Industrial Engineering Chapter 7 Homework Applied Statistics And Probability For Engineers 7th

subject Type Homework Help
subject Pages 9
subject Words 1780
subject Authors Douglas C. Montgomery, George C. Runger

Unlock document.

This document is partially blurred.
Unlock all pages and 1 million more documents.
Get Access
page-pf1
Applied Statistics and Probability for Engineers, 7th edition 2017
7-1
CHAPTER 7
Section 7.2
7.2.2
X
7.2.3
3.5
75.5psi 1.429
6
XX
n

= = = =
7.2.4 Let
6YX=−
7.2.5
2 = 25
7.2.6
μX = 8.2 minutes
n = 49
page-pf2
Applied Statistics and Probability for Engineers, 7th edition 2017
7-2
7.2.7
=
=
1
1
16
75
n
=
=
2
2
9
70
n
 
+ − +
1
12
12
22
22 2
1 2 1 2 12
~ ( , ) ~ ( , )
XX
XX
X X N N nn
7.2.8 a)
= = =
1.60 0.51
10
X
X
SE n
7.2.10 a)
==19.86, 23.65
X
XS
, When n = 8,
= = =
23.65 8.36.
8
XX
s
SE n
7.2.11 a) Point estimate of the mean proton flux is
=4958.X
page-pf3
Applied Statistics and Probability for Engineers, 7th edition 2017
7-3
7.2.12 a) Let
X
denotes the mean miles and
=()E X
, we further let Y denotes the additional miles
Section 7.3
7.3.1 a)
= = → =
10.25
SE Mean 2.05 25
SN
NN
7.3.2
( )
( )

=
=

 

= = = =

 

2
2
1
11
11
2
2 2 2
n
in
ii
i
X
E X E E X n
n n n
ˆ
ˆ
7.3.5

=
1
ˆ
()E
No bias

==
11
ˆˆ
( ) 12 ( )V MSE
page-pf4
Applied Statistics and Probability for Engineers, 7th edition 2017
7-4
To compare the three estimators, calculate the relative efficiencies:
3
2
7.3.7
Variable N Mean Median TrMean StDev SE Mean
Oxide Thickness 24 423.33 424.00 423.36 9.08 1.85
7.3.8 a)
= = = =
11
ˆ
( ) ( ) ( )E p E X n E X np p
7.3.9 a)

= = −
1 2 1 2 1 2
( ) ( ) ( )E X X E X E X
page-pf5
Applied Statistics and Probability for Engineers, 7th edition 2017
7-5
7.3.10 X ~ norm(μ = 10,
2 = 42), n = 16, nB = 200, the original sample (n = 16):
#
1
2
3
4
5
6
7
8
Value
4.26
6.59
12.36
7.47
10.84
1.17
17.02
14.10
7.3.11
a)

= = = − =


12 1 2 1 1 2 2 1 2 1 2
1 2 1 2 1 2
1 1 1 1
( ) ( ) ( )
XX
E E X E X n p n p p p E p p
n n n n n n
7.3.12 Suppose that two independent random samples (of size n1 and n2) from two normal distributions are available. Explain
how you would estimate the standard error of the difference in sample means
12
XX
with the bootstrap method.
page-pf6
Applied Statistics and Probability for Engineers, 7th edition 2017
7-6
Section 7.4
7.4.1.
=− 1
( ) (1 )x
f x p p
7.4.3
=
= = =
1
01
() 2
n
i
i
a
E X X X
n
, therefore:
=
ˆ2aX
7.4.4 a)

+ = = + =
1
12
11
(1 ) 1 ( ) 2
2
x
c x dx cx c c
7.4.5 a)


    
=


−−

 

==
   
==
   
   

1
11
11
(,)
ni
i
i
x
x
nn
ii
ii
xx
L e e
page-pf7
Applied Statistics and Probability for Engineers, 7th edition 2017
7-7
b)
( ) ( )( )
 
 
 
= +

ln ( , ) ln ln
i i i
x x x
Ln
better than the first.
page-pf8
Applied Statistics and Probability for Engineers, 7th edition 2017
7-8
Supplemental Exercises
7.S13
7.S14
=
=
1
1
1
()
n
i
ni
Lx
Upon setting the last equation equal to zero and solving for the parameter of interest, we obtain the maximum
likelihood estimate
=−
1
ˆln( )
n
i
x
n
page-pf9
Applied Statistics and Probability for Engineers, 7th edition 2017
7.S15
+ + + +
= = =
23.1 15.6 17.4 28.7
ˆ21.86
10
x

Trusted by Thousands of
Students

Here are what students say about us.

Copyright ©2022 All rights reserved. | CoursePaper is not sponsored or endorsed by any college or university.