Formulário
P(X=x) = n
xpx(1 −p)n−x, x = 0,1, ..., n;E(X) = np, V (X) = np(1 −p)
P(X=x) = e−λλx
x!, x = 0,1, ...;E(X) = V(X) = λ
P(X=x) = p(1 −p)x−1, x = 1,2, ...;FX(x)=1−(1 −p)⌊x⌋, x ≥1; E(X) = 1
pV(X) = 1−p
p2
fX(x) = 1
b−a, a ≤x≤b;E(X) = b+a
2V(X) = (b−a)2
12
fX(x) = λe−λx, x ≥0E(X) = 1
λV(X) = 1
λ2
fX(x) = 1
√2πσ2exp −(x−µ)2
2σ2, x ∈RE(X) = µ V (X) = σ2
fX(x) = λe−λx (λx)n−1
(n−1)! , x ≥0, E(X) = n
λ, V (X) = n
λ2
{N(t), t ≥0} ∼ P P (λ); N(t)∼P oisson(λt); Tn∼Exp(λ); N(t)≥n⇔Sn≤t;
N(s)|N(t) = n∼Bin(n, s/t)
{B(t), t ≥0} ∼ MB standard ;B(t)∼ N(0, t); P(Tm≤t, B(t)≤w) = P(B(t)≥2m−w), w ≤m, m > 0
B(s)|B(t) = x0∼ N sx0
t,s(t−s)
t;P(Ta< T−b) = b
a+b, a > 0, b > 0
Xi∼
i.i.d X;¯
X=1
n
n
X
i=0
Xi;Sn=
n
X
i=1
Xi;¯
X∼ N E(X),V(X)
n;Sn∼ N (nE(X), nV (X))
X≥0, P (X≥a)≤1
aE(X); P(|X−µ| ≥ k)≤σ2
k2, k > 0
