Un sujet d`annales : Ecricome 2002

c c
n n >2
c= 0
n
X n
Y
Y= 0
X E(X)V(X)
k∈ {1, . . . , n}P(Y=k) (Y=k)
P(Y= 0)
k=n
X
k=0
P(Y=k) = 1
x6= 1 n∈N∗
k=n
X
k=1
kxk=nxn+2 −(n+ 1)xn+1 +x
(1 −x)2
E(Y)
c6= 0
(Xi)16i6n
i p {2, . . . , n}Zp
Zp=
k=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
PZp=k(Xp+1 = 1) k∈Zp(Ω)
P(Xp+1 = 1) = 1 + cE(Zp)
2 + pc
Xp
1
2