Variable aléatoire discrète - Fichier

X
X
n= 5 p=3
5P(A)=1−(2 5)4= 0.9744 P(B) =
4
2(2
5)2(3 5)2= 0.3456
X
n= 10 p=3
5np = 6 np(1−p) = 12 5
A
B
C
P(A)=1−(10
3)
(15
3)= 0.736 26
P(B) = (5
3)
(15
3)= 2.197 8 ×10−2
P(C) = (5
1)(10 2)
(15
3)= 0.494 51
X
X
X

X
X
n= 20 p= 0.75 np = 15
pnp(1 −p) = √15 ·0.25 X
20
150.75150.255= 0.202 33
X
3{0,1,2,3}
X[X=k]k
0 3 k60
3−k40
P[X= 3] = (60
3)
(100
3)
P[X= 2] = (60
2).(40 1)
(100
3)
P[X= 0] = (40
3)
(100
3)
X{0,1,2,3}
P[X=k] = 60
k.40 3−k
100
3
k=0:P[X= 0] '6.110 ×10−2
k=1:P[X= 1] '0.289
k=2:P[X= 2] '0.438
k=3:P[X= 3] '0.212
E(X) = 1.8E(X) = np

20
420
1
4X
k0 20 P[X=k] =
Ck
20(1
4)k(1 −1 4)20−k
E(X) = np = 5
n n + 1
p= 0.1
X
60 X
n= 60 p= 0.1
X λ = 60 ×
0.1=6 X E(X)=6
P[X=k] = 6ke−6
k!
P[X= 3] '0.9%; P[X= 4] '
13.4%; P[X= 5] = P[X= 6] '16.1%; P[X= 7] '13.8%; P[X= 8] '
10.3 %.
λ
K P [X=K−1] = KK−1e−K
(K−1)! =KKe−K
K!=P[X=K].
10
10 11 P[X≥10] = 1 −P9
k=0 6ke−6
k!'
8.392 ×10−2.
100
200
p=1
100
100p= 1 X
P[X≥1] = 1 −P[X= 0] = 1 −e−1'63%

200 P[X0≥1] =
1−e−2'86%.[X0= 1] [X0= 2]
0.14
0.14
2X
K
[X=K−1] [X=K].
X
X
P[X= 5]
P a
P(HU) = P(HU/P a)P(P a)+P(HU/nonP a)P(nonP a) =
0.3·0.75 + 0.4·0.7=0.505
P(P a/HU ) = P(HU/ P a)P(P a)/P (HU) =
0.4·0.7/0.505 = 0.554 46
X n = 10 p= 0.4
4
P[X= 5] = 10
5(0.3)5(0.7)5= 0.102 92
X
100
80

1−P[X= 0] = 1 −e−100
80 = 1 −e−5 4= 0.713 50
1−P[Y= 0] = 1 −e−300
80 = 0.976 48