TD 5

◦5
c X f
∀x∈R, f(x) = c
x21x∈[5;+∞[.
c
X
Y= 1/X Y Y
E[√X]
λ T
t= 0
λ
−3 4
t∈RFT(t)t
FT
t050% t0
t, s > 0
P(T > t +s) = P(T > t)P(T > s).
T1T2λ1λ2
λ1, λ2>0Y= min(T1, T2)Y
a > 0fR
∀x∈R, f(x) = 4
a2x1{x∈[0;a/2[}+ (a−x)1{x∈[a/2,a[}.
f X
f
b]0; a/2[
A=nX > a
2o, B =na 2−b<X≤a 2+bo.
A B
X

X[a;b] 0 < a < b
Y=X2
X[0; 1] λ
Y= (−1/λ) ln(1 −X)E[Y]
X[−0.5; 0.5]
Y= cos(πX)
∀x∈R, FX(x) = 1
1 + exp(−x),
Y=exp(X)+1
exp(X)−1Y
∀x∈R, f(x) = 0x < 0,
xexp(−x2/2)
f
X f Y =X2
X λ
Y=bXcZ=X−bXc
X0, . . . , Xn[0; 1]
k0≤k≤n Uk= min(X0, . . . , Xk)Uk
NB(n, 1/2) U= min(X0, . . . , XN)