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IE 305/404
Spring 2009
Review Questions for Exam 2 (ignore that we start at question 4)
Question 4
(Chapter 7)
In the table below is output from EXCEL for the random number generator:
X
i+1
= 59X
i
@ 512
X
0
= 73
i
X(i)
aX(i)
aX(i)@M
U(i)
(2 digits)
0
73
4307
211
1
211
12449
161
0.41
2
161
9499
283
0.31
3
283
16697
313
0.55
4
313
18467
35
0.61
5
35
2065
17
0.07
6
17
1003
491
0.03
7
491
28969
297
0.96
8
297
17523
115
0.58
9
115
6785
129
0.22
10
129
7611
443
0.25
a)
What will X
11
be?
What will U
11
be?
Explain or show work.
X
11
= _____________
U
11
= _____________
b)
What will X
128
be?
What will U
128
be?
Explain or show work.
X
128
= ___________
U
128
= ___________
Question 5
(Chapter 6)
Below is an actual plot of the empirical CDF of the 10 data points in question 1 along
with the CDF for the U(0,1) distribution.
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0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0
0.2
0.4
0.6
0.8
1
a)
Perform the KolmogorovSmirnov Goodness of Fit Test at α=0.05 to test if the
data comes from a U(0,1) distribution.
b)
Perform a ChiSquared Goodness of Fit test at α=0.05 to test if the data comes
from a U(0,1) distribution.
Use 2 cells.
c)
Construct a PP Plot for the 10 data points in question 1 to see if the data are from
a U(0,1) distribution.
Question 6
(Chapter 6)
Below is a picture of the Uniform(
θ
0.5 ,
θ
+0.5) Distribution.
You are given the following dataset of size 5 from this distribution:
0.6, 0.75, 1.1, 1.25, 0.9
a)
Find a maximum likelihood estimator of
θ
.
Be sure to show work and/or provide
adequate explanation.
b)
Find the method of moments estimator of
θ
.
Be sure to show work and/or
provide adequate explanation.
1.0
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 Spring '08
 Storer

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