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E F X Y
E F (X, Y )
E×F
N
∀(i, j)∈N2:P(X > i +j|X > i) = P(X > j).
X1, X2
θ1>0θ2>0
X1+X2
X1X1+X2
E(X1|X1+X2)
N
N λ > 0
Gii N, G1, G2, . . .
p
1−p X

? X N
E(X) = X
n≥0
P(X > n).
X1, . . . , XpNpk=P(X=
k), k ∈Nrn=Pk≥npk
E(min(X1, . . . , Xp)) = X
n≥1
rp
n.
X1, . . . , Xnp
P(Xj=n) = p(1 −p)n−1, n ∈N∗.
X= min(X1, . . . , Xn)Y= max(X1, . . . , Xn)
(X, Y )
n r (Yi)1≤i≤r(Xi)1≤i≤r
Yi=i
Xi= 1 i0.
YiXiE[Xi] Var(Xi)
i6=jCov(Xi, Xj)
SrE[Sr] Var(Sr)
X1, . . . , Xn
p∈]0,1[ S=X1+. . . +Xn
s∈ {0, . . . , n}X1S=sE(X1|S)
(Xn)n∈N
p n ≥1Tn= inf{k > Tn−1;Xk= 1}
Tn=∞T0= 0
T1, T2−T1, . . . , Tn−Tn−1, . . .
T1Tn
Tn

a
X
X
M
M
p∈]0,1[
Xnn Xn=M
Xm=M m ≥n Xn
NE(N)
N Xn
TE(T)
{T > j}Xn
p
q n
N K
0≤K≤N≤n
N
K{N=m}
K