TP7 - SAMM

2016 −2017
n0
[0,1]
0 1
X: Ω →[0,1]
[0,1] X X(ω)ω∈Ω
(X1,··· , Xn)n X (X1,··· , Xn)
(X1(ω),··· , Xn(ω))
(X1(ω),··· , Xn(ω))
27%%10 27 10 27 10 7 27 = 2 ∗10 + 7
19%%7 %%
pseudo1.m pseudo1y=pseudo1(x)=3∗x%%10
(xn)n= 0,1,··· ,20 xn+1 =pseudo1(xn)x0= 0
0 9
(xn)n= 1,··· ,100
(xn, xn+1)n= 0,1,··· ,99
(xn, xn+1) (xn, xn+2) (xn, xn+7)
xn10 [0,1]
pseudo2

x0
Y=runif(1000,0,1)
3Y Y =runif(1000,0,1)
X=P seudo2(1000,123456)
x0cpu
[a, b]
Z Z {z1< z2<
··· < zn}IP(Z=zi) = pip1+p2+···+pn= 1 p
X[0,1] W=Pn
i=1 ziIIp0+p1+···+pi−1<X≤p0+p1+···+pi
p0= 0 W Z
runif(n, 0,1)
n1/2 1/4rbinom(n, 1,1/4)
n1+floor(runif(n, 0,6))
Z
FZ(z) = IP(Z≤x)
Z I I R
]0,∞[F−1
Z]0,1[
I W =F−1
Z(X)X[0,1]
Z runif(n, 0,1)
n2rexp(n, 2)
n f(x) = 1
π(1+ x2)−1x∈R
rexp(n)
2
(Z1, Z2)
2
M(Z1, Z2)
\
Ox, OM [0,2π]OM
0.5
1000 N(−2,42)
(Xn)n∈N
(Ω,A,IP) IE(|X0|)<∞
Xn=1
nX1+X2+··· +XnP
−→
n→+∞m= IE(X0)

n Xn
m0ε
ε > 0 IP(|Xn−m| ≥ ε)L −→
n→+∞0
N= 104
Xnmean(·)n∈ {1,2,··· , N}
(n, Xn)n∈ {1,2,··· , N}m= IE(X0)
2 1000
A
(Xn)n∈N
(Ω,A,IP) σ2= (|X0|)<∞
√nXn−m)L
−→
n→+∞N(0 , σ2)
n√nXn−m)
σ22(X1,··· , Xn)
M(X1,··· , Xn)
2M n M =n= 1000
M√nXn−m)
(100,1/3)
[0,1]
θ= 1/15
θ30 30
θ
θ30 θ= 1/15 95%