e9terministe quand, pour les m\u00eames conditions initiales, il peut fournir une multiplicit\u00e9 de r\u00e9sultats possibles. Ces r\u00e9sultats possibles, qu&#8217;ils soient uniques ou multiples, sont \u00e9galement connus comme <strong>\u00e9tats.<\/strong> \u00c0 leur tour, on tente de comprendre les processus \u00e0 travers des mod\u00e8les, et ceux-ci sont, de mani\u00e8re analogue, d\u00e9terministes ou ind\u00e9terministes.<\/p>\n<p style=\"text-align: justify; color: #000000;\">C&#8217;est dans le contexte des processus ind\u00e9terministes que <strong>l&#8217;\u00e9tude des probabilit\u00e9s<\/strong> \u00e9merge. C&#8217;est une <strong>science formelle<\/strong> (comme la <a href=\"https:\/\/toposuranos.com\/category\/ciencias\/matematica\/logica\/\" rel=\"noopener\" target=\"_blank\"><strong>logique<\/strong><\/a>) avec laquelle nous pouvons extraire des informations sur la fr\u00e9quence \u00e0 laquelle un processus ind\u00e9terministe tend \u00e0 produire un certain \u00e9tat ou ensemble d&#8217;\u00e9tats.<\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h2>Processus D\u00e9terministes et Ind\u00e9terministes dans la Nature<\/h2>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=DsDU0MjD_XY&amp;t=288s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #d00000;\">Supposons que nous voulons mod\u00e9liser le processus de lancement d&#8217;un projectile.<\/span><\/strong><\/a> Si nous sommes dans un environnement contr\u00f4l\u00e9, la <strong>m\u00e9canique de Newton<\/strong> nous indique que pour chaque vitesse et position initiale, le projectile aura un lieu d\u00e9termin\u00e9 comme point d&#8217;impact, ce qui repr\u00e9sente un mod\u00e8le d\u00e9terministe de la r\u00e9alit\u00e9. Cependant, dans la vie r\u00e9elle, les environnements absolument contr\u00f4l\u00e9s n&#8217;existent pas, et ce que nous verrons est que le projectile tend \u00e0 tomber dans une certaine r\u00e9gion, ce qui implique une multiplicit\u00e9 d&#8217;\u00e9tats possibles.<\/p>\n<p><center><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/12\/basket.jpg\" alt=\"tir parabolique, Processus D\u00e9terministes et Ind\u00e9terministes\" width=\"500\" height=\"500\" class=\"aligncenter size-full wp-image-22067 lazyload\" \/><noscript><img decoding=\"async\" src=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/12\/basket.jpg\" alt=\"tir parabolique, Processus D\u00e9terministes et Ind\u00e9terministes\" width=\"500\" height=\"500\" class=\"aligncenter size-full wp-image-22067 lazyload\" \/><\/noscript><\/center><\/p>\n<p style=\"text-align: justify; color: #000000;\">Il est g\u00e9n\u00e9ralement dit que nos limitations pour contr\u00f4ler et mesurer \u00e0 la fois l&#8217;environnement et les conditions initiales ne nous permettent pas de d\u00e9terminer les \u00e9tats finaux d&#8217;un syst\u00e8me, ce qui nous oblige \u00e0 faire face \u00e0 une multiplicit\u00e9 d&#8217;entre eux et \u00e0 des mod\u00e8les non d\u00e9terministes. Au fur et \u00e0 mesure qu&#8217;un processus gagne en complexit\u00e9, il en va de m\u00eame pour le manque de contr\u00f4le sur l&#8217;environnement et les conditions initiales.<\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h2>Les probabilit\u00e9s et le hasard<\/h2>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=DsDU0MjD_XY&amp;t=561s\"><strong><span style=\"color: #d00000;\">Le hasard est une caract\u00e9ristique inh\u00e9rente aux processus ind\u00e9terministes.<\/span><\/strong><\/a> Un processus est dit <strong>al\u00e9atoire<\/strong> ou <strong>hasardeux<\/strong> lorsque, pour un certain ensemble de conditions initiales, aucun des \u00e9tats possibles ne semble se produire plus fr\u00e9quemment que les autres. L&#8217;exemple le plus simple est le lancement d&#8217;une pi\u00e8ce de monnaie. \u00c0 mesure que le nombre de lancers augmente, on observe que la fr\u00e9quence d&#8217;apparition des faces et des piles tend \u00e0 \u00eatre similaire. En d&#8217;autres termes :<\/p>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{N\\to \\infty} \\dfrac{C}{N} = \\lim_{N\\to \\infty} \\dfrac{S}{N} = \\dfrac{1}{2} <\/span>\n<p style=\"text-align: justify; color: #000000;\">o\u00f9 <span class=\"katex-eq\" data-katex-display=\"false\">N<\/span> est le nombre total de lancers, <span class=\"katex-eq\" data-katex-display=\"false\">C<\/span> et <span class=\"katex-eq\" data-katex-display=\"false\">S<\/span> sont le nombre de faces et de piles obtenus parmi les lancers <span class=\"katex-eq\" data-katex-display=\"false\">N<\/span>.