Kurs_Theor
.pdf, .
.
MS Excel |
[4]. |
, , 16
.
.
.
, .
,
.
- 3 -
1. |
|
|
, |
, |
|
, |
, |
. |
|
|
|
2. |
|
|
|
( |
, |
|
) |
. |
|
|
|
3. |
|
|
|
|
|
( |
, |
) |
|
. |
|
4. |
|
( |
, |
|
) |
. |
|
5. |
|
|
|
|
. |
|
|
6. |
|
|
. |
7. |
|
|
|
|
. |
|
|
8. |
|
|
|
. |
|
|
|
9. |
|
. |
|
10. |
|
|
- |
. |
|
|
|
11. |
|
|
|
|
. |
|
|
12. |
|
|
|
|
. |
|
|
13. |
|
|
|
. |
|
|
|
14. |
|
|
|
|
- |
. |
|
- 4 -
15.
.
16. |
. |
- 5 -
I.
.
.
§ 1 .
, x
(..) X. ..
|
F (x) |
P{ X |
x} |
|
||||
|
|
|
( |
, |
||||
) |
: F (x) |
F (x) |
F (x |
|
) . |
|
|
n |
|
||||||||
|
|
|
|
|
|
|
|
|
x(n) (x1,..., xn ) .. X.
.. X1,..., X n .
, .
, () ,
, |
P , |
. E , D , .
F (x) .. X.
.
T T (x(n) ) ,
.
.
- 6 -
§ 2 .
.
, H0 , F
. , ,
H1
F . ,
i)H0 : F F0 F
F0. ,
, , Random
Pascal,
[0;1] ;
ii) H0 : F |
F |
.
,
. H1
,
.
( [0;1]); iii) H0 : 0
0 .
,
? , ?.
, ,
.
, , , .
.
. (x(n) ) ,
- 7 -
1, , 0, . A ,
.
T (x(n) ) , , () C.
.
.
()
.
i) 1-,
.
2-,
. ,
, .
.
ii) |
1- |
(,
) . iii) ,
, |
, |
|
|
|
|
.
, ( )
:
PF { H0 |
} |
F H0 . |
1-, , . ,
.
.
- 8 -
,
.
,
2-.
, ,
.
0,05 (- 5%-
). |
0,10 |
0,01.
.
T |
T ( X (n) ) |
T C , |
|
1- |
|
PF {T ( X (n) ) C } , |
(*) |
|
F , |
H0 .
T ( X (n) ) ,
. ,
i) |
|
|
|
|
|
T |
|
|
( |
|
|
, T |
C ); |
|
|
|
|
ii) |
|
|
|
|
|
C |
|
T |
|
|
|
(*) |
|
|
1- |
; |
|
iii) |
|
|
|
|
|
|
|
|
|
|
|
T |
t |
( |
t |
C ) |
( |
t |
|
C |
) |
|
|
. |
|
|
|
. |
|
C , |
|
|
|
, |
|
|
|
|
|
T , |
|
|
. |
, |
25% , 50%, , ,
- 9 -
( |
C ) |
.
.
,
|
sup PF {T |
t |
} |
|
|
F H 0 |
|
|
|
( |
p |
p - |
). |
|
H0 |
, |
|
. |
|
, , C
T t .
C ,
, .
,
T ,
. , , .
(T t |
, T t |
| T | t ) |
p -.
(
, ,
) ,
, , ,
|
. |
|
|
|
: |
0.15 |
|
; |
0.10 |
0.15 |
; |
|
|
- 10 - |
0.05 |
0.10 |
|
|
|
|
; |
0.01 |
0.05 |
|
|
|
; |
|
|
0.01 |
|
|
|
|
. |
|
|
, |
|
|
1- |
|
|
|
|
|
. |
|
|
|
, |
|
|
|
|
|
|
. |
, |
, |
|
5 |
|
|
|
|
, |
5 |
|
|
|
. |
, |
|
|
|
1/25. |
|
, |
|
( , |
|
) |
|
|
0.03, |
, |
, |
|
|
|
. |
, |
|
|
|
|
|
|
, |
|
, |
, |
|
|
. |
|
|
|
, |
|
|
|
, |
|
2- |
, |
|
|
|
|
|
|
|
, |
, |
|
, |
|
|
, |
|
|
|
|
|
|
. |
, |
|
|
|
|
|
|
, |
|
|
|
|
|
? |
|
|
|
. |
|
|
|
|
|
§ 3 .
, |
|
, |
(x(n) ) , |
|
. |
; |
|
; |
|
. |
|
- 11 -
.
,
E ,
, , ,
, .
, , ,
, |
, |
.
.
i) |
X |
E X :
E X .
: , .
ii) A
(,
n) p P{A}:
E p n p .
iii) S 2
2 D X E ( X )2 :
E |
2 S 2 |
n |
1 |
2 . |
|
|
n |
|
|||
|
|
|
|
S 2 |
|
n |
|
|
|
S2 . |
|
n |
|
||
|
1 |
.
: lim E |
. |
n |
|
- 12 -