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Copyright © 2011 @Gebr@Tic - Tous droits réservés-Hichem Khazri 1
Lycée Rue A.Amara Hichem Khazri Le Kef
Mai20104
eSc-tec1
CORRECTION DU DEVOIR DE SYNTHESE N°3
EXERCICE N°1 (5pts)
Semaine n° 1 2 3 4 5 6 7 8 9 10
Recette du lundi :X
46 63 56 60 56 52 50 48 49 57
Recette de samedi :Y
75 92 85 86 84 74 70 68 69 81
1)
2) G(53.7,78.4)
3) a) G1(56.2 ,84.4) G2(51.2,72.4) b) (G1G2) :Y =2.4X −50.48
c) X=66 sig Y=2.4*66-50.48=107.92 4) a) Y=5.17X+1.36
b) Y=1.36X+5.17=94.39=95
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Copyright © 2011 @Gebr@Tic - Tous droits réservés-Hichem Khazri 2 EXERCICE N°2(3pts)
1) a)
3 3 3 5
( ) 1
10 P A C
=C =
2 1
2 3 3
( ) 10 10
P B =C xC =
b)
1 2 1 1 1
1 2 1 1 2 3
( ) 10 10
C xC C xC xC
P S = + =
2) a) 5 3 7 5
( ) ( ) .( )
10 10
k k k
P X =k =C − loi binomiale de paramètre (5, 3/10)
b) 3 3
( ) 5
10 2
E x = x = =1.5 3 7 21
( ) 5
10 10 20
V X = x x = =1.05
EXERCICE N°3(4pts) 1) X ( )Ω = − −
{
2, 1, 0,1, 2, 4}
2)
2 8
2 14
( 2) 28
91 P X C
= − =C =
1 1
8 2
2 14
( 1) 16
91 P X C xC
= − = C =
2 2 2 14
( 0) 1
91 P X C
= =C =
1 1
8 4
2 14
( 1) 32
91 P X C xC
= = C =
1 1
4 2
2 14
( 2) 8
91 P X C xC
= = C =
2 4 2 14
( 4) 6
91 P X C
= =C =
xi -2 -1 0 1 2 4
Pi 28/91 16/91 1/91 32/91 8/91 6/91
3) E x( )=0 jeu équitable EXERCICE N°4(4pts)
1) / 4
0
² 4
(2 1)
I + =J
∫
π x + dx =π 16+ π 2)2 1 ' 2 ' cos 2 v=1sin 2
2
u x u
v x x
= + =
= Remarque : cos 2x =cos ²x −sin ²x
/ 4 / 4 0 0
1(2 1) sin 2 sin 2
2 4
I J x x xdx
π π π
− = + −
∫
=3)
² 4 16 4 I J I J
π π
π +
+ =
− =
sig
² 8 32
² 32 I J
π π
π +
=
=
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Copyright © 2011 @Gebr@Tic - Tous droits réservés-Hichem Khazri 3 EXERCICE N°5(4pts)
Courbe non demandée
1) lim g
+∞ = −∞ limg 1
−∞ =
2) b)
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Copyright © 2011 @Gebr@Tic - Tous droits réservés-Hichem Khazri 4 c) g(0)=0
d)
