2.2.1. , 40 . . 3 : ) 20% ; ) 25% .
. ) n = 3, F3=40 . ., d = 0,2, (67) :
. .
:
. .
) d = 0,25,
. ., . .
, , , .
2.2.2. 70 . . 4 32 24% . , .
. (67). , n = 32/12 = 8/3. Fn =70 . ., d = 0,24, :
. .
, w = 2, f = 2/3 (68) :
. .
, .
2.2.3. 1 . . , 18% 30 , 90 , 180 , 1 , 2 , 3 , 5 . 360 .
. F = Fn = 1 . . d = 0,18 (19), - (67), , :
(. .)
30 (n= 1/12) | 90 (n= 1/4) | 180 (n= 1/2) | 1 (n= 1) | 2 (n= 2) | 3 (n= 3) | 5 (n= 5) | |
0,985 | 0,955 | 0,91 | 0,82 | 0,64 | 0,46 | 0,1 | |
0,9836 | 0,9516 | 0,9055 | 0,82 | 0,6724 | 0,5514 | 0,3707 |
, 1 . . , , . , 90 : - 955 . .; 951,6 . ., .. 3,4 . . , , .
, 5,56 , ( ). . , 15 : . .
2.2.4. 46 . . 4 . , : ) ; ) ; ) 24% .
|
|
. n = 4, Fn = F2 = 46 . . (69).
) m = 2, d(m) = d(2) =0,24, :
. .
= 4, d(m) = d (4) = 0,24, :
. .
) = 12, d(m) = d (12) = 0,24, :
. .
, , .
2.2.5. , 30 . . 25 , d (4) =20% . .
. n = 25/12, = 4, F = F 25/12 = 30 . . (69),
. .
(70). = ,
. .
, .
2.2.6. 80 . . 62 . . , : ) 28%, ) 28%?
. ) (71) = 62 . ., F = 80 . ., = 1, d (4) = 0,28, :
.
, 360 , = 360 0,776 = 279,36 . , , 280 .
) (22), F = 80 . ., d = 0,28:
, 289,44 .
, = 290 .
2.2.7. 2,5 , . , : ) ; ) ?
. ) (72), = 0,25 Fn, = 2,5, = 4, :
.. d (4)=54,78%
) = 12,
.. d (4)=54,19%
, , .
2.2.8. , 18% .
. (74), :
def | 0,18 | 0,1719 | 0,1682 | 0,1659 | 0,1653 | 0,1648 |
, def ( (74) ). , > 1 def <d(m) .
2.2.9. , 30% : ) ; ) ; ) .
. def =0,3 (73).
|
|
a) m = 2,
32,67%.
) = 12,
35,14%
) 360 , m =360 :
35,65%.
d (2), d (12) d (360) , . 30% , 2 32,67% , 12 35,14% , (360 ) 35,65% . , d (2)< d (12)< d (360), .. , . , : d (m) d (1) - m > l, d (m) > d (l).
2.2.10. 12 . . 3 6 , 5 . . .
. (75) n = 3,5, = 5, F 3,5 = 12, :
22,13%.
2.2.11. 90 . ., 5 , 24% . , : ) ; ) ; ) . 24% .
. (77), = 90 . ., = 5, d (2)= d (12) = d (360) = 0,24. m =2, m = 4, m = 12, :
) . .;
) . .;
) . .
, (76), 10, 20 60, 12% (24%: 2), 6% (24%: 4) 2% (24%: 12).
, ), ), ) (58) :
) . .;
) . .;
) . .,
.., , . . , , , , . , , , . , m = 365 ( ), 24% 298,928 . ., 298,693 . ., 235 ., , , m = 4 21 592 .
2.2.12. 20 . . 5 , : 16%, 19% 23%. . ?
. (76), Fn =20, = 2, d = 0,16: . . (76), , n = 2, d = 0,19: . . , d = 0,23; , 5 :
. .
() , , , , :
|
|
, 18,64%.
2.2.13. 1 3% , . , .
. F , F 0,03 F = 0,97 F. (64), = 0,97 F, Fn = F n = 1/12:
, 44,12%.
ref; :
, 44,12% , d (12) = 3% 12 = 36%.
, , .
2.2.14. 28% . : ) 3 ; ) .
. ) (23), ; F - , n, F (77), = 0,25, m = 2, d (2) = 0,28. ,
, 31,32% .
, (85): , r d(m):
) =1, (85) :
, , r = 35,21%, , d (2)= 28%. , (26):
(74) :
2.2.15. 3 26% . , 2% , . 2 6 ?
. 3 F 3. , , : , , 2% : . , : . (75) :
.. d ef = 26,50%, 26% .
, .
2 , , : , :
, , :
.. , 3 .
6 :
.. , 3 .
2.2.16. 320 . . 8 , 50 . . , .
|
|
. d . , Pn n k - .
Pd P Pd = P (1 d). P (1 d) P (1 d) d P (1 d) P (1 d) d = P (1 d) 2. , , k - P (1 d) k (.. P k d).
n - Pn, Pn=P (1 d) n, d : , (75) ). n = 8 , = 320 . ., = 8 = =50 . ., :
20,71%.
:
) :
Pd = 320 0,2071 = 66,272 . .,
-Pd = 320 66,272 =253,728 . .;
) :
(1 d) d = 253,728 0,2071 = 52,547 . .,
P (1 d)2 = 253,728 - 52,547 = 201,181 . .
, :
, . . | , . . | |
66,272 | 253,728 | |
52.547 | 201,181 | |
41,665 | 159,516 | |
33,036 | 126,48 | |
26.194 | 100,286 | |
20,769 | 79,517 | |
16,468 | 63,049 | |
13,057 | 49,992 |
50 . . ( 49,992 . .) .
. , , . .
, , , . , (), - .
, .
, , .