Enoncé

X F (x) = (0x < 0
1−e−x
23x≥0
X X
f x →6x(1 −x) 0 ≤x≤1
0f
Y f
Y(Ω) Y
Y
a∈Rf x →a
x3x≥1
0x < 1X
X
P(−1< X < 3) P(X > 2)
X
X fX
Y=−2X+ 3 fYY
fX
Z=eXfZZ fX
X(Ω) ⊂R+V=√X fV
V fX
U=X2fUU fX
X[−1,1]
Y=|X|E(Y)Y
Z=eXE(Z)Z
X1
2
Y=√X
Y
Z=X2
U[0,1] λ
V= 1 −U
X=−ln(1−U)
λ
λ
rand()

X Y λ
U= sup(X, Y )V= inf(X, Y )
g U
V V
U+V X Y U
X U (Ω,A, P )
X U {−1,1}
Y=UX
∀x∈RP(Y≤x) = 1
2P(X≤x) + 1 2P(X≥ −x)
Y
U E(XY )=0
cov(X, Y ) = 0
x x
xbxc
bxc ≤ x < bxc+ 1
b2,83c= 2
b−2,83c=−3
bxc=−3⇔ −3≤x < −2
X Y =bXc
Y(Ω) P(Y=k)∀k∈Y(Ω)
P(Y= 0) P(Y= 1)
Z=Y+ 1
E(Y)V(Y)
X D =X− bXc
∀t < 0, FD(t)=0 ∀t≥1, FD(t) = 1
∀t∈[0,1[ (D≤t) =
+∞
S
n=0
[n≤X≤n+t]
[D≤1
3]
∀t∈[0,1[ FD(t) = 1−e−t
1−e−1
D D
XN(0,1) P(X≤ −0,81) P(|X| ≤ 1,17)
XN(0,1) t > 0P(|X|< t)=0,95
XN(8,4) P(X > 8,5) P(6,5< X < 10) P[X>5](X > 6)
X X
P(X < −1) = 0,025
P(X > 3) = 0,242