Chapter 1
1.1
1.2
11
2212
11
nn
ii
ni n nn



1.3 (a)
300
4n
320
3n
(b)
443...21 32
2 Mathematical Statistics, 8E
1.6 (a)
10
10
10
10! 0 (7.92665)(3.678797) (7.92665)(454,002.49) 3,598,719
e
π

 


1.7 Using Stirling’s formula in
22!
! !
nn
nnn



yields
2
222
22
4
1
22
2
n
nn
n
nn
nn
nn
e
ne
ππ
π
π
π
 
  
  








Chapter 1 3
1.11 (b) Seventh row is 1, 6, 15, 20, 15, 6, 1
Eighth row is 1, 7, 21, 35, 35, 21, 7, 1
1.14 (a) Set x = 1 and y = 1
(b) Set x = 1 and y = 1
(c) Set x = 1 and y = a 1
1.20 (a)
( 1)( 2)…( ) (1)
!
r
r
r
 
(b)
( )( 1)…( 1) ( 1)…( 1)
(1)
!!
1
( 1)…( 1)
(1) (1)
!
r
rr
nnn nr nn nr
rrr
nr
nr n n
r
r
  





 
  

4 Mathematical Statistics, 8E
1.24 Note: If there are 0 turn-ons the first night, 6 turn-ons in four nights can only occur if there are 2
turn-ons on each of the subsequent three nights. Thus, we need to show only that part of the tree
following this event.
Chapter 1 5
1.25
1.27 (a) 5
(b) 4
1.28
1.30 (a)
65 30;
(b)
66 36;
1.31 (a) 6; (b)
65 30;
(c)
54 20
first one fixed; (d)
6302056
6 Mathematical Statistics, 8E
1.32 (a)
452 40; 
(b)
563 90
1.33 (a)
54 20;
(b)
543 60
1.38
6! 720
1.39
6! 720 90
2! 2! 2! 8

1.40
5! 120
and
120 2 4! 72 
1.41
7! 5040
1.45
8! 40320 280
3! 4! 6 24

1.46 (a)
20 77,520
7



; (b)
20 184,755
10



Chapter 1 7
1.48
37 37 321 17 63 7 70
22 31
 

 
 
1.49
473 6 35 3 630
231

 


1.53
5
5 15,625
1.54
12 6 1 17 17 6,188
12 12 5

 

 
 
1.55
12 1 11 462
66



