TD_esp_var_sergene_16_17

TD
Chapitre 17
PP
(Xn)n∈N∗
b(p)p∈]0,1[
k∈N∗(Ek)
p k
(Ek)\,[
{Xi= 1} {Xi= 0}i∈N∗
P
X → P(λ)λ > 0
2X
P
XP(λ)
P
S
S
S
S
PP CCP PSI 2015
a > 0X
N∗
∀n∈N∗,P[X=n] = a
n(n+ 1)
a
X
PP
XN
E[X2]E[X]X
PP
X
λ > 0
E1
X+ 1
P
X
P(λ) E(X) E(X2) V(X)
PP
n n
n X
X
PPP
X → P(λ)λ > 0n∈N
P[X≤n] = 1
n!Z+∞
λ
−xxndx
approximation binomiale-Poisson PP
0.1%
n
1n
n= 2000
N
N
3
N
3

Maths M. Roger
PPP Modèle d’assurance
p∈]0,1[ C
π
(Xi)1≤i≤N
N b(p)N
S
S
π
99%
PP
X
p∈]0,1[
E[X(X−1) . . . (X−r+ 1)]
PP
X Y
(Ω, P )
|(X, Y )|6pV(X)V(Y)
PP Sondage
p∈]0,1[
n Xi= 1
i
Xi
p
Sn=X1+· · · +Xn
Sn/n
ε > 0
P
Sn
n−p
> ε61
4nε2
ε= 0,05 n Sn/n
p ε
PP Casino
1/2
2n−1
n
PP
X P (λ)
A i
b(p)Yi1p i
A0 1 −p
(Xi, Yi)
S=
X
X
k=1
Yk
S
P{X=n}({Y=k})
S
P{Y=k}({X=n})
PPP estimateurs statistiques
X1, . . . , Xn
m σ2
¯
Xn=1
n
n
X
i=1
Xi¯ Vn=1
n−1
n
X
i=1 Xi−¯
Xn2
¯
Xn
¯
Vn
PP
XR
E[X2]E[X]