Solutions to exercises 651
- (i)λ 1 = 1 − 28
(ii)x 1 = 1 −(28 1 + 15 z) 23 ,y 1 = 1 (34 1 + 12 z) 23
Section 20.8
33.x 1 = 1 −0.7b
1
1 + 1 0.2b
2
1 + 1 0.3b
3
y 1 = 1 −1.3b
1
1 − 1 0.2b
2
1 + 1 0.7b
3
z 1 = 1 0.8b
1
1 + 1 0.2b
2
1 − 1 0.2b
3
Section 20.9
- (i)0.800000;0.640000;0.512000;
0.409600;0.327680
(ii)0.810000;0.656100;0.531441;
0.430467;0.348678
(iii)0.814506;0.663420;0.540360;
0.440127;0.358486
- (i)0.892626 (ii)0.027961
- (i)2.845387 (ii)−0.413504
- (i)2.191160 (ii)−0.036251
- (i)0.370740 (ii)0.368541
- (i)0.367885 (ii)0.367880
- (i)0.864660 (ii)−0.000004
- (i)3.258821 (ii)−0.00009
- (i)2.2274120 (ii) 0.0000007
Chapter 21
Section 21.2
- (i)
result 0 1 2 3 4 5 6 7 8 9 10
frequency 0 0 3 4 11 13 8 6 2 2 1
- (i)
class 36 41 46 51 56 61 66 71
–40 –45 –50 –55 –60 –65 –70 –75
frequency 2 2 9 8 14 8 11 6
3.5.22, 5 , 5
- (i)58.68, 60 ,59.5
(ii)58.67,(56−60),(56−60)
5.3.172,1.781
- (i)5.22,30.42,194.6
(ii)1.781,0.474
−...
−. −..
..−.
07 02 03
13 02 07
08 02 02
Section 21.4
- (i)0.6 (ii)0.1 (iii)0.7
(iv)0.7 (v)0.9
- (i)0.24 (ii)0.14 (iii)0.38
(iv)0.82 (v)0.62
- 1236 , 2236 , 3236 , 4236 , 5236 , 6236 , 5236 ,
4236 , 3236 , 2236 , 1236
- (i) 32216 (ii) 212216
(iii) 242216 (iv) 102216
- (i)
(ii)(a)P
0
1 = 11 ,P
1
1 = 1 P
2
1 = 10
(b)P
0
1 = 1 P
1
1 = 1 P
2
1 = 1123
(ii)
Section 21.5
- (i)0.5 (ii)0.31754
- (i)0.3487 (ii)0.001488
(iii)0.9298
- (i) 10236
2
(ii) 16236
2
(iii) 9236
2
(iv) 35236
2
- 456236
3
Section 21.6
16.ABCD,ABDC,ACDB,ACBD,
ADBC,ADCB,BACD,BADC,
BCDA,BCAD,BDAC,BDCA,
CABD,CADB,CBDA,CBAD,
CDAB,CDBA,DABC,DACB,
DBCA,DBAC,DCAB,DCBA
17.AB,AC,AD,AE,BA,BC,BD,
BE,CA,CB,CD,CE,DA,DB,
DC,DE,EA,EB,EC,ED
18.AB,AC,AD,AE,BC,BD,BE,
CD,CE,DE
19.AAABB,AABAB,AABBA,
ABAAB,ABABA,ABBAA,
BAAAB,BAABA,BABAA,
BBAAA
- 3
8
- (i)(a) 4
3
1 = 164 (b)3! 1 = 16
(ii)(a) (b) 1
4
3
4
=
8
431
280
!
!!!
=
Pe q
ijkijkkT,,
()=
−++εε ε
3qe e e
kt kt kt=++
−−−εεε012