Mi parcours 20 21

X
α > 0
25
25 50
50
•
•
25
25

p∈]0; 1[
p
T1
T1
k∈Nk≥2Ak
k−1P(Ak)
T2
T2
X Y G(p)
X+Y
T2
X p V(X) = 1−p
p2
λ > 0h x ∈R
h(x) = (2λe−λx(λx −1 + e−λx)x≥0
0x < 0.
y∈Rey−y−1≥0h
Y∼Γ(2, λ)Z∼ E(2λ)
Y+Z Γ (2) = 1
•X∼ B(p)P(X= 0) = 1 −p, P(X= 1) = p
•X∼ B(n, p)∀k∈[[0; n]],P(X=k) = n
kpk(1−p)n−kn k=n!
k!(n−k)!
•X∼ G(p)∀k∈N∗,P(X=k) = p(1 −p)k−1
•X∼ P(α)∀k∈N,P(X=k) = e−ααk
k!
•X∼ U([a;b]) ∀x∈R, f (x) = 1
b−a[a;b](x)
•X∼ E(λ)∀x∈R, f(x) = λe−λx [0;+∞[(x)
•X∼ N(m, σ2)∀x∈R, f(x) = 1
σ√2πe−(x−m)2
2σ2
•X∼Γ(a, λ)∀x∈R, f(x) = xa−1λae−λx
Γ(a)[0;+∞[(x)Γ(a) = ´+∞
0ta−1e−tdt
•X∼ C(m, α)∀x∈R, f (x) = 1
π
α
(x−m)2+α2