Probabilités.pdf

N
N λ
p∈]0,1[
D
D
D N N −D D
N N −D D
X Y N∗XY
n∈N∗X[Y=n]
{1,...,n}
Y−X+1X
X Y p ∈]0,1[
U=X−YV=(X, Y )
(U, V )
U V
XN
∑P(X>n)X
E(X)=+∞
∑
n=0
P(X>n)
XN∗
E1
X⩾1 E(X)
X λ
E1
X+1X
n X1,...,XnB(p)
Y=n
∏
k=1
XkW=1⩽k⩽nXkZ=1⩽k⩽n(Xk+1−Xk)

2N T
N
X1X2X3
p=1
T
E1=min(X1, X2)E2=max(X1, X2)
U1U2
n∈NXnU1
n
n∈NUn=
P(Xn=0)
P(Xn=1)
P(Xn=2)
U0=
p
q
r
A=
12 14 0
12 12 12
0 14 12
A
A a <b<c
c
1
0
−1
b P
P−1AP
n∈NUn+1=AUnXn
(Un)
l0
l1
l2
X∀k∈{0,1,2}P(X=k)=lk
(Yn)n∈N∗
n∈N∗Sn=n
∑
k=1
Yk
a>0PSn
n−E(Y1)⩾a⩽V(Y1) na2

(Xn)n⩾1
n∈N∗P(Xn=−1)=p P (Xn=1)=1−p p ∈[0,1]
n∈N∗Zn=X1X2. . . Xnan=P(Zn=−1)
an+1anann∈N∗
Znn∈N∗
ZnZn+1n∈N∗
(Z1, Z2)
p∈]0,1[
X
Y
X
Y[X=0] [Y=0]
(k, h)∈(N∗)2(X=k, Y =h)
X
Y
p X1,...,Xp
C=(Xi, Xj)(i,j)∈J1,pK2
u=
u1
⋮
up
∈Mp,1(R)Vd
∑
k=1
ukXk=uTCu
C
u V d
∑
k=1
ukXk
L
n p
p>n⩾2
Pn,p(k)k k =1k=2k=n
Sn,k n k
a Sn,k =(Sn−1,k +Sn−1,k−1)a
Sn,k Pn,p(k)
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