Université des Sciences et Technologies de Lille U.F.R. de

n
Q
50 m
20 m 10 m 50 m
40 m
A C B
Q(A)Q(B)Q(C)A B
C a =Q(A)b=Q(B)
c=Q(C)
n
(Ω,F, P )
X Y Z
A B C
X+Y+Z=n
P(X, Y, Z) = (i, j, k)=
n!
i!j!k!aibjcki+j+k=n
0

k= 1, . . . , n k
X Y X +Y
AR2(X, Y )
A X Y
A={(x, y)∈R2,1≤y≤2xet y≤6−x}
A=(x, y)∈[0,1]2, x ≥y+1
2ou x≤y≤x+1 2
A
(X, Y )
f(x, y) = 1
4(2x+y)1[0,1]×[0,2](x, y).
P(X∈[0,1]) P(X≤1
2)P(Y≤1) P{X≤1 2}∩{Y≤1}P(X+
Y≤1)
X Y
X Y
E(X)E(Y)E(XY )
X Y X
P(Y= 1) = P(Y=−1) = 1
2
Z=XY
X Z
U=X+Z U
(X1, X2)R2
f(x1, x2) = 4
πexp −(x2
1−6x1x2+ 25x2 2).
(X1, X2)X1
X2
a b a 6= 0
R2(Y1, Y2) := (aX1+bX2, X2)
X f
f(t) = c(t−a)(b−t)1[a,b](t), t ∈R,
a b c a < b
/

XiXi
X F
X n Mn= max1≤i≤nXi
x0=a+ 0.9(b−a)
a b
X Y
α−Y X +Y X −Y
L f
X[0,1] L
L1L2L1=XL L2= (1−X)L
L1L2
L
(L1, L2)L1L2
(L1, L2)f(y) = α2ye−αy 1[0,+∞[(y)α > 0
Z= min{L1, L2}
/