Quiz — 66224aa89353e_Corrigé_Séries n° 41-42 Probabilité-Variables aléatoires.pdf

Question 1 sur 5 10:00

[{"id":2464,"question":"Quelle est l'espérance d'une variable aléatoire X suivant une loi de Bernoulli de paramètre p ?","option_a":"E(X) = p","option_b":"E(X) = 1 - p","option_c":"E(X) = p(1 - p)","option_d":"E(X) = 1\/p","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'espérance d'une loi de Bernoulli est égale au paramètre p, car E(X) = 1×p + 0×(1-p) = p.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"E(X) = p\", \"b\": \"E(X) = 1 - p\", \"c\": \"E(X) = p(1 - p)\", \"d\": \"E(X","_debug_options_count":4},{"id":2465,"question":"Si X suit une loi binomiale B(n, p), quelle est la variance de X ?","option_a":"V(X) = np","option_b":"V(X) = np(1 - p)","option_c":"V(X) = n²p(1 - p)","option_d":"V(X) = p(1 - p)","option_e":"","option_f":"","bonne_reponse":"b","explication":"La variance d'une loi binomiale est V(X) = np(1 - p), car Var(X) = n×p×(1 - p) pour une loi de Bernoulli répétée n fois.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"V(X) = np\", \"b\": \"V(X) = np(1 - p)\", \"c\": \"V(X) = n²p(1 - p)\", \"","_debug_options_count":4},{"id":2466,"question":"Quelle est la propriété fondamentale de l'espérance mathématique ?","option_a":"E(aX + b) = aE(X) + b","option_b":"E(X + Y) = E(X) + E(Y) si X et Y sont indépendantes","option_c":"E(XY) = E(X)E(Y)","option_d":"E(X²) = [E(X)]²","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'espérance est linéaire : E(aX + b) = aE(X) + b, où a et b sont des constantes.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"E(aX + b) = aE(X) + b\", \"b\": \"E(X + Y) = E(X) + E(Y) si X et Y so","_debug_options_count":4},{"id":2467,"question":"Dans une loi normale N(μ, σ²), quel est le pourcentage de valeurs comprises entre μ - σ et μ + σ ?","option_a":"≈ 68%","option_b":"≈ 95%","option_c":"≈ 99,7%","option_d":"≈ 50%","option_e":"","option_f":"","bonne_reponse":"a","explication":"Environ 68% des valeurs d'une loi normale se situent dans l'intervalle [μ - σ, μ + σ], d'après la règle empirique.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"≈ 68%\", \"b\": \"≈ 95%\", \"c\": \"≈ 99,7%\", \"d\": \"≈ 50%\"}}","_debug_options_count":4},{"id":2468,"question":"Quelle est la formule de la variance d'une variable aléatoire discrète X ?","option_a":"V(X) = E(X²) - [E(X)]²","option_b":"V(X) = E(X²) + [E(X)]²","option_c":"V(X) = E(X)² - E(X²)","option_d":"V(X) = E(X) - [E(X)]²","option_e":"","option_f":"","bonne_reponse":"a","explication":"La variance se calcule par V(X) = E(X²) - [E(X)]², où E(X²) est l'espérance du carré de X.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"V(X) = E(X²) - [E(X)]²\", \"b\": \"V(X) = E(X²) + [E(X)]²\", \"c\": ","_debug_options_count":4}]