1. Variables aléatoires finies 2. Probabilités d`événements

(Ω,P)
p
2n n
N!∼√2πN(N/e)N
2n n (4p(1 −p)n/√πn
X(2n, 1/2) n≥1
P{X≤n}=P{X≥n}P{X≤n}=1+2−2nCn
2n
2
P{X≤n}n
X(2n, 1/2) n
0≤k≤n−1Ck
2n≤Ck+1
2n
P{X∈2N, X < n} ≤ P{X∈2N+ 1, X < n} ≤ P{X∈2N, X < n}+P{X=n}.
P{X∈2N} − P{X=n} ≤ P{X∈2N+ 1} ≤ P{X∈2N}+P{X=n}.
P{X∈2N}n
F:t7→ 0 si t < 0 ; 1/4 si 0 ≤t < 1 ; 3/4 si 1 ≤t < 2 ; 1 si t≥2.
X(Ω,P){0,1,2}
(p0, p1, p2) (p0, p1, p2)
t∈R P{X≤t}=F(t)
(Ω,P)
Ω = (N∗)2
PΩ
(pn=P({n, n}))n≥0
(An)n≥1
limn→+∞PSn
k=1 Ak=PSn≥1An

PSn≥1An≤Pn≥1P(An)
(An)n≥1
Tn≥1An{=Sn≥1A{
n
(An)n≥1An+1 ⊂Ann≥1
(A{
n)n≥1limn→+∞P(An) = PTn≥1An
(An)n≥1
limn→+∞PAn6=PSn≥1An
N
∆p
p
X(Ω,P)
Tn≥1{X≥n}=∅
limn→+∞P{X≥n}= 0
X FX:t∈R7→
P{X≤t}FXt
−∞ X
FX:t∈R7→ P{X≤t}.
pN∗
p p =λ/N λ > 0N
t≥0
FX(tN)→1−exp(−λt).
p=λ∆λ > 0
∆p < 1
∆
X1−exp(−1) N∗
exp(−X+ 1)