1. Exercice 11
(a)
+∞ 1
f (x)dx = 1 → ax dx = 1
−∞ 0
1
ax 2 a 0
=1 → − =1 → a=2
2 0
2 2
(b)
1 1
E(x) = x · f (x)dx = x · 2x dx
0 0
1
2x 3 2 0 2
= = − =
3 0
3 3 3

2. Exercice 11 (suite..)
(c)
V (X ) = E(X 2 ) − E(X )2
1 1
E(X 2 ) = x2 · f (x) dx = x 2 · 2x dx
0 0
1
2x 4 2 0 2
= = − =
4 0
4 4 4
2
2 2 1
Donc V (X ) = − =
4 3 18