Formulário AV2

Prévia do material em texto

Ministe´rio da Educac¸a˜o
Universidade Tecnolo´gica Federal do Parana´
Campus Pato Branco
Prof. Me. Matheus H.D.M. Ribeiro Disciplina: PE22NB
Alunos: Data:24/05/2018
Formula´rio
P (X = k) =
(
n
k
)
pk(1− p)n−k
E(X) = np V ar(X) = np(1− p).
(
n
k
)
=
n!
k!(n− k)!
P (X = k) =
(
r
k
)(
N−r
n−k
)(
N
n
)
E(X) = np e V ar(X) = np(1− p)N − n
N − 1 .
P (X = k) = p(1− p)k, P (X = k) = p(1− p)k−1
E(X) =
1
p
e V ar(X) =
1− p
p2
.
P (X = k) =
e−λλk
k!
E(X) = V ar(X) = λ.
f(t) =
{
λe−λt, se t ≥ 0;
0 se t < 0;
F (t) = P (T ≤ t) = 1− e−λt
z1 =
a− µ
σ
z2 =
b− µ
σ
P (a ≤ X ≤ b) = Φ
(
b− µ
σ
)
− Φ
(
a− µ
σ
)
P (X ≤ a) = Φ
(
a− µ
σ
)
P (X ≥ a) = 1− Φ
(
a− µ
σ
)
p =
ni
N
pˆ =
ni
n
µ =
1
N
N∑
i=1
xi x =
1
n
n∑
i=1
Xi
s2 =
1
N − 1
N∑
i=1
(Xi − x)2
Ic[µ, 1− α] =
[
x− t(α
2
;n−1)
s√
n
;x+ t(α
2
;n−1)
s√
n
]
e = t(α
2
;n−1)
s√
n
Ic[µ, 1− α] =
[
x− zα
2
σ√
n
;x+ zα
2
σ√
n
]
e = zα
2
σ√
n
Ic[p, 1− α] =
[
pˆ− zα
2
√
pˆ(1− pˆ)
n
; pˆ+ zα
2
√
pˆ(1− pˆ)
n
]