Feuille d`exercices

◦
Z f(x) = 1
√2πexp(−x2
2)z > 0
F(z) = P[Z < z] = Zz
−∞
f(x)dx.
z1= 1,15 z2= 1,37 z3= 1,116 z4= 1,227
F(z1)F(z2)F(z3)F(z4)
P[z1< Z < z2]P[−z2< Z < −z1]P[z1< Z < 5] P[−z2< Z < z1]P[−z1< Z < z1]P[Z > z2]
P[Z < z1]P[Z < −z1]
z1z2z3F(z1) = 0,591 F(z2) = 0,93 F(z3) = 0,37
z1z2z3P[Z6z1] = 0,98 P[Z > z2] = 0,91 P[Z < z3] = 0,65
1,5
−1 1
−2 2
−3 3
µ= 123 σ= 9 X N(123; 9)
µ+ 1,5σ
µ−σ µ +σ
µ−2σ µ + 2 σ
µ−3σ µ + 3 σ
N(12,53; 1,34)
300
40 X
[10; 15[ [15; 20[ [20; 25[ [25; 30[ [30; 35[ [35; 40[ 9 48 89 97 51 6
m s X
XN(m;s)
X
µ'10,16
σ'4,32
XN(10,16; 4,32)
13
aP[X < a]'0,95
X
20 %
35 %
25%
n Sn
n= 18 pk=P[Sn6k]k= 0; 1; 2; 3
n= 150 P[30 6Sn642]
P[30 6Sn642]
SnP[30 6Sn642]
n= 200 P[44 6Sn675]
n= 150 aP[S150 < a]'0.03

X
X < 16,5 16,56X < 18,5 18,56X < 25 25 6X < 30 30 6X < 35 35 6X < 40 X>40
[−∞ ; 18,5[ [18,5 ; 25[ [25 ; 30[ [30 ; 35[ [35 ; 40[ [40 ; +∞[
3,5 49,2 32,3 10,7 3,1 1,2
XN(25; 5)
XN(25; 5)
P[X>35]
Pr[X>35]
Pr[X>35] P[X>35]
2,3%
4,3%
N(25; 5)
µ= 50 σ= 10
70
50000
60% n X
n= 28 XP[15 6X618]
n= 280
X
P[X>180] P[150 6X6185]