Applied Statistics and Probability for Engineers

682 APPENDIX C ANSWERS TO SELECTED EXERCISES

5-9.

5-11. E(X) 1 8, E(Y) 1  4

5-13. X0, Y0 and XY 4

5-15. (b)fX(0)0.2338, fX(1)

0.4188,fX(2)0.2679,

fX(3)0.0725, fX(4)

0.0070

(c)E(X)1.2

(d)

(e)

Section 5-2

5-17. (a) 0.5 (b) 0.35 (c) 0.5

(d) 0.8 (e) 1.5

5-19.

5-21. (a) 0 (b) 0.072 (c) 0.736

(d) 1

5-23. (a)x 0, y 0, z 0,

x y z 4

(b) No

5-25. (a) 0.1758 (b) 0.2198

(c)E(X)1.067,

V(X)0.6146

5-27. (a) Yes (b) 0.1944

(c) 0.0001

5-29. (a) 0.7347 (b) 0

(c)

(c)

5-31. (a) binomial p0.03, n 3

E(X)0.03, V(X)0.0297

(b)P(X 0 Y2)0.98958,

P(X 1 Y2) 0.01042

(c)E(XY2) 0.01042,

V(XY2) 0.01031

Section 5-3

5-35. (a) 0.4444 (b) 0.6944

(c) 0.5833 (d) 0.3733 (e) 2

(f ) 0

5-37. 1  24

5-39. (a) (2x1)12 for 0 x 3

(b) (y1)6 for 1 y 3

(c) 2.111

(d) 0.4167

(e) (2 x)6 for 0 x 2

5-43. 10

5-45. (a) 10(e^2 xe^5 x)3 for 0 x

(b) 3.157e^3 yfor 0 y 1

(c) 0.089 (d) 2e^2 x^4 for 2 x

E 1 X 0 Y 22 1.7142

P 1 X 20 Y 22 0.7347

P 1 X 10 Y 22 0.2449,

P 1 X 00 Y 22 0.0204,

P 1 X 20 Y1, Z 22 0.6

P 1 X 10 Y1, Z 22 0.4,

E 1 Y 0 X 32 0.143

fY 03112 0.143,

fY 03102 0.857,

f 1 x, y 2 0, g f 1 x, y 2  (^1) 5-49. 2  15
5-51. (a) (x1)7.5 for 0 x1,
2 7.5 for 1 x 4
(b) 0.5 for 0 y 2
(c) 1 (d) 0.25
5-53. (a) 0.0439, 0.0019
(b) 0.065
Section 5-4
5-55. (a) 0.25 (b) 0.0625 (c) 1
(d) 1 (e) 2 3
5-57. (a) 2xfor 0 x 1
(b) 0.25
5-61. 6
5-63. (a) 3(x1)^2 for 0 x 1
(b) 6(1 xy) for 0 x,
0 yand xy 1
(c) 1 for x 0
(d) 4(1  2 x) for x0.5
5-65. (a) 0.032 (b) 0.0267
Section 5-5
5-67. XY0.703, (^) XY0.885
5-69. c 1 36, XY 1 36,
(^) XY0.0435
5-71. XY 1 3, (^) XY 1  2
5-73. c9.5, XY1.852,
(^) XY0.928
5-75. Xand Yare independent and
XY XY 0
Section 5-6
5-81. 0.827
Section 5-7
5-87. (a) 30 (b) 97 (c) 0.5
(d) 0.846
5-89. (a)E(T)4, T0.1414
(b) 0.017
5-91. (a)E(D) 1 8, D0.140
(b) 0.187 (c) 0.187
5-93. (a) 0.05 (b) 0.023
(c) 12.129
(d) 0.388 (e) 136
5-95. (a) 0.023 (b) 4558
Supplemental
5-97. (a) 38 (b) 34 (c) 3 4
(d) 3 8
(e)E(X) 7 8, V(X)
39 64, E(Y) 7 8,
V(Y) 39  64
5-99. (a) 0.0631 (b) 0.122
(c)E(X)2, V(X)1.8
(d)fX 19 (0) 0.667,
fX 19 (1) 0.333
(e) 1 3
5-103.(b) 13 (c) No
5-105.(a) 0.0093 (b) 0.5787
(c) 0.75 (d) 0.2199
(e) 2.25 (f ) 1.3333
5-107.(a) 12 (b) 14 (c) 1 for
x^2 y^2  1
(d) for 1 x 1
5-109. 3  4
5-111.(a) 0.085 (b) Bin(10, 0.3)
(c) 3
5-113.(a) 0.499 (b) 0.5
5-115.(a) 0.057 (b) 0.057
5-119.(a)E(T)1.5, V(T)0.078
(b) 0
(c)E(P)4, V(P)0.568
5-121.5,
CHAPTER 6
Section 6-1
6-1. ,s0.00473
6-3. ,s226.5
6-5. ,s12.294
6-7. 5.44
6-11. (a)
(b)s0.02066
6-13. (a) ,s12.16
(c) , s10.74
Section 6-3
6-19.
Variable N Median Q1 Q3
cycles 70 1436.5 1097.8 1735.0
6-21.
Variable N Median Q1 Q3
yield 90 89.250 86.100 93.125
6-25. ,s13.03, and
6-27. (b) ,s2.8, and
(c) 22 40
Section 6-5
6-43. (a) (b)s^2 0.867,
s0.931
6-45. (a) ,s^2 9.55,
s3.09
(b) , largest value can
increase by any amount
x~ 953
x952.44
x4.0
x~ 90
x 89
x~261.15
x260.7
x66.86
x65.85
x7.184
x43.975
x7068.1
x74.0044
 13
221 x^2
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