{"id":2356,"date":"2020-12-01T18:54:08","date_gmt":"2020-12-01T17:54:08","guid":{"rendered":"http:\/\/caneri.gmollet.free.fr\/?page_id=2356"},"modified":"2023-09-13T16:07:11","modified_gmt":"2023-09-13T14:07:11","slug":"activite-xiv-variables-aleatoires","status":"publish","type":"page","link":"https:\/\/courscaneri.ovh\/?page_id=2356","title":{"rendered":"Activit\u00e9 XIV – Variables al\u00e9atoires"},"content":{"rendered":"

On consid\u00e8re une variable al\u00e9atoire X<\/code> et sa loi de probabilit\u00e9s.<\/p>\n\n\n\n\n\n
\"x_i\"<\/code><\/th>\n\"x_0\"<\/code><\/th>\n\"x_1\"<\/code><\/th>\n\"x_2\"<\/code><\/th>\n…<\/th>\n\"x_{n-1}\"<\/code><\/th>\n\"x_n\"<\/code><\/th>\n<\/tr>\n<\/thead>\n
\"\mathbb{P}\left(X=x_i\right)\"<\/code><\/td>\n\"p_0\"<\/code><\/td>\n\"p_1\"<\/code><\/td>\n\"p_2\"<\/code><\/td>\n…<\/td>\n\"p_{n-1}\"<\/code><\/td>\n\"p_n\"<\/code><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Le but est de cr\u00e9er trois fonctions en Python retournant l’esp\u00e9rance, la variance et l’\u00e9cart type de la variable al\u00e9atoire \"X\"<\/code>.<\/p>\n

I. Esp\u00e9rance de la variable al\u00e9atoire \"X\"<\/code><\/h2>\n

Cr\u00e9er une fonction esperance<\/code> qui prend en param\u00e8tres une liste valeurs<\/code> des valeurs prises par \"X\"<\/code> et une liste probabilites<\/code> des probabilit\u00e9s correspondantes. Cette fonction retournera l’esp\u00e9rance de \"X\"<\/code>.<\/p>\n

II. Variance de la variable al\u00e9atoire \"X\"<\/code><\/h2>\n

Cr\u00e9er une fonction variance<\/code> qui prend en param\u00e8tres une liste valeurs<\/code> des valeurs prises par \"X\"<\/code> et une liste probabilites<\/code> des probabilit\u00e9s correspondantes. Cette fonction retournera la variance de \"X\"<\/code>.<\/p>\n

III. Ecart Type de la variable al\u00e9atoire \"X\"<\/code><\/h2>\n

Cr\u00e9er une fonction ecartType<\/code> qui prend en param\u00e8tres une liste valeurs<\/code> des valeurs prises par \"X\"<\/code> et une liste probabilites<\/code> des probabilit\u00e9s correspondantes. Cette fonction retournera l’\u00e9cart type de \"X\"<\/code>.<\/p>\n

IV. Tests<\/h2>\n

On pourra tester nos fonctions avec la loi ci-dessous:<\/p>\n\n\n\n\n\n
\"x_i\"<\/code><\/th>\n1<\/code><\/th>\n2<\/code><\/th>\n3<\/code><\/th>\n4<\/code><\/th>\n5<\/code><\/th>\n6<\/code><\/th>\n<\/tr>\n<\/thead>\n
\"\mathbb{P}\left(X=x_i\right)\"<\/code><\/td>\n0,1<\/code><\/td>\n0,1<\/code><\/td>\n0,1<\/code><\/td>\n0,1<\/code><\/td>\n0,1<\/code><\/td>\n0,5<\/code><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
>>> esperance([1, 2, 3, 4, 5, 6], [0.1, 0.1, 0.1, 0.1, 0.1, 0.5])\r\n4.5\r\n>>> variance([1, 2, 3, 4, 5, 6], [0.1, 0.1, 0.1, 0.1, 0.1, 0.5])\r\n3.25\r\n>>> ecartType(([1, 2, 3, 4, 5, 6], [0.1, 0.1, 0.1, 0.1, 0.1, 0.5])\r\n1.8027756377319946<\/code><\/pre>\n","protected":false},"excerpt":{"rendered":"
On consid\u00e8re une variable al\u00e9atoire X et sa loi de probabilit\u00e9s. … … Le but est de cr\u00e9er trois fonctions en Python retournant l’esp\u00e9rance, la variance et l’\u00e9cart type de la variable al\u00e9atoire . I. Esp\u00e9rance de la variable al\u00e9atoire Cr\u00e9er une fonction esperance qui prend en param\u00e8tres une liste valeurs des valeurs prises par […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":287,"menu_order":1,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-2356","page","type-page","status-publish","czr-hentry"],"_links":{"self":[{"href":"https:\/\/courscaneri.ovh\/index.php?rest_route=\/wp\/v2\/pages\/2356","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courscaneri.ovh\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/courscaneri.ovh\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/courscaneri.ovh\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/courscaneri.ovh\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2356"}],"version-history":[{"count":3,"href":"https:\/\/courscaneri.ovh\/index.php?rest_route=\/wp\/v2\/pages\/2356\/revisions"}],"predecessor-version":[{"id":3942,"href":"https:\/\/courscaneri.ovh\/index.php?rest_route=\/wp\/v2\/pages\/2356\/revisions\/3942"}],"up":[{"embeddable":true,"href":"https:\/\/courscaneri.ovh\/index.php?rest_route=\/wp\/v2\/pages\/287"}],"wp:attachment":[{"href":"https:\/\/courscaneri.ovh\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2356"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}