{"id":237964,"date":"2022-06-02T17:12:26","date_gmt":"2022-06-02T15:12:26","guid":{"rendered":"https:\/\/sherpas.com\/blog\/?p=237964"},"modified":"2024-08-28T22:47:23","modified_gmt":"2024-08-28T20:47:23","slug":"couples-de-variables-aleatoires-discretes","status":"publish","type":"post","link":"https:\/\/sherpas.com\/blog\/couples-de-variables-aleatoires-discretes\/","title":{"rendered":"M\u00e9thode : couples de variables al\u00e9atoires discr\u00e8tes"},"content":{"rendered":"\n

Vous \u00e9tudiez actuellement la notion de couples de variables al\u00e9atoires discr\u00e8tes<\/strong> ? Gr\u00e2ce \u00e0 ce cours d\u00e9di\u00e9 \u00e0 la notion de couples de variables al\u00e9atoires discr\u00e8tes<\/strong>, vous allez pouvoir apprendre des m\u00e9thodologies efficaces pour r\u00e9ussir vos prochaines interrogations orales et \u00e9crites sur cette notion !<\/p>\n

Pour approfondir davantage vos comp\u00e9tences et \u00e9largir votre horizon en math\u00e9matiques, prenez un cours de soutien scolaire en math\u00e9matiques<\/strong><\/a> et devenez un as des statistiques et des probabilit\u00e9s. \ud83d\udd22<\/p>\n\n\n\n

M\u00e9thode : Donner la loi d’un couple de variables al\u00e9atoires discr\u00e8tes<\/h2>\n\n\n\n
<\/p>\nOn dispose de $\"n\"$ bo\u00eetes num\u00e9rot\u00e9es de $\"1\"$ \u00e0 $\"n\"$ . La bo\u00eete $\"k\"$ contient $\"k\"$ boules num\u00e9rot\u00e9es de $\"1\"$ \u00e0 $\"k\"$ . On choisit au hasard une bo\u00eete, puis une boule dans cette bo\u00eete. Soit $\"X\"$ le num\u00e9ro de la bo\u00eete et $\"Y\"$ le num\u00e9ro de la boule.
\nDonnons la loi du couple $\"\left( X, Y \right)\"$ .
\nOn rappelle que donner la loi d’un couple de variables al\u00e9atoires, c’est donner son support (les valeurs prises par le couple) et les probabilit\u00e9s que le couple prenne chacune des valeurs.\n
On a $\"\left( X, Y \right) \left( \Omega \right) = \big\{(i,j),\; i\geq j\big\}\"$ . <\/li>\n
Soit $\"\left( i , j \right) \in [[1, n]]^2\"$ . D’apr\u00e8s le protocole, on a \n
<\/span> <\/span> $\"\[\mathbb{P} \left( \left( X = i \right) \cap \left( Y = j \right) \right) = \dfrac{1}{ni} .\]\"$ <\/p> <\/li>\n\n\n\n
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$\"livre$ <\/a><\/figure>\n<\/div>\n\n\n\n
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Cet article est extrait de l’ouvrage Maths MPSI-MP2I. Tout-en-un : cours, m\u00e9thodes, entra\u00eenement et corrig\u00e9s <\/a><\/em>(\u00e9ditions Vuibert, juin 2021) \u00e9crit par E. Thomas, S. Bellec, G. Boutard. ISBN n\u00b09782311408720<\/em><\/p>\n\n <\/div>\n <\/section>\n<\/div>\n<\/div>\n\n\n
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\n Tu as aim\u00e9 cet article ?<\/span>\n <\/div>\n <\/div>\n","protected":false},"excerpt":{"rendered":"
Vous \u00e9tudiez actuellement la notion de couples de variables al\u00e9atoires discr\u00e8tes ? Gr\u00e2ce \u00e0 ce cours d\u00e9di\u00e9 \u00e0 (…)<\/p>\n","protected":false},"author":158,"featured_media":163471,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"category":[803,810],"tag":[78,345,783],"class_list":["post-237964","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-apprendre-matiere","category-maths","tag-prepa","tag-prepa-scientifique","tag-probabilites"],"acf":[],"_links":{"self":[{"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/posts\/237964","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/users\/158"}],"replies":[{"embeddable":true,"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/comments?post=237964"}],"version-history":[{"count":0,"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/posts\/237964\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/media\/163471"}],"wp:attachment":[{"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/media?parent=237964"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/category?post=237964"},{"taxonomy":"tag","embeddable":true,"href":"https:\/\/sherpas.com\/blog\/wp-json\/wp\/v2\/tag?post=237964"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}