Variables aléatoires : loi et espérance (suite).

X λ ∈R
eλX E[eλX ]
X[a, b]
X θ > 0
XN(0,1)
XNX2
X X
m≥1X
NXkk1mE[Xm+1] = +∞
f:R→Rf(t) = 1
π
1
1 + t2
fR
X f
X
X
Y= arctan(X)
XN(0,1)
n∈NXnE[Xn]
n≥0E[Xn]n
{1, . . . , n}
θ > 0X
θ n ≥1Xn
E[Xn]θ= 1
λ > 0X
λ k ≥1X(X−1) . . . (X−k+ 1)
E[Xm]m={1,2,3,4}λ= 1
mE[Xm]

m m ≥1
X
P(X > 0) >0E[X]>0
λ, µ > 0 Ω = N2F=P(N2)
(Ω,F)P
∀(n, m)∈N2,P({(n, m)}) = e−(λ+µ)λn
n!
µm
m!.
(Ω,F,P)X(n, m) = n Y (n, m) = m
P(Ω) = 1
X Y
X+Y
λ > 0p∈[0,1] Ω = N2
F=P(N2) (Ω,F)P
∀(n, k)∈N2,P({(n, k)}) = e−λλn
n!n kpk(1 −p)n−kk≤n.
(Ω,F,P)X(n, k) = n Y (n, k) = k
P(Ω) = 1
X Y