Economics 120A
Name:
_________________________
Professor Yongil Jeon
Winter 2008
Student ID#: _________________________
Answer to Homework #1 – Winter 2008
(Part of Midterm Exam, Summer 2007)
1. True/False (4 points each)
1.
The optimal solution to a mathematical model is always the policy that should be
implemented by the company.
Answer: False
2.
Microcomputers have made most quantitative approaches to decision making more
accessible to even moderate size firms.
Answer: True
3.
Past data might be used to test the validity of a mathematical model.
Answer: True
4.
Pr(A|B)=1 – Pr(B|A) for all events A and B.
Answer: False
5.
If A and B are mutually exclusive, Pr(A) + Pr(B) must equal 1.
Answer: False
2. (10 points)
. Prove that the
average
of deviations about the sample mean is zero.
Answer: The question asks you to show that for sample size n, that the
average
of deviations
about the sample mean is zero:
Using the definition of the sample mean, this can easily be shown:
(
)
1
1
0.
n
i
i
n
X
X
=
−
=
∑
(
)
1
1
1
1
1
1
0.
n
n
n
i
i
i
i
i
n
n
n
n
n
X
X
X
X
X
X
=
=
=
⎡
⎤
⎡
⎤
−
=
−
=
−
=
⎢
⎥
⎣
⎦
⎣
⎦
∑
∑
∑

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