Feuille d`exercices n°25

X Y p
U=X+Y V =X−Y(U, V )
X N
(X, N)
n1n k k
1k X
Y(X, Y )
X Y
X Y X(Ω) = Y(Ω) = {1; 2; . . . ;n}P((X=
i)∩(Y=j)) = a×i×j
a
X
Y
X Y
P(X=Y)
U= max(X, Y )U
n+ 1 0 n
XkX1= 1
Xi= 1 i Xi= 0
X2

Xin
n+ 1i−1
i < j P ((Xi= 1) ∩(Xj= 1)) = (n−1)i−1nj−1
(n+ 1)j−1
XiXj
XiXj
Zpp
Zp
p+∞
n1n
X1X2X3X
Z Y (X, Y, Z)
X Y Z
n= 3
X Y Z
ΩX, Y Z U{1;2;...;n}
(X, Y )
∀k∈ {2; 3; . . . ;n+ 1}P(X+Y=k) = k−1
n2
∀k∈ {n+ 1; . . . ; 2n}P(X+Y=k) = 2n−k+ 1
n2.
P(X+Y=Z) = n−1
2n2
T=n+ 1 −ZU{1;2;...;n}
T X Y
P(X+Y+Z=n+ 1)
X
Y
X
(X, Y )
Y
j≥2X Y =j
i≥1Y−n X =n

X Y
p U = max(X, Y )V= min(X, Y )
U V
U
E(V)
E(U)
C1C2C3
C1C2C3
X1X2X3C1
C2C3
X1X2X3p
p∈]0; 1[ q= 1 −p
A C3
A(min (X1, X2) + X3)>max (X1, X2)
A
X1E(X1)V(X1)
∆ ∆ = |X1−X2|
P (∆ = 0)
n
P (X1−X2=n) =
+∞
X
k=1
P (X1=k) P (X2=n+k)
P (∆ = n) = 2 pqn
1 + q
∆E(∆)
E(X1−X2)2= 2V(X1) ∆ V(∆)
A(X3>∆)
P (A) =
+∞
X
k=0
P (∆ = k) P (X3> k)
P (A)p q