Aaa fwefwer

Departamento de Matem´tica – Sec¸˜o de Estat´ a ca ıstica e Aplica¸˜es co Probabilidades e Estat´ ıstica EXERC´
ICIOS

Edi¸˜o de Fevereiro de 2007 ca Formul´rio a P (X = x) =

nx p (1 − p)n−x x P (X = x) =

x = 0, 1 , . . . , n
E (X ) = np

e−λ λx x! P (X = x) = p(1 − p)x−1

x = 0, 1 , . . .

x = 1, 2 , . . .

V ar (X ) = np(1 − p) E (X ) = V ar (X ) = λ

P (X = x) =

M
N

V ar (X ) = n

fX (x) = √

E (X ) =

¯
X −µ
√ ∼ t(n−1)
S/ n

¯
X −µ a
√ ∼ N (0, 1)
S/ n

S2 =

¯
¯
X 1 − X2 − ( µ 1 − µ 2 )
+

fX (x) = λe−λx , x ≥ 0

V ar (X ) = σ 2

¯
X −µ
√ ∼ N (0, 1) σ/ n

2
S1
n1

M N −M N −n
N
N N −1

1
(x − µ )2
,x∈I
R exp −
2σ 2
2πσ 2

E (X ) = µ

2 σ1 n1

2

V ar (X ) =

2 σ2 n2

+

¯
¯
X1 − X2 − (µ1 − µ2 )

a

2
2
(n1 −1)S1 +(n2 −1)S2 n1 +n2 −2

(Oi − Ei )2 a 2
∼ χ(k−β −1)
Ei
i=1

1 n1 r

s

n

ˆ
ˆ¯
¯ β0 = Y − β1 x

Yi = β0 + β1 xi + εi

ˆ β1 =

xi Yi − nxY
¯¯

i=1 n i=1 n 1
ˆ
ˆ
ˆ2ˆ
σ=
ˆ
Yi − Yi , Yi = β0 + β1 xi n − 2 i=1

ˆ β0 − β0
1
n

+

x2 x 2 −nx 2
¯
i

σ2
ˆ

∼ t(n−2)

ˆ β1 − β1

i=1 i=1 x2 i i=1

ˆ
¯
− nY 2 − β1

1 n xi Yi − nxY
¯¯

− nx2 ×
¯

x2 − nx2
¯
i
2

n i=1 x2 − nx2
¯
i

ˆ
ˆ
β0 + β1 x0 − (β0 + β1 x0 )

∼ t(n−2)

σ2
ˆ
¯ x 2 −nx 2 i n

Yi2

2

n

R2 =

n

1 σ= ˆ n−2 2

∼ N (0, 1)

∼ t(n1 +n2 −2)

1 n2 +

n i=1 1 λ2 (Oij − Eij )2 a 2
∼ χ(r−1)(s−1)
Eij
i=1 j =1

k

(n − 1)S 2
∼ χ2n−1)
(
σ2

1 λ ¯
¯
X1 − X2 − ( µ 1 − µ 2 )

n
1
¯
Xi − X n − 1 i=1

∼ N (0, 1)

2
S2
n2

(1 − p) p2 fX (x) =

x = max {0, n − N + M } , . . . , min {n, M }
E (X ) = n

V ar (X ) =

1
,a≤x≤b
b−a b+a (b − a)2
E (X ) =
V ar (X ) =
2
12

N n N −M n−x M x 1 p E (X ) =

2

¯
Yi2 − nY 2

+

(¯−x0 )2 x x 2 −nx 2
¯
i

σ2
ˆ

∼ t(n−2)