Solutions Manual For John E. Freund's Mathematical Statistics with Applications 8th Edition By Irwin Miller, Marylees Miller (All Chapters, 100% Original Verified, A+ Grade)

SOLUTIONS MANUAL
For



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


Irwin Miller

Maryless Miller

, 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




iii

, Chapter 1
1.1




n1
(a) n
i 1
2i



0123
(b) 0123
012   13
01

n1 n1
1.2 n i  n
i 1
2
i 1
2  n1n2


1.3 (a)
n300  4 n320  3
n301  4 n321  2
n302  3 n322  1
n303  2 n330  2
n310  4 n331  1
n311  3
n312  2
n313  1

(b)   4  4  3  ...  2  1  32
n1 n2
1.4  n
i 1 j 1
2  n1n2 n3




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, 2 Mathematical Statistics, 8E


1.5 (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
 10 
1.6 (a) 10!  0π    (7.92665)(3.678797)10  (7.92665)(454,002.49)  3,598,719
e
3.6288  3.5987
% error   100  0.83%
3.6288
12
 12 
12!  24π    (8.683215)(4.41455)12  475,683,224
e
4.7800  4.7568
% error   100  0.69%
4.7900

52
 52 
104π  
 52  52!  e 
(b) 13   13! 39!  13 39
 13   39 
26π 78π    
e  e 
1352  452 452
   639 billion
19.5π 1313  1339  339 19.5π 339

 2n  2n !
1.7 Using Stirling’s formula in    yields
 n  n! n!
 2n   2n 
2n

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

1.8 n r and 123 = 1,728

 r  n  1  5  3  1  7 
1.9  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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