1. d , C D. . 903 D, 898 d, 98 d, 102 D. . . , ?
2. , , , , , . , , :
424 - ;
99 - ;
102 ;
415 .
.
3. , . 59 ; 62 ; 22 20 . , , , , , , . .
4. , , . ) , , , . , . ) ; , . ? ) , , , . : , ?
5. ( ) . 9.8 %. ) , , , , . . ) , , , , . , , ?
6. , ( ), . 10 . III , I . II , , I . .
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7. . (m), ( d ), (h), (G). (g), (), (i) (). , m 7% d, 11% G, 16 % p. G 4% d, 5% p, 8% h. h 12% d. , Xg ac 28% , Xg i - 11%, Xg a 18%, a ac 10%, i a 7%. .
8. . , , . 118 , 121 , 7 , 6 . 115 , 118 , 5 4 . .
9. . , , 3 , 3 , 47 - , 47 . ?
10. :
1 | 2 | 3 | 4 | |
:
) ;
)
)
) , , ;
) .
.
, . , . , , .
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, , . , , :
1. .
2. , .
3. .
4. .
5. .
, , , , .
, .
, q.
+ q = 1. , . , 0.4, :
+ q = 1, = 0.4, q = 1 0.4, q = 0.6
, . , . , .
, . , ,
= | = q | |
= | 2 | 2q |
= q | 2q | q2 |
, (p + q)2 = 2 + 2q + q2 = 1, 2 , 2q , q2 . , = 0.7, q = 0.3, 2 = (0.7)2 = 0.49 ( 49 % ), 2q = 2 0.7 0.3 = 0.42 ( 42 % ), q2 = (0.3)2 = 0.09 ( 9 % ).
, . , = 0.6, q = 0.4. 2 ()= 0.36, 2q () = 0.48, q2 () = 0.16. : 0.36 0.24 . : 0.24 0.16 . = 0.36 + 0.24 = 0.6; q =0.24 + 0.16 = 0.4. , .
? , , . , , , , , . , , . .
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, . (, ), : + q + r = 1, p2 + q2 + r2 + 2pq + 2pr + 2qr = 1.
1. . 84000 210 . .
, , . (q2) 210/84000 = 1/400 = 0,0025. √0,0025. , q = 0,05.
2. ( ). : 4169 , 756 3708 . ?
.
,
,
(4169), (3780), - (756), 8705. . 756: 8705 =0.09. q2 =0.09. q = √ 0,09 = 0,3. = 1 q. , = 1 - 0,3 = 0,7.
3. . 1 / 20 000. .
.
. 1/20000 -
q2. , : q = √1/20000 =
= 1/141. : = 1 - q; = 1 - 1/141 = 140/141.
2pq. 2 pq = 2 (140/141) (1/141) = 1/70. .. 20000 1/ 70 20000 = 286 .
4. : . , . 0.458. 80%. .
.
: = 0,458. q= 1 0,458 = 0,542. - 2, 2pq q2. 2 = 0,2098; 2 pq = 0,4965; q2 = 0,2937. %, , 20,98%; 49,65%; 29,37%.
-- , , . . 2 + 2pq = 80 %, 0,8. -, : q2 = 100% - 80% = 20%, : 1 - 0,8 = 0,2.
, q = 0,45. = 1 0,45 = 0,55. (2) 0,3 30%. (2pq) 0,495, 50%.
5. 25%. 6:10 000. .
.
, , ( ). . 2 + 2pq +. q2=1 , (2+2q). 6/10000 (25%) . , 2 + 2pq = (4 6)/10 000 = 24/10000. q2 ( ) 1 - (24/10000) = 9976/10000 9976 .
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6. :
I - 0.33
II - 0.36
III - 0.23
IV - 0.08
.
.
, 1, IA IB. _ I 11, II I A1A IAIo; IBI 11 - , IV 11. 1 , / q, 1 r. : + q + r = 1, : 2 + q2 + r2 + 2pq + 2pr + 2qr. . , I 11 2. II : 11, 2 11 2r. III
; IBIB - q2 11 - 2qr. IV 1A1, 2pq. .
I r2= 0.33
II 2 + 2r = 0,36
III - q2 + 2qr = 0,23
IV - 2pq = 0,08
/: 0.33. r = 0,574.
1 / : I II I III. 2 + 2r + r2, q2 + 2qr + r2.
2 + 2r + r2 = ( + r)2 = 0,69. , + r = √0,69 = 0,831. , r = 0,574. = 0,831 - 0,574 = 0,257. 1 0,257.
IB = q2 + 2qr + r2 = (q + r)2 = 0,56; q + r = 0,748; q = 0,748 - 0,574 = 0,174. IB 0,174.
+ q + 1 0,005, .