Variables aléatoires

TSI2
X p E 1
X
X λ > 0E1
X+ 1
λ > 0
p0<p<1
r r >1
5
E(X)
V(X)
Z

Z r >1
50
n= 100
P(N= 110) P(N= 100)
E(N)V(N)
P(X=k)k

TSI2
r > 0
P|X−4/5|>r610−2
1,2 3
•1
•2
•3
k1 3 Ukk
P(U1) = P(U2) = P(U3) = 1
3
X
X0
X
PU1(X= 1) PU2(X= 1) PU3(X= 1)
P(X= 1) = 1
2
j2PU1(X=j) = 0 PU3(X=j)=0
j2PU2(X=j)
j2P(X=j) = 1
31 2j
P(X= 0)
x]0,1[
+∞
X
k=1
kxk−1=1
(1 −x)2
E(X)X
E(X)
U1U2
R
P(R) = 1
10
U1
X
X X(Ω) P(X=k)k X(Ω)
X Z P(λ)
λ= 4

1
Y1
Y Y (Ω) P(Y=k)k Y (Ω)
A
A
P(J) = 11
15
X A
X X k
P(X=k)
E(X)V(X)X
N
N= 3X−40
N
60%
Y
Y
XN(Ω, P )
GX(s) = E(sX) = X
P∈N
P(X=k)sk.
GX[−1,1]
GXX
X X2G0
XG00 XGX
E(X) = G0
X(1) E(X2) = G00 X(1) + G0 X(1) V(X)