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Formul´rio de Estat´
a
ıstica
Medidas descritivas
xi

i

µ=

σ2 =

n

i xi
n
S
CV = 100
x
¯

S2 =

x=
¯

(oi − ei )2
ei

χ2 =
i

r=

1
n

n

C=

xi − x
¯
sxi=1

yi − y
¯
sy

=

− µ)2
=
n
¯2
i (xi − x)
=
n−1
i (xi

x2 − nx2
¯
i
n
2
¯2
i xi − nx
n−1
i

χ2
+n

C∗ =

χ2

i

(

2
i xi

C
(t − 1)/t

xi yi − nxy¯¯

− nx2 )(
¯

i

2
yi − ny 2 )
¯

Probabilidades
E [X ] =

xi P (X = xi )
i

E [X ] =

i

xfX (x)dx

Distribui¸˜o
ca

Densidade

X ∼ U (k )

V ar[X ] =

(x − E [X ])2fX (x)

Distribui¸˜es de Probabilidade
co
Dom´
ınio
E[X]

1
k

Var[X]
(max(X )−min(X )+1)2 −1
12

x = 1, 2, . . . , k

n
x

X ∼ B (n, p)

x2 P (X = xi )
i

V ar[X ] =

px (1− p)n−x

min(X )+max(x)
2

x = 0, 1, 2, . . . , n

np

np(1 − p)

X ∼ HG(N, K, n)

(K )(N −K )
x
n−x
(N )
n

x = 0, 1, 2, . . . , min(K, n)

np

np(1 − p) N −n
N −1

X ∼ P (λ)

e− λ λ x
x!

x = 0, 1, 2, . . .

λ

λ

X ∼ G(p)

(1 − p)x−1 p

x = 1, 2, . . .

1
p

(1−p)
p2

x = r, r + 1, r + 2, . . .

r
p

r (1−p)
p2

x ∈ (−∞, ∞)

µ

σ2X ∼ BN (r, p)

x− 1
r −1

X ∼ N (µ, σ 2 )

√1
2πσ 2

X ∼ Exp(λ)

λ exp(−λx)

x≥0

1
λ

1
λ2

X ∼ G(α, β )

1
Γ(α) β α

x≥0

αβ

αβ 2

X ∼ W ei(γ, β )

γ
β

x≥01
β 1/γ Γ(1 + γ )

2
1
β 2/γ Γ(1 + γ ) − Γ2 (1 + γ )

X ∼ Beta(α, β )

Γ(α+β )
Γ(α)Γ(β )

0≤x≤1

α
α+β

αβ
(α+β )2 (α+β +1)

(1 − p)x−r pr

1
exp{− 2σ2 (x − µ)2 }

xα−1exp{−x/β }

xγ −1 exp{−xγ /β }

∞

Γ(α) =
0

xα−1 (1 − x)β −1

xα−1 exp{−x} dx

Γ(α) = (α − 1)!

Γ(α + 1) = α Γ(α)

p(1 − p)
)
n

S2
)
n

2

p1 − p2 ∼ N
ˆ
ˆ

p1 − p2 ,S
¯
d ∼ tn−1 (µd , d )
n

x1 − x2 ∼ tν µ1 −
¯
¯

x1 − x2 ∼ tν
¯
¯

p1 (1 − p1 ) p2 (1 − p2 )
+
n1
n2

1
1
+
n1
n2

S2
S2
µ1 − µ2 , 1 + 2
n1
n2

2
µ2 , Sp

µ1 − µ2 ,...