CC1 proba 2007

A, B, C, D (Ω, P )
A∩B⊂C P (A) + P(B)≤1 + P(C)
A∩B∩C⊂D P (A) + P(B) + P(C)≤
2 + P(D)
A=B=
C=
a, b, c
J=
J A, B C P (J)
a, b, c
N= 11A+ 11B+ 11C
E
n∈E pn=P([N=n]p0
p3
N
N GN(t) = E[tN]
t∈RN
n1n
1 3 (Ω, P ) Ω
PΩ
Ω
N1N2N31
2 3 N1N2N3
n1∈ {0, ..., n}
n1P[N1=n1]
n1n2n3n
n1n2n3

1 2 3
P([N1=n1;N2=n2]) = 1
3n
n!
n1!n2!(n−n1−n2)! .
N1N2
(Ω, P )A
B
P(A) = 2/3P(B) = 1/2P(B|A) = PA(B) = 1/4
P(A∩B)P(A∪B)P(Ac∩B)P(Ac∩Bc)
X= 211A−11B
X
E(X) Var (X)X