Probabilités

−−−−−−−−−−−−−−−−−−
∗
E n, A, B ∈P(E)E
(A, B)
(A, B)A∩B=∅
(A, B)A∪B=E
(A, B)E A ∩B=∅A∪B=E
n
k06k6n
0,1

X
ΩX
X
X
X
n
40% 60%
n= 10
X
X X
(X=k)
n= 10
20%
1%
10%
1
41

(Ω, P )
P(A) = P(B) = 0,9P(A∩B)>0,8
P(A∩B)>P(A) + P(B)−1
p q
1
8
7×6
8×7×6=1 8
7×6×5×4
8×7×6×5×4=1 8
7×6×5×4×3×2
8×7×6×5×4×3×2×1=1 8
40% 30%
D1
R1
R1
30%
20%
D2
R2
R
R
n(n > 1)
n
90%

40%
30% 15%
ε
T+p
(T−q
60% 40% M75%
90% M
n−2
X
Y
X Y
(X, Y )
X Y
(X, Y )
n n
X1, X2,··· ,
(Ω,A, P )
Y
X1
k>2Bk= (Xk< X1)
P(B2∩B3∩ ··· ∩ Bk)
P+∞
i=2
Bi= 0
ωΩY(ω)
Ω
m>1P(Y=m+ 1) = 1
n
n−1
i=0 ×i
nm−1
×1−i
n
Y E(Y) = 1 +
n
j=1
1
j
n Y (n)
Y

m>1pm= lim
n→+∞P(Y(n)=m+ 1)
(pm)m>1ZN∗
a∈R
X Y (Ω,A;P)
E={0,1,2,··· , n}
Z T
Z=|X−Y|T= inf(X, Y )
E(A)A
Z T
E(Z) = n(n+ 2)
3(n+ 1)
E(T)n
UNK∈N∗06U6K
K
j=1
P(U>j)E(U)
K
j=1
j2P(U>j)E(U), E(U2), E(U3)
j∈NP(T>j)
E(T)
E(Z2)σ2
XX
X
pn(X=n)cn
(X6n)
p1p2p3p4
c2c3c4
n>2pn=cn−cn−1
n>1, pn+3 = 2 ×1
33(1 −cn)
n>2, pn+3 −pn+2 +2
27 pn= 0
n>2un=pn+2 −2
3pn+1 −2 9pn
u2(un)n>2
n>2, pn=1
6√31+√3
3n−2−1−√3 3n−2
pn
∞
n=2
pn
X
n∈Nfnfn(x) = xn+ 16x2−4
fn(x) = 0 [0,+∞[
un
(un)