<\/p>\n<p style=\"text-align: justify; color: #000000;\">Ce nombre est la <strong>probabilit\u00e9<\/strong> d&#8217;obtenir face ou pile, et sa compr\u00e9hension est obtenue en analysant les <strong>exp\u00e9riences aux r\u00e9sultats \u00e9quiprobables<\/strong>. Cela est l&#8217;essence des processus d\u00e9terministes et ind\u00e9terministes et leur relation avec les probabilit\u00e9s et le hasard.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Processus D\u00e9terministes et Ind\u00e9terministes, Probabilit\u00e9s et Hasard R\u00e9sum\u00e9Dans cette classe d&#8217;introduction \u00e0 la Th\u00e9orie des Probabilit\u00e9s, nous explorerons la connexion entre les processus d\u00e9terministes et ind\u00e9terministes et leur relation avec les probabilit\u00e9s et le hasard. Nous verrons comment les processus dans la nature sont classifi\u00e9s en deux esp\u00e8ces mutuellement exclusives et comment on essaie de [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":25367,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":5,"footnotes":""},"categories":[569,682],"tags":[],"class_list":["post-25385","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mathematiques","category-probabilites-et-statistiques"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Processus D\u00e9terministes et Ind\u00e9terministes - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"Apprends \u00e0 diff\u00e9rencier les Processus D\u00e9terministes et Ind\u00e9terministes dans la nature et comment ils influencent notre compr\u00e9hension du hasard\" \/>\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\/fr\/processus-deterministes-et-indeterministes\/\" \/>\n<meta property=\"og:locale\" content=\"es_ES\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Processus D\u00e9terministes et Ind\u00e9terministes\" \/>\n<meta property=\"og:description\" content=\"Apprends \u00e0 diff\u00e9rencier les Processus D\u00e9terministes et Ind\u00e9terministes dans la nature et comment ils influencent notre compr\u00e9hension du hasard\" \/>\n<meta property=\"og:url\" content=\"https:\/\/toposuranos.com\/material\/fr\/processus-deterministes-et-indeterministes\/\" \/>\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=\"2021-03-10T00:00:00+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2024-05-21T09:45:06+00:00\" \/>\n<meta property=\"og:image\" content=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/12\/DETERMINISTASVSINDETERMINISTAS-1024x585.jpg\" \/>\n<meta name=\"author\" content=\"giorgio.reveco\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:title\" content=\"Processus D\u00e9terministes et Ind\u00e9terministes\" \/>\n<meta name=\"twitter:description\" content=\"Apprends \u00e0 diff\u00e9rencier les Processus D\u00e9terministes et Ind\u00e9terministes dans la nature et comment ils influencent notre compr\u00e9hension du hasard\" \/>\n<meta name=\"twitter:image\" content=\"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/12\/DETERMINISTASVSINDETERMINISTAS.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=\"4 minutos\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/toposuranos.com\/material\/fr\/processus-deterministes-et-indeterministes\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/toposuranos.com\/material\/fr\/processus-deterministes-et-indeterministes\/\"},\"author\":{\"name\":\"giorgio.reveco\",\"@id\":\"https:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1\"},\"headline\":\"Processus D\u00e9terministes et Ind\u00e9terministes\",\"datePublished\":\"2021-03-10T00:00:00+00:00\",\"dateModified\":\"2024-05-21T09:45:06+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/toposuranos.com\/material\/fr\/processus-deterministes-et-indeterministes\/\"},\"wordCount\":830,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/toposuranos.com\/material\/#organization\"},\"image\":{\"@id\":\"https:\/\/toposuranos.com\/material\/fr\/processus-deterministes-et-indeterministes\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/12\/DETERMINISTASVSINDETERMINISTAS.jpg\",\"articleSection\":[\"Math\u00e9matiques\",\"Probabilit\u00e9s et Statistiques\"],\"inLanguage\":\"es\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/toposuranos.com\/material\/fr\/processus-deterministes-et-indeterministes\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/toposuranos.com\/material\/fr\/processus-deterministes-et-indeterministes\/\",\"url\":\"https:\/\/toposuranos.com\/material\/fr\/processus-deterministes-et-indeterministes\/\",\"name\":\"Processus D\u00e9terministes et Ind\u00e9terministes - 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