Probabilités, cours, première S - MathsFG

•
•
xii
i
E={x1;x2;. . . ;xr}
E xi
pi
•i06pi61
•p1+p2+. . . +pn= 1
pixi
{x1;x2;. . . ;xn}
n
•fixif1+f2+. . . +fr= 1
06fi61
•n
pi
12
100 = 0,12 f1+f2+. . . +f6= 1
1
6
p1p2p1+p2= 1
p1= 2 ×p22p2+p2= 1 3p2= 1 p2=1
3p1= 1 −1 3=2 3

r p
p=1
r
i pipi=1
6
E
•
A
•
• ∅
•E
•
•
•
P E
•P(∅) = 0
•P(E) = 1
•A06P(A)61
A
P(A) =

A B
•A∩B A B A B
A B
•A B A ∩B=∅
A B
•A∪B A B A B
A B
•¯ A A
A
P E
•A B
P(A∪B) = P(A) + P(B)−P(A∩B)
•A B
P(A∪B) = P(A) + P(B)
•A B
P(¯ A) = 1 −P(A)
•
•A B A ∩B=∅P(A∩B)=0
•E=A∪¯ A A∩¯ A=∅A¯ A P (E) = P(A∪¯ A) = P(A)+P(¯ A)
P(E) = 1 1 = P(A) + P(¯ A)P(¯ A) = 1 −P(A)
E
ER

X E
I X ={x1;x2;. . . ;xn}pi
X xi
(X=xi)X I
xip(X=xi)
•X E(X)
E(x) = x1p1+. . . +xnpn
•X V (X)V(X)=(x1−
E(X))2p1+. . . + (xn−E(X))2pn
•X σ(X)σ(X) = pV(X)