{"id":34482,"date":"2019-08-20T10:20:18","date_gmt":"2019-08-20T09:20:18","guid":{"rendered":"https:\/\/groupe-reussite.fr\/?page_id=34482"},"modified":"2022-07-20T11:45:47","modified_gmt":"2022-07-20T10:45:47","slug":"cours-en-ligne-exercices-variables-aleatoires-densite-ecs1","status":"publish","type":"page","link":"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-exercices-variables-aleatoires-densite-ecs1\/","title":{"rendered":"Variables al\u00e9atoires \u00e0 densit\u00e9 en ECG1 &#8211; Exercices"},"content":{"rendered":"<div class=\"Latex_page\">\n<section class=\"has_ae_slider elementor-element elementor-section-full_width elementor-reverse-mobile elementor-section-stretched elementor-section-height-default elementor-section-height-default ae-bg-gallery-type-default elementor-section elementor-top-section\">\n<div class=\"elementor-container elementor-column-gap-no\">\n<div class=\"elementor-row\">\n<div class=\"elementor-column-wrap elementor-element-populated colone_elementor\">\n\t\t<div data-elementor-type=\"page\" data-elementor-id=\"88449\" class=\"elementor elementor-88449\">\n\t\t\t\t\t\t<div class=\"elementor-inner\">\n\t\t\t\t<div class=\"elementor-section-wrap\">\n\t\t\t\t\t\t\t\t\t<section class=\"has_ae_slider elementor-section elementor-top-section elementor-element elementor-element-30229867 elementor-section-content-bottom elementor-hidden-mobile elementor-section-boxed elementor-section-height-default elementor-section-height-default ae-bg-gallery-type-default\" data-id=\"30229867\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-no\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_ae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-6a356d88 sticky_badeau_colone strick_col elementor-hidden-mobile ae-bg-gallery-type-default\" data-id=\"6a356d88\" data-element_type=\"column\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t<div class=\"elementor-column-wrap\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_ae_slider elementor-section elementor-top-section elementor-element elementor-element-7ccae7e7 elementor-hidden-mobile elementor-section-boxed elementor-section-height-default elementor-section-height-default ae-bg-gallery-type-default\" data-id=\"7ccae7e7\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-no\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_ae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-6e77d559 strick_col ae-bg-gallery-type-default\" data-id=\"6e77d559\" data-element_type=\"column\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-17b9742a elementor-widget elementor-widget-heading\" data-id=\"17b9742a\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<p class=\"elementor-heading-title elementor-size-default\"><a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-ecs1\/\">Cours en ligne Maths en ECG1<\/a><\/p>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-73a4684f elementor-widget elementor-widget-heading\" data-id=\"73a4684f\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<p class=\"elementor-heading-title elementor-size-default\">Chapitres Maths en ECG1<\/p>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6ebcc4f9 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"6ebcc4f9\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-exercices-strategies-calcul-ecs1\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Strat\u00e9gie de Calcul<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-7ff87283 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"7ff87283\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-espace-probabilise-ecs1\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Espace Probabilis\u00e9<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-57d652c3 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"57d652c3\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-raisonnement-ensembliste-ecs1\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Raisonnement et Vocabulaire Ensembliste<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-65809d15 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"65809d15\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-nombres-complexes-ecs1\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Nombres Complexes<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-55f287a9 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"55f287a9\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-polynomes-ecs1\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Polyn\u00f4mes<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5de71e57 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"5de71e57\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-suites-reelles-ecs1\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Suites R\u00e9elles<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-2e13b47d elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"2e13b47d\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-matrices-ecs1\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Matrices<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-b80cd71 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"b80cd71\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-espaces-vectoriels-ecs1\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Espaces Vectoriels et Applications Lin\u00e9aires<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-515ac59b elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"515ac59b\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-fonctions-variables-reelles-ecs1\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Fonctions R\u00e9elles \u00e0 Variables R\u00e9elles<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-37b7a48c elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"37b7a48c\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-probabilites-univers-fini-ecs1\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Probabilit\u00e9s (univers infini)<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-a165fbf elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"a165fbf\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-formules-taylor-developpements-limites-ecs1\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Formules de Taylor et D\u00e9veloppements Limit\u00e9s<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-444d2f06 