{"id":2954,"date":"2020-05-18T09:09:21","date_gmt":"2020-05-18T07:09:21","guid":{"rendered":"http:\/\/jhmaths.fr\/?page_id=2954"},"modified":"2025-06-02T07:05:43","modified_gmt":"2025-06-02T05:05:43","slug":"variables-aleatoires","status":"publish","type":"page","link":"https:\/\/jhmaths.fr\/index.php\/premiere-technologique\/variables-aleatoires\/","title":{"rendered":"Variables al\u00e9atoires"},"content":{"rendered":"\n<h1 class=\"wp-block-heading\">R\u00e9p\u00e9tition de deux \u00e9preuves al\u00e9atoires ind\u00e9pendantes<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">Lors de la r\u00e9p\u00e9tition de deux \u00e9preuves ind\u00e9pendantes, la probabilit\u00e9 \\(P ( A \\cap B)\\) est le produit des probabilit\u00e9s le long des branches passant par \\(A\u00a0 \\) et par \\(B \\)<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"436\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/05\/deux-epreuves-1024x436.png\" alt=\"\" class=\"wp-image-2955\" srcset=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/05\/deux-epreuves-1024x436.png 1024w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/05\/deux-epreuves-300x128.png 300w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/05\/deux-epreuves-768x327.png 768w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/05\/deux-epreuves-806x343.png 806w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/05\/deux-epreuves-558x237.png 558w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/05\/deux-epreuves-655x279.png 655w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/05\/deux-epreuves-820x349.png 820w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/05\/deux-epreuves.png 1081w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"Calculer une probabilit\u00e9 sur une exp\u00e9rience \u00e0 deux \u00e9preuves (2) - Premi\u00e8re Techno\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/xeuRc8WlQn4?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<h1 class=\"wp-block-heading\">Loi de Bernoulli et variables al\u00e9atoires<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">Une \u00e9preuve de Bernoulli de param\u00e8tre \\(p\\) donne un succ\u00e8s \\((S) \\) avec une probabilit\u00e9 \\(p\\) et un \u00e9chec \\( ( \\overline{S} )\\) avec une probabilit\u00e9 \\(1-p\\)<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"328\" height=\"325\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/05\/bernoulli.png\" alt=\"\" class=\"wp-image-2958\" srcset=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/05\/bernoulli.png 328w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/05\/bernoulli-300x297.png 300w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/05\/bernoulli-150x150.png 150w\" sizes=\"auto, (max-width: 328px) 100vw, 328px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Lorsqu&rsquo;on r\u00e9p\u00e8te plusieurs exp\u00e9riences de Bernoulli, on peut compter le nombre de succ\u00e8s dans une variable al\u00e9atoire \\(X\\) et calculer la probabilit\u00e9 d&rsquo;obtenir un nombre \\(x_i\\) de succ\u00e8s (on \u00e9crit alors \\(P(X=x_i)\\))<\/p>\n\n\n\n<h1 class=\"wp-block-heading\">Loi de probabilit\u00e9, esp\u00e9rance<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">La loi de probabilit\u00e9 de \\(X\\) est\u00a0 l&rsquo;ensemble des valeurs qu&rsquo;elle prend associ\u00e9es aux probabilit\u00e9s correspondantes (souvent repr\u00e9sent\u00e9es en tableau)<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td>\\(x_i\\)<\/td><td>\\(x_1\\)<\/td><td>\\(x_2\\)<\/td><td>&#8230;<\/td><td><\/td><\/tr><tr><td>\\(p_i=P(X=x_i)\\)<\/td><td>\\(p_1\\)<\/td><td>\\(p_2\\)<\/td><td><\/td><td><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"D\u00e9terminer la loi de probabilit\u00e9 d&#039;une variable al\u00e9atoire (1) - Premi\u00e8re\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/2Ge_4hclPnI?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">L&rsquo;esp\u00e9rance de \\(X\\) est le nombre<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(E(X)=x_1 \\times P(X=x_1) + x_2 \\times P(X=x_2) + x_3 \\times P(X=x_3) \\times &#8230;\\)<\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"Calculer une esp\u00e9rance - Premi\u00e8re\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/AcWVxHgtWp4?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">Quizz<\/h3>\n\n\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-68\" class=\"h5p-iframe\" data-content-id=\"68\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"1STHR variables al\u00e9atoires\"><\/iframe><\/div>\n","protected":false},"excerpt":{"rendered":"<p>R\u00e9p\u00e9tition de deux \u00e9preuves al\u00e9atoires ind\u00e9pendantes Lors de la r\u00e9p\u00e9tition de deux \u00e9preuves ind\u00e9pendantes, la probabilit\u00e9 \\(P ( A \\cap B)\\) est le produit des probabilit\u00e9s le long des branches passant par \\(A\u00a0 \\) et par \\(B \\) Loi de Bernoulli et variables al\u00e9atoires Une \u00e9preuve de Bernoulli de param\u00e8tre \\(p\\) donne un succ\u00e8s \\((S) [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":2319,"menu_order":9,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"folder":[],"class_list":["post-2954","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/pages\/2954","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/comments?post=2954"}],"version-history":[{"count":11,"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/pages\/2954\/revisions"}],"predecessor-version":[{"id":4070,"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/pages\/2954\/revisions\/4070"}],"up":[{"embeddable":true,"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/pages\/2319"}],"wp:attachment":[{"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/media?parent=2954"}],"wp:term":[{"taxonomy":"folder","embeddable":true,"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/folder?post=2954"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}