Un sujet d`annales : Ecricome 2002

c
n n >2
c= 0
n
X
n Y
(Y=k k`eme
Y= 0 n
X E(X)V(X)
k∈ {1, . . . , n}P(Y=k) (Y=k)
P(Y= 0)
n
X
k=0
P(Y=k) = 1.
x6= 1 n
n
X
k=1
kxk=nxn+2 −(n+ 1)xn+1 +x
(1 −x)2.
E(Y)
c6= 0
(Xi)16i6n
(Xi= 1 i`eme
Xi= 0
26p6n Zp
Zp=
p
X
i=1
Xi.
Zp
X1E(X1)X1

PX1=0(X2= 0) PX1=0(X2= 1) PX1=1(X2= 0)
PX1=1(X2= 1) X2E(X2)
Z2
Zp(Ω) Zp
p6n−1
P(Xp+1 = 1 /Zp=k)k∈Zp(Ω)
P(Xp+1 = 1) = 1 + cE(Zp)
2 + pc .
Xp
1
2
p X1X2Xp
1
2E(Zp)