Solutions Manual for John E. Freund's Mathematical Statistics with Applications 8th Edition by Irwin

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SOLUTIONS MANUAL For

J OHN E. F REUND ’ S M ATHEMATICAL S TATISTICS WITH A PPLICATIONS EIGHTH EDITION

Irwin Miller Maryless Miller

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Table of Contents Chapter 1 .............................................................................................................................. 1 Chapter 2 .............................................................................................................................. 8 Chapter 3 ............................................................................................................................ 23 Chapter 4 ............................................................................................................................. 46 Chapter 5 ............................................................................................................................. 61 Chapter 6 ............................................................................................................................. 80 Chapter 7 ............................................................................................................................ 95 Chapter 8 .......................................................................................................................... 112 Chapter 9 ........................................................................................................................... 130 Chapter 10 ....................................................................................................................... 139 Chapter 11 ....................................................................................................................... 162 Chapter 12 ....................................................................................................................... 171 Chapter 13 ....................................................................................................................... 182 Chapter 14 ....................................................................................................................... 199 Chapter 15 ....................................................................................................................... 226 Chapter 16 ....................................................................................................................... 245 Appendix A ...................................................................................................................... 258

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Chapter 1 1.1

n1

n

(a)

2i

i 1

0123 0123 012 01

(b)

n1

1.2

n1

n i  n  n n 2

2

i 1

1.3

1 2

i 1

(a) n300  4 n301  4 n302  3 n303  2 n310  4 n311  3 n312  2 n313  1

n1

n320  3 n321  2 n322  1 n330  2 n331  1

  4  4  3  ...  2  1  32

(b)

1.4

  13

n2

 n  n n n 2

1 2 3

i 1 j 1

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1

2

1.5

Mathematical Statistics, 8E

(b)

6, 20, and 70  1  2   “2 out of 3” m = 2 2         2(1  2)  6  1 1   2 3  4 “3 out of 5” m = 3 2            2(1  3  6)  20   2  2  2    3  4   5   6   “4 out of 7” m = 4 2               2(1  4  10  20)  70   3  3   3  3   10

1.6

(a)

 10  10!  0π    (7.92665)(3.678797)10  (7.92665)(454,002.49)  3,598,719 e

3.6288  3.5987  100  0.83% 3.6288 12  12  12!  24π    (8.683215)(4.41455)12  475,683,224 e

% error 

% error 

(b)

 52  52! 13   13! 39!  

1.7

4.7800  4.7568  100  0.69% 4.7900  52  104π    e 

52

13

 13   39  26π 78π     e  e 

39

1352  452 452   639 billion 19.5π 1313  1339  339 19.5π 339

 2n  2n !

Using Stirling’s formula in    yields  n  n! n!

2n  2n   2n  n π n 4 π  n    πn e   2n  1 2n 2 n 2 2  π    2π n    e   

1.8

n r and 123 = 1,728

1.9

 r  n  1  5  3  1  7   r  and  5    5   21

1.10 Substitute r  n for r into result of 1.9  r  n  n  1  r  1   5  1  4   r  n    r  n  and  5  3   2   6

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