X
n
G.
X1 , X2 , ..., Xn
x1 , x2 , ..., xn
(X1 , X2 , ..., Xn ),
Xi
X.
g(X1 , X2 , ..., Xn ),
g(x1 , x2 , ..., xn ).
µ=
V (X) =
1
N
N
!
xi
i=1
N
!
1
2
σ =N
(xi
" i=1
X=
n
!
xi
i=1
− µ)
2
# N
# !
√
σ = σ 2 = $ N1
(xi − µ)2
2
S =
1
n−1
n
!
i=1
S=
√
i=1
π=
1
n
fi
N
S2 =
%
(xi − X)2
1
n−1
p=
n
!
i=1
(xi − X)2
fi
n
xi
n
N =4
X 0, 1, 2, 3
µ=
V (X) = σ 2 =
σ=
n=2
n
2
N = 4 = 16
X
X
(0, 0)
0
(0, 1)
0.5
(0, 2)
1
(0, 3)
1.5
(1, 0)
0.5
(1, 1)
1
(1, 2)
1.5
(1, 3)
2
X
(2, 0)
1
(2, 1)
1.5
(2, 2)
2
(2, 3)
2.5
(3, 0)
1.5
(3, 1)
2
(3, 2)
2.5
(3, 3)
3
M = N n = 42 = 16
X
X
X
X
E(X) = µX =
V (X) =
&
V (X) = σX =
µX = µ.
σ
σX = √ .
n
X
X ∼ N (µ, σ).
σ
X ∼ N (µ, √ ).
n
Xi
√σ
n
'
N −n
N −1
X ∼ N (µ, σ)
X ∼ N (µ, √σn )
µ = 740
20
760
760
X1 , X2 , . . .
µ
σ2
Sn =
X1 + X 2 + . . . + Xn
lim P
n→∞
(
Sn − nµ
√
≤x
nσ
)
= Φ(x),
Φ(x)
X
X
X
µ
X
X
µ
q
X.
C = f (X1 , X2 , ..., Xn ).
n
C
q
E(X) = µ.
σ2
n
1 !
S =
(Xi − X)2
n − 1 i=1
2
E(S 2 ) = σ 2
p
p=
K
K
,
n
X
38, 5
X
42
(X1 , X2 , · · · , Xn )
q
1−α
L = f (X1 , X2 , · · · , Xn )
n
[L, D] :
D = g(X1 , X2 , · · · , Xn ),
1−α
q.
P (L ≤ q ≤ D) = 1 − α.
1 − α ∈ {0.90; 0.95; 0.99; 0.999}.
x1 , x2 , ..., xn
(X1 , X2 , ..., Xn )
q,
[l, d]
P (q ∈ [l, d]) = 1 − α = 0.95.
q.
[l, d]
q
[l, d]
α
q
α
α,
1−α
α
n
q
q
(1 − α)
100(1 − α)
q
µ
N (µ, σ)
σ
µ∈
(
1−α
)
σ
σ
X − zα √ , X + z α √ .
n
n
2D : 4D
2D : 4D
135
2D : 4D
0.988
σ = 0.028
95%