Map 311 - Introduction aux probabilités et à la simulation

n
nmin 0.5
ln(1 + x)∼x x << 1
n
n→ ∞
p
40 30
Ω := {ω1, ω2, ω3, ω4}A:= {ω1, ω2}
B:= {ω1, ω3}C:= {ω2, ω3}A B C
P(A∩B∩C)P(A)P(B)P(C)
1
2
1
3

R
Rx∼y x −y∈QA

I A(x)6=∅x I f
f(x)∈A(x)x∈I A ∈[0,1[
A α =λ(A)
r, s ∈Qr6=s(A+s)∩(A+r) = ∅A+x={y+x:y∈A}
λ(A+s) = λ(A)
1 = λ[0,1]≤λ[
r∈Q∩]−1,1[
(A+r)≤λ[−1,2]= 3.
σ λ α = 0
α > 0