Lois de distributions

0 0.02
7.97 8.03
D
p= 1−P[7.97 ≤D≤8.03] P[7.97 ≤D≤
8.03] = P[−0.03
0.02 ≤D−8 0.02 ≤0.03 0.02 ] = F(1.5)−F(−1.5) = 0.866 4
p= 13.4%
X
X m = 0.3σ= 0.1
X
X
n1
n Xi
i Z n
n= 20 Z
X
P[X≤0.36] = P[X−0.3
0.1≤0.6] = 0.726,72.6
X0.25 0.35
P[0.25 ≤X≤0.35] = 2F(0.5) −1=0.383 38.3
n= 20 Z=PXi
E(Z) = 20m= 6 Z= 20σ= 0.2
n1n
n= 2000
N
N
N

n= 2000 N
P[N≤3] = 0.86
P[N≤3] '0.76,
P[N≤3] '0.85.
m= 0.6σ= 0.1X
X
X14.3
56 165
34 165 180
10 180
10 000
182
X m σ Y =X−m
σ
P[X≤165] P[X−m
σ≤165−m σ]=0,56
F(0.15) = 0.5596
P[X≥180] P[X−m
σ≥180−m σ]=0.1P[X−m σ≤
180−m
σ] = 0.9F(1.28) = 0.8997.
m σ 165−m
σ=
0.15 180−m
σ= 1.28 σ'13.27 m'163 P[X≥182] =
P[X−m
σ≥182−m σ]=1−F(1.43) = 0.0764
10 000
764
4
365

B(365; 4
365 ),
B(6; 1
2)3 2
p= 0.02
X
X
X P [18 ≤X≤
22]
X B(1000; 0.02)
√19.6
m=
20 √19.6P[18 ≤X≤22] = P[(17.5−20)/√19.6≤
(X−20)/√19.6≤(22.5−20)/√19.6] '0.428
P[(17 −20)/√19.6≤(X−
20)/√19.6≤(22 −20)/√19.6] '0.348
P[18 ≤X≤22] '0.423
P[18 ≤X≤22] '0.427
p= 0,05
p0= 0,02 500 150
350
X
X
X

F U
D
P(F) = P(F/U)P(U) + P(F/D)P(D) = 2.9%
P(U/F ) = P(F/U)P(U))/P (F) = 51.7%
X
B(1000; 5%) σ=√47.5
N(50; σ)
X P [(47.5−50)/σ ≤(X−
50)/σ ≤(52.5−50)/σ]'28.3%
X
X
X
X B(180; 1
6)
σ=√25 = 5
N(30 σ)
X P [(28.5−30)/σ ≤(X−30)/σ ≤
(32.5−30)/σ]'30.94%
X30.86%
20
200 X
X
X45 X
30 50
2Y
100
Y5Y
1 4
0.2.
X n = 200 p= 0.2;
np = 40 X
m= 40 √40 ×0.8=4√2

P[X≥45] = 1 −P[X≤44] '1−F(44.5−40
4√2)'21%
45
200 P[30 ≤X≤50] 'F(50.5−m
σ)−F(29.5−m σ)'
93.6%
2
n= 100 p= 0.02
λ= 2 P[Y≥5] =
1−P[Y≤4] = 1 −P4
k=0
e−22k
k!5
P[1 ≤Y≤4] = P4
k=1
e−22k
k!'0.812
p
n
p= 0.10 n= 700
0.75
p= 0.50 n= 300
0.75
B(700; 0.1) N(70; √63)
P[60 ≤X≤80] = P[−10/√63 ≤X≤10/√63] '2F(10.5/√63)−
1=0.814
81.4
1,12×700 = 784
aX a
a P [aX ≥784] ≥0.75 : P[aX ≤
784] ≤0.25 : a= 784/64.642 = 12.128
1,12 ×300 = 336
bX
b X