,,,
.
ߠ
:
262
..
:
___________ ..
2006.
1. 充.3.
2. 3
3. 腅. 3
4. 充.. 4
5.
4
6. .. 9
7. 12
8. ,
16
9. 充19
10. ..20
1. .
, .
, , .
:
1) .
2) , . .
3) :
, , .
2. .
.
3.
:
1)
2)
3) .
4) , 蠠
.
5) .
4.
14
( .):
32 31 34 32 31 29 32 34 33 31 31 34 32 31 35 32
34 33 31 30 30 32 32 34 31 31 35 32 34 33 32 31
34 32 31 29 32 34 33 31 31 34 32 31 35 32 34 33
31 30 34 32 31 29 32 34 33 31 30 32 32 31 36 32
34 33 31 30 32 33 31 28 32 34 33 31 30 32 33 30
35 32 34 33 32 30 31 33 30 33 32 34 33 31 30 32
33 30 31 32 34 33 31 30 32 33 30 31 32 33 33 31
30 32 33 30 31 32 33 30 34 33 31 30 32 33 30 31
32 33
5.
. , .
, .
- .
.
.
xi - (, )
ni - ( )
*i
xi |
28 |
29 |
30 |
31 |
32 |
33 |
34 |
35 |
36 |
ni |
1 |
3 |
18 |
29 |
32 |
24 |
18 |
4 |
1 |
ni Pi* n |
1 130 |
3 130 |
18 130 |
29 130 |
32 130 |
24 130 |
18 130 |
4 130 |
1 130 |
, .
xi<x≤xi+1 |
(27;29] |
(29;31] |
(31;33] |
(33;35] |
(35;37] |
ni |
4 |
47 |
56 |
22 |
1 |
Pi* |
4/130 |
47/130 |
56/130 |
22/130 |
1/130 |
: min=28
max=36
R= 36-28=8
:
, , .
, cc () - () .
C .
, () () .
.
, ( ) .
:
xi |
(27;29] |
(29;31] |
(31;33] |
(33;35] |
(35;37] |
ni |
4 |
47 |
56 |
22 |
1 |
hi = ni Δx |
4/2 |
47/2 |
56/2 |
22/2 |
1/2 |
|
|
Δx=2 |
|||||||
hi |
|||||||||
56⁄ 2 |
|||||||||
47⁄ 2 |
|||||||||
22⁄ 2 |
|||||||||
4/2 |
|||||||||
1/2 |
|||||||||
27 |
29 |
31 |
33 |
35 |
37 |
||||
xi |
|||||||||
, ( ) .
:
xi |
(27;29] |
(29;31] |
(31;33] |
(33;35] |
(35;37] |
*i |
4/130 |
47/130 |
56/130 |
22/130 |
1/130 |
hi = P*i Δx |
4/260 |
47/260 |
56/260 |
22/260 |
1/260 |
Δx=2
|
|||||||||
h*i |
|||||||||
56∕ 260 |
|||||||||
47⁄ 260 |
|||||||||
22⁄ 260 |
|||||||||
4∕ 260 |
|||||||||
1 ∕ 260 |
|||||||||
0 |
27 |
29 |
31 |
33 |
35 |
37 |
|||
xi |
|||||||||
6.
() , ,
F*() = * = P* (X |
( ) , , . 1.
|
1) ∞ < ≤ 28
F*(x)=P*(X<28)=0
2) 28 F*(x)=P*(X<29)=P*(X=28)=1/130 3) 29 F*(x)=P*(X=28)+ P*(X=29)=1/130+3/130=4/130 4) 30 F*(x)=P*(X<31)= P*(X=28)+ P*(X=29) P*(X=30)+1/130+3/130+18/130=22/130 5) 31 F*(x)=P*(X<32)= P*(X=28)+
+P*(X=29)+P*(X=30)+P*(X=31)=1/130+3/130+18/130+29/130=51/130 6) 32 F*(x)=P*(X<33)=
P*(X=28)+P*(X=29)+P*(X=30)+P*(X=31)
P*(X=32)=1/130+3/130+18/130+29/130+32/130=83/130 7) 33 F*(x)=P*(X<34)=
P*(X=28)+P*(X=29)+P*(X=30)+P*(X=31)+
+P*(X=32)+P*(X=33)=1/130+3/130+18/130+29/130+32/130+24/130=107/130 8)34 F*(x)=P*(X<35)=
P*(X=28)+P*(X=29)+P*(X=30)+P*(X=31)+
+P*(X=32)+P*(X=33)
P*(X=34)= =1/130+3/130+18/130+29/130+32/130+24/130+18/130=125/130 9) 35 F*(x)=P*(X<36)=
P*(X=28)+P*(X=29)+P*(X=30)+P*(X=31)+
+P*(X=32)+P*(X=33)
P*(X=34)+ P*(X=35) =1/130+3/130+18/130+29/130+32/130+24/130+18/130+4/130=129/130 10) x>36 F*(x)=1
0, -∞<≤28 1/130, -∞<≤29 4/130, 29<≤30 22/130,
30<≤31 F*(x) 51/130,
31<≤32 83/130,
32<≤33 107/130,
33<≤34 125/130,
34<≤35 129/130,
35<≤36 1,
>36
. : =i =F*(x) F* 1 129/130 125/130 107/130 83/130 51/130 22/130 4/130 1/130 0 xi 28 29 30 31 32 33 34 35 36 7.
