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n personnes se répartissent au hasasrd dans les 3 hôtels d'un village, chaque hôtel disposant d'au moins n places. On désigne par X (respectivement Y, Z) le nombre de personnes allant dans l'hôtel A (B, C).X, Y, Z ~ Bin(n, 1/3)X + Y = X + Y = var(X + Y) =Sans calculer 𝔼[XY], donner la valeur de ρ(X, Y) :
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