Probabilités

Ω
Ω∅
A
A∪B
A∩B
A∩B=∅
Ω
ΩP(A)
P(Ω) = 1
A A ⊂ΩP(A>
A1, A2, ..., Ann
P(A1∪A2∪... ∪An) =
n
P
k=0
P(Ak)
ΩP
A
ωi
P(∅)=0
PA= 1 −P(A)
P(A∪B) = P(A) + P(B)−P(A∩B)
A⊆B P (A)6P(B)
p(A) = A
Ω=
3
6=1 2
Ω
XΩ Ω R
ωΩx x ∈Rω∈Ω
X(ω) = xΩX=x
Ω
Ω

ΩP
x1, x2, ..., xnXΩ
X
xiX=xi
xi
ΩP
x1, x2, ..., xnXΩ
P(X=xi) = pi16i6n
E(X)E(X) =
n
P
i=1
pixi
V(X)V(X) =
n
P
i=1
pi(xi−E(X))2
σ(X)σ(X) = pV(X)
V(X) =
n
P
i=1
pix2
i−(E(X))2
B
A
N b
B a A s A
B
P(B) = b
NP(A) = a NP(A∩B) = r N
PB(A)
PB(A) = r
b
r
b=
r
N
b
N
PB(A) = P(A∩B)
P(B)
Ω
PΩP(B)6= 0 AΩ
PBA∈ΩPB(A) = P(A∩B)
P(B)
Ω
PB(A)
P(A|B)
PB(B)=1 PB(∅)=0 PB(A)=1−pB(A)
Ω
P(Ai)16i6nΩ
Ω
Ω
p(B) =
n
P
i=1
p(B∩Ai) =
n
P
i=1
pAi(B)p(Ai)
AΩP(A)6= 0 p(B) =
p(B∩A) + pB∩A

B
ΩP
Ω
A B P (A∩B) = P(A)×P(B)
ΩP
Ω
A B PA(B) = P(B)PB(A) = P(A)
A
B
A B Ω
P
A B
A B
A B
p(A∩B) = 0 p(A)×p(B)6= 0
Ω
(xi)16i6n(yi)16i6p
16i6n
16j6p X =xiY=yj
(X;Y) (xi)16i6n(yi)16i6p
p((X;Y)=(xi;yj)) = p(X=
xi)×p(Y=yj)
En
(Ei)16i6n
ΩiEiPi
i n
E(a1, a2, ..., an)
(Ei)16i6n
nEi
EP P ((a1, a2, ..., an)) =
n
Q
i=1
Pi(ai)