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"444d2f06\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-extrema-convexite-ecs1\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Extrema et convexit\u00e9<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f57142c elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"f57142c\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-series-numeriques-ecs1\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">S\u00e9ries Num\u00e9riques<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-51fc1a2 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"51fc1a2\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-integration-ecs1\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Int\u00e9gration<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-b8561ca elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"b8561ca\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-variables-aleatoires-finies-ecs1\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Variables Al\u00e9atoires Finies<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-c2a9e2f elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"c2a9e2f\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-variables-aleatoires-discretes-ecs1\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Variables Al\u00e9atoires Discr\u00e8tes<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6a7fab3 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"6a7fab3\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-variables-aleatoires-densite-ecs1\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Variables Al\u00e9atoires \u00e0 Densit\u00e9<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-8b2a052 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"8b2a052\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-convergences-approximations-ecs1\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Convergence et Approximations<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-3275bf4d elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"3275bf4d\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/nous-contacter\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">CONTACTEZ-NOUS<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_ae_slider elementor-section elementor-top-section elementor-element elementor-element-7b89084 elementor-hidden-desktop elementor-hidden-tablet elementor-section-boxed elementor-section-height-default elementor-section-height-default ae-bg-gallery-type-default\" data-id=\"7b89084\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-no\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_ae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-78ae9e4 ae-bg-gallery-type-default\" data-id=\"78ae9e4\" data-element_type=\"column\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-2e97065 elementor-widget elementor-widget-heading\" data-id=\"2e97065\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<p class=\"elementor-heading-title elementor-size-default\"><a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-ecs1\/\">Cours en ligne Maths en ECG1<\/a><\/p>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-eafadd7 elementor-widget elementor-widget-heading\" data-id=\"eafadd7\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<p class=\"elementor-heading-title elementor-size-default\">Chapitres Maths en ECG1<\/p>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-8180968 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"8180968\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-exercices-strategies-calcul-ecs1\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Strat\u00e9gie de Calcul<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-38acf6a elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"38acf6a\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-espace-probabilise-ecs1\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Espace Probabilis\u00e9<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-b7ca681 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"b7ca681\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-raisonnement-ensembliste-ecs1\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Raisonnement et Vocabulaire Ensembliste<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-33a3c17 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"33a3c17\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-nombres-complexes-ecs1\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Nombres Complexes<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-ccd9c89 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"ccd9c89\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-polynomes-ecs1\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Polyn\u00f4mes<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-51de2d5 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"51de2d5\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-suites-reelles-ecs1\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Suites R\u00e9elles<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-ef0680e elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"ef0680e\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-matrices-ecs1\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Matrices<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5bb4a9c elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"5bb4a9c\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-espaces-vectoriels-ecs1\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Espaces Vectoriels et Applications Lin\u00e9aires<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f4868e8 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"f4868e8\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-fonctions-variables-reelles-ecs1\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Fonctions R\u00e9elles \u00e0 Variables R\u00e9elles<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-87d53c5 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"87d53c5\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-probabilites-univers-fini-ecs1\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Probabilit\u00e9s (univers infini)<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-87744be elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"87744be\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-formules-taylor-developpements-limites-ecs1\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Formules de Taylor et D\u00e9veloppements Limit\u00e9s<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-41f4808 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"41f4808\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-extrema-convexite-ecs1\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Extrema et convexit\u00e9<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-77acc16 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"77acc16\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-series-numeriques-ecs1\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">S\u00e9ries Num\u00e9riques<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-672728a elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"672728a\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-integration-ecs1\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Int\u00e9gration<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-52a2f88 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"52a2f88\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-variables-aleatoires-finies-ecs1\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Variables Al\u00e9atoires Finies<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6c1102b elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"6c1102b\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-variables-aleatoires-discretes-ecs1\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Variables Al\u00e9atoires Discr\u00e8tes<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-cd78ac0 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"cd78ac0\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-variables-aleatoires-densite-ecs1\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Variables Al\u00e9atoires \u00e0 Densit\u00e9<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-52d8afc elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"52d8afc\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-convergences-approximations-ecs1\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Convergence et Approximations<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-b364a45 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"b364a45\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/nous-contacter\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">CONTACTEZ-NOUS<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\n<\/div>\n<div class=\"elementor-column-wrap elementor-element-populated colone_latex\">\n<div class=\"style_pag\" style=\"color: #000; font-family: 'Lato', Sans-serif;\">\n<div class=\"elementor-text-editor elementor-clearfix\">\n<h1 class=\"Latex_page_title\">Exercices : Variables al\u00e9atoires \u00e0 densit\u00e9 en ECG1<\/h1>\n<\/div>\n<p class=\"colone_latex_ancres\"><a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-variables-aleatoires-densite-ecs1\/\">R\u00e9sum\u00e9 de cours<\/a> <a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-exercices-variables-aleatoires-densite-ecs1\/\">Exercices<\/a> <a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-corriges-variables-aleatoires-densite-ecs1\/\">Corrig\u00e9s<\/a><\/p>\n<p class=\"colone_latex_ancres\"><a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-ecs1\/\">Cours en ligne de Maths en ECG1<\/a><\/p>\n<h2 style=\"text-align: justify;\">Exercices &#8211; Variables al\u00e9atoires \u00e0 densit\u00e9<\/h2>\n<h3 style=\"text-align: justify;\"><b>Exercice :\u00a0<\/b><\/h3>\n<p style=\"text-align: justify;\">On consid\u00e8re une variable al\u00e9atoire <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-d4ee28752517d6062a3ca0314890342d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#88;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: 0px;\"\/> suivant la loi normale centr\u00e9e r\u00e9duite (d&rsquo;esp\u00e9rance nulle et de variance <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-4868771cbc422b5818f85500909ce433_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"7\" style=\"vertical-align: -1px;\"\/>) et on note <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-5b2be26c0c1341f54b29baddda771346_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#105;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"11\" style=\"vertical-align: -4px;\"\/> la fonction de r\u00e9partition de <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-212bfc4b9affbdd85917cfdfb9392590_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#88;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"19\" style=\"vertical-align: 0px;\"\/><\/p>\n<p style=\"text-align: justify;\">On pose <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-366ed63bae2123399538a0dd6922737c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#89;&#32;&#61;&#32;&#92;&#108;&#101;&#102;&#116;&#124;&#32;&#88;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"62\" style=\"vertical-align: -4px;\"\/> et on admet que <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-82606c3098bb09002088b0f6f9ffbb2a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#89;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"\/> est une variable al\u00e9atoire. On note <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-10dde56bca59feee81abbe98966ae038_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#95;&#89;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"22\" style=\"vertical-align: -3px;\"\/> la fonction de r\u00e9partition de <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-26d5ea5357e6f0b3cea073ba692e72cc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#89;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"15\" style=\"vertical-align: 0px;\"\/><\/p>\n<p style=\"text-align: justify;\"><b>1) a)<\/b>\u00a0Exprimer, pour tout <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-f5da98d6fbe4a18efdf673816d53a14c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#32;&#62;&#32;&#48;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"47\" style=\"vertical-align: -4px;\"\/> <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-6a7445610d17d278adf922ab7e322668_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#95;&#89;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#32;&#120;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"49\" style=\"vertical-align: -4px;\"\/> \u00e0 l&rsquo;aide de <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-239231c10a5e5741ca2a6e87dd200af0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#105;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#32;&#120;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"44\" style=\"vertical-align: -4px;\"\/><\/p>\n<p style=\"text-align: justify;\"><b>\u00a0 \u00a0 \u00a0b)<\/b>\u00a0En d\u00e9duire que <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-82606c3098bb09002088b0f6f9ffbb2a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#89;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"\/> est une variable al\u00e9atoire \u00e0 densit\u00e9 et donner une densit\u00e9 <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-d0ad17f2a834e08eaf191b89a8c42d11_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#95;&#89;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"20\" style=\"vertical-align: -4px;\"\/> de <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-26d5ea5357e6f0b3cea073ba692e72cc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#89;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"15\" style=\"vertical-align: 0px;\"\/><\/p>\n<p style=\"text-align: justify;\"><b>\u00a0 \u00a0 \u00a0c)<\/b>\u00a0Montrer que <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-82606c3098bb09002088b0f6f9ffbb2a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#89;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"\/> poss\u00e8de une esp\u00e9rance et la calculer.<\/p>\n<p style=\"text-align: justify;\"><b>\u00a0 \u00a0 \u00a0d)<\/b> Montrer que <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-82606c3098bb09002088b0f6f9ffbb2a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#89;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"\/> poss\u00e8de une variance et la calculer.<\/p>\n<p style=\"text-align: justify;\"><b>2)<\/b>\u00a0On consid\u00e8re la <a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-fonctions-variables-reelles-ecs1\/\">fonction<\/a> d\u00e9finie par :<\/p>\n<p style=\"text-align: justify;\">\n<p class=\"ql-center-displayed-equation\" style=\"line-height: 65px;\"><span class=\"ql-right-eqno\"> &nbsp; <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-ceb6ac3155fec71e36ab3538642ed5fc_l3.png\" height=\"65\" width=\"201\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#091;&#103;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#32;&#120;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#32;&#61;&#32;&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#99;&#97;&#115;&#101;&#115;&#125;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#32;&#101;&#94;&#123;&#45;&#32;&#120;&#125;&#32;&#125;&#123;&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#112;&#105;&#32;&#120;&#125;&#125;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#105;&#125;&#32;&#92;&#59;&#32;&#120;&#62;&#32;&#48;&#32;&#92;&#92;&#32;&#48;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#105;&#125;&#32;&#92;&#59;&#32;&#120;&#32;&#92;&#108;&#101;&#32;&#48;&#32;&#92;&#101;&#110;&#100;&#123;&#99;&#97;&#115;&#101;&#115;&#125;&#46;&#92;&#093;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\n<\/p>\n<p style=\"text-align: justify;\"><b>\u00a0 \u00a0 \u00a0a)<\/b>\u00a0V\u00e9rifier, en justifiant que l&rsquo;on peut utiliser le changement de variable <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-a9b2496ccf1fd61f1668a8c0b5e0c817_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#117;&#32;&#61;&#92;&#115;&#113;&#114;&#116;&#123;&#50;&#116;&#125;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"68\" style=\"vertical-align: -4px;\"\/> que :<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-1e9a896c084629e9c6806b2b66a3f44b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#105;&#110;&#116;&#95;&#48;&#94;&#123;&#43;&#92;&#105;&#110;&#102;&#116;&#121;&#125;&#32;&#103;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#32;&#116;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#32;&#100;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"90\" style=\"vertical-align: -6px;\"\/> <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-e6c2108ce1f89b74244f7f7f2cbdd9ba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#61;&#32;&#92;&#115;&#113;&#114;&#116;&#123;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#92;&#112;&#105;&#125;&#32;&#125;&#32;&#92;&#105;&#110;&#116;&#95;&#48;&#94;&#123;&#43;&#92;&#105;&#110;&#102;&#116;&#121;&#125;&#32;&#101;&#94;&#123;&#45;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#117;&#94;&#50;&#125;&#123;&#50;&#125;&#32;&#125;&#32;&#100;&#117;&#32;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"56\" width=\"159\" style=\"vertical-align: -15px;\"\/><\/p>\n<p style=\"text-align: justify;\"><b>\u00a0 \u00a0 \u00a0b)<\/b>\u00a0En d\u00e9duire que <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-d208fd391fa57c168dc0f151de829fee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\"\/> est une densit\u00e9.<\/p>\n<p style=\"text-align: justify;\"><b>3)<\/b>\u00a0Dans cette question, <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-761fd3ca09ad29ba6f86aa02ff540254_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#90;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\"\/> est une variable al\u00e9atoire de densit\u00e9 <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-d208fd391fa57c168dc0f151de829fee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\"\/> de fonction de r\u00e9partition <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-f21f9d7dcef4071511444f1abf900650_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#71;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\"\/><\/p>\n<p style=\"text-align: justify;\"><b>\u00a0 \u00a0 \u00a0a)<\/b>\u00a0On note <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-425afd936e3c81efac0f7f089bcea992_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#84;&#61;&#92;&#115;&#113;&#114;&#116;&#123;&#50;&#32;&#90;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"74\" style=\"vertical-align: -2px;\"\/> et on admet que <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-f9ed275b0bf1633b7ee83b78fcc28273_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#84;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"13\" style=\"vertical-align: 