. , , ,

,,,

.

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 .

, () () .

.

, ( ) .

:

xii+1

(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

, ( ) .

:

xii+1

(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.

9

Σ Pi* = 1

i=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 xni

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

I

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 .

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.-( ).

 

 

 

! , , , .
. , :