Colle de Mathématiques : Semaine du 30 / 01 / 2017

 X (Ω,A, P )FX
X FXR
C1
X fXfX=F0
XFX
I
fR
f
fR
∀x∈Rf(x)>0
Z+∞
−∞
f(t)dt Z+∞
−∞
f(t)dt = 1
 X f X
X(Ω)
X(Ω) = {x∈R/ f(x)6= 0}. 
I
FR
FR
lim
x→−∞F(x) = 0 lim x→+∞F(x) = 1
FRC1R
F X
f X x F f(x) = F0(x)
n n ∈N

Y=eXZ=X2T=aX +b
•a > 0fRf(t) = ae−at t∈[0,+∞[
f(t) = 0 t∈]−∞,0[
99K f
99K X f X
99K
•F(F(t) = 1 −1
tt∈[1; +∞[
F(t) = 0 t∈]−∞; 1[
99K F Y
99K Y
99K Y(Ω)
•X f :x7→ e−xx>0
0x < 0
99K Z=bXcZ
99K X
99K X
•Y g :x7→ 
1
x2x>1
0x < 1
99K Y
99K √Y
99K X g :t7→ 
2
t3t>1
0t < 1
99K X