0px;\"\/> est une variable \u00e0 densit\u00e9. Exprimer la fonction de r\u00e9partition <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-3fc71d70bf7ac22f6d69d527d42f5c49_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#95;&#84;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"21\" style=\"vertical-align: -3px;\"\/> de <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-f9ed275b0bf1633b7ee83b78fcc28273_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#84;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"13\" style=\"vertical-align: 0px;\"\/> en fonction de <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-30a79c32f18567063fe44716929e7ced_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#71;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"\/> puis en d\u00e9duire une densit\u00e9 <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-d31bde1d031314416b4f6343eeb8167c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#95;&#84;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"19\" style=\"vertical-align: -4px;\"\/> de <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-f9ed275b0bf1633b7ee83b78fcc28273_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#84;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"13\" style=\"vertical-align: 0px;\"\/> et v\u00e9rifier que <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-f9ed275b0bf1633b7ee83b78fcc28273_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#84;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"13\" style=\"vertical-align: 0px;\"\/> suit la m\u00eame loi que <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-26d5ea5357e6f0b3cea073ba692e72cc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#89;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"15\" style=\"vertical-align: 0px;\"\/><\/p>\n<p style=\"text-align: justify;\"><b>\u00a0 \u00a0 \u00a0b)<\/b> En d\u00e9duire que <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-761fd3ca09ad29ba6f86aa02ff540254_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#90;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\"\/> poss\u00e8de une esp\u00e9rance et la calculer.<\/p>\n<p>&nbsp;<\/p>\n\t\t<div data-elementor-type=\"section\" data-elementor-id=\"84983\" class=\"elementor elementor-84983\">\n\t\t\t\t\t<div class=\"elementor-section-wrap\">\n\t\t\t\t\t\t\t\t<section class=\"has_ae_slider elementor-section elementor-inner-section elementor-element elementor-element-51d9c4d elementor-section-content-bottom full_width elementor-section-full_width elementor-section-height-min-height elementor-section-height-default ae-bg-gallery-type-default\" data-id=\"51d9c4d\" data-element_type=\"section\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-narrow\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_ae_slider elementor-column elementor-col-66 elementor-inner-column elementor-element elementor-element-610eeeb9 ae-bg-gallery-type-default\" data-id=\"610eeeb9\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-5bf69eb8 elementor-widget elementor-widget-heading\" data-id=\"5bf69eb8\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">COURS DE MATHS<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-49568da4 elementor-widget elementor-widget-heading\" data-id=\"49568da4\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">Les meilleurs professeurs particuliers<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1eb9e0cb elementor-widget elementor-widget-heading\" data-id=\"1eb9e0cb\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">Pour progresser et r\u00e9ussir<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-15c3e28d elementor-align-left elementor-mobile-align-center elementor-widget elementor-widget-button\" data-id=\"15c3e28d\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/cours-particuliers\/maths\/tous-niveaux\/france\/\" target=\"_blank\" class=\"elementor-button-link elementor-button elementor-size-md\" role=\"button\" id=\"CTA_PRD_CP\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Cours particuliers maths<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1a5c10e7 elementor-widget elementor-widget-text-editor\" data-id=\"1a5c10e7\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<p style=\"text-align: left\"><b>Avis Google France <\/b><span style=\"color: #e5a430\"><b>\u2605\u2605\u2605\u2605\u2605<\/b><\/span><b> 4,9 sur 5<\/b><\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"has_ae_slider elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-6913d4fe ae-bg-gallery-type-default\" data-id=\"6913d4fe\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\n<p>&nbsp;<\/p>\n<p>L&rsquo;ensemble de nos cours en ligne de maths en ECG1 proposent aussi des exercices et corrig\u00e9s sur de nombreux autres chapitres :<\/p>\n<ul style=\"text-align: justify;\">\n<li><a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-convergences-approximations-ecs1\/\">les convergences et les approximations<\/a><\/li>\n<li><a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-exercices-strategies-calcul-ecs1\/\">les strat\u00e9gies de calcul<\/a><\/li>\n<li><a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-espace-probabilise-ecs1\/\">les espaces probabilis\u00e9s et les nouveaux r\u00e9sultats<\/a><\/li>\n<li><a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-raisonnement-ensembliste-ecs1\/\">raisonnement et vocabulaire ensembliste<\/a><\/li>\n<li><a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-nombres-complexes-ecs1\/\">les nombres complexes<\/a><\/li>\n<\/ul>\n<div class=\"style_pag\" style=\"color: #000; font-family: 'Lato', Sans-serif;\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Exercices : Variables al\u00e9atoires \u00e0 densit\u00e9 en ECG1 R\u00e9sum\u00e9 de cours Exercices Corrig\u00e9s Cours en ligne de Maths en ECG1 Exercices &#8211; Variables al\u00e9atoires \u00e0 densit\u00e9 Exercice :\u00a0 On consid\u00e8re une variable al\u00e9atoire suivant la loi normale centr\u00e9e r\u00e9duite (d&rsquo;esp\u00e9rance nulle et de variance ) et on note la fonction de r\u00e9partition de On pose [&hellip;]<\/p>\n","protected":false},"author":7,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"yoast_head":"<!-- This site is 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