.
.
: 1)
, ..
. , ; 2)
; 3)
;
. ,
.
N .
.
_ 1+2+.+N = = N N =Σ xi i=1 N
1,2,.
N1,N2..Nk,
: _ 1×N1+x2×N2+...xk×Nk
= = N k =Σ xi×Ni i=1 N
n.
1+2+.n
= = n n =Σ xi i=1 n
1,2,.k n1,n2,.nk,
:
_ 1×n1+x2×n2++xk×nk =______________________
= n k =Σ xi×ni i=1 n xi 28 29 30 32 32 33 34 35 36 ni 1 3 18 29 32 24 18 4 1 _
28×1+29×3+30×18+31×29+32×32+33×24+34×18+35×4+36×1
=
=
130 = 4158
= 31,98 130
. : _ _ _ _ (1-)2
+ (2-)2 + .(n-)2 D=
n = n _ =Σ (i-x )2 i=1 n
.
1,2..x k n1,n2.nk, :
_ _ _ _ (1-)2× n1 + (2-)2 ×n2+ .(k-)2×nk = D= n k _ =Σ (i-x )2× ni i=1 n |
_ (28-31,98)2×1+(29-31,98)2×3+(30-31,98)2×18+(31-31,98)2×29+
D= +(32-31,98)2×32+(33-31,98)2×24+(34-31,98)2×18+(35-31,98)2×
×4+(36-31,98)2×1 =
130
= 291,972 = 2,24
130
- .
_ __ σ = D |
__
σ = √ 2,24 = 1,5
, :
1 -(x-a)2 F(x) = σ √2 × e 2σ2 |
SHAPE * MERGEFORMAT
8.
0 . 0 , .
.
χ2 .
χ2 . :
SHAPE * MERGEFORMAT
xi-x Zi = _ σ |
xi+1-x Zi+1= _ σ |
_
=31,98
_
D=2,24
_
σ=1,5
N |
xi |
ni |
xi |
xi^2 |
xi-x |
xi+1-x |
Zi |
Zi+1 |
(Zi) |
(Zi+1) |
Pi=(Zi+1)-(Zi) |
ni*=n*Pi |
ni-ni* |
(ni-ni*)^2 |
(ni-ni*)^2/ni* |
1 |
27 |
4 |
28 |
784 |
-4,98 |
-2,98 |
-3,32 |
-1,987 |
-0,4991 |
-0,4699 |
0,03 |
3,7999 |
0,2001 |
0,04004 |
0,01053712 |
2 |
29 |
47 |
30 |
900 |
-2,98 |
-0,98 |
-1,987 |
-0,653 |
-0,4699 |
-0,2357 |
0,23 |
30,446 |
16,554 |
274,03492 |
9,00068699 |
3 |
31 |
56 |
32 |
1024 |
-0,98 |
1,02 |
-0,653 |
0,68 |
-0,2357 |
0,2357 |
0,47 |
61,282 |
-5,282 |
27,899524 |
0,45526458 |
4 |
33 |
22 |
34 |
1156 |
1,02 |
3,02 |
0,68 |
2,0133 |
0,2357 |
0,4699 |
0,23 |
30,446 |
-8,446 |
71,334916 |
2,34299796 |
5 |
35 |
1 |
36 |
1296 |
3,02 |
5,02 |
2,0133 |
3,3467 |
0,4699 |
0,49913 |
0,03 |
3,7999 |
-2,7999 |
7,83944 |
2,06306482 |
Σ |
|
130 |
|
|
|
|
|
|
|
|
|
|
|
|
13,8725515 |
k (ni-ni*)2
χ2 .=Σ
i=1 ni
χ2 =13,8725515
χ2 £=0,05 .
=S-3
5-3=2
χ2.=6,0
χ2 =13,8725515 > χ2=6,0
.
9.
, .
.
, .
.
0 :
-
-
- .
. , .
1. .. : .- .: , 1988.
2. .. : . .; .: , 1986.
3. .., .. : . .- .: - - , 1994.
4. .., .. : . .- .: - - , 1994.
5. .. , .. , .. , .. , .. ,.., .. , ... : / ....-.:-, 2005.-656.-( ).
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