Bonjour,
Univers des probabilités et variable aléatoire
X = 1+2 = 3
X = 1+3 = 4
X = 1+4 = 5
X = 1+5 = 6
X = 2+3 = 5
X = 2+4 = 6
X = 2+5 = 7
X = 3 + 4 = 7
X = 3+5 = 8
X = 4 + 5 = 9
a. Loi de probabilité:
P(X = 3) = P(X = 4) = P(X = 8) = P(X = 9) = 1/10
P(X = 5) = P(X = 6) = P(X = 7) = 2/10 = 1/5
b. E(X) = somme xi * P(xi)
E(X) = (3 + 4 + 8 + 9) * 1/10 + (5 + 6 + 7) * 2/10 = 24/10 + 36/10 = 60/10 = 6
V(X) = Somme (xi - E(X))² P(xi)
V(X) = ((6 - 3)² + (6 - 4)² + (8 - 6)² + (9 - 6)²)/10 + ((7 - 6)² + (7 - 5)²)/5
V(X) = (9 + 4 + 4 + 9)/10 + (4 + 4)/5 = (26 + 16)/10 = 4,2
