ECON 5350 Midterm Exam Fall 2012
1. Probability and Statistics (50 pts). Let X have a Pareto cdf where F (x; ) = 1
and zero elsewhere;
(1=x) for x
1
> 3.
(a) Find the pdf for X , f (x), and verify it is a valid pdf.
(b) Find the mean and variance of X .
(
ECON 5350 Solutions to the Midterm Exam Fall 2013
1. (50 pts) Consider the following (true population regression model without a constant (i.e.,
)
yi =
where i = 1; :; n and
i:i:d:N (0;
2
2 xi
1
= 0):
+ i;
).
(a) (10 pts) Derive the OLS estimator for
2
in
ECON 5350 Midterm Exam Fall 2013
1. (50 pts) Consider the following (true population regression model without a constant (i.e.,
)
yi =
where i = 1; :; n and
i:i:d:N (0;
2
2 xi
1
= 0):
+ i;
).
(a) (10 pts) Derive the OLS estimator for
2
in summation form.
ECON 5340 Solutions to the Final Exam Fall 2007
1. Linear Regression (50 pts). Consider the following regression model
yi =
where
i
i:i:d:(0;
2
1
+
2 x2;i
+
3 x3;i
+
i
); e0 e = 200;
2
6 103
6
X 0X = 6 0
6
4
0
0
200
(a) Find the least squares estimators f
ECON 5340 Final Exam Fall 2007
1. Linear Regression (50 pts). Consider the following regression model
yi =
where
i
i:i:d:(0;
2
1
+
2 x2;i
+
3 x3;i
+
i
); e0 e = 200;
2
6 103
6
X 0X = 6 0
6
4
0
0
200
0
(a) Find the least squares estimators for
(b) Test the
Solutions to the Final Exam
ECON 5350 Fall 2011
Consider the following cross-sectional regression model:
yi =
1
+
2 xi
+
i
where i = 1; :; N . The error terms are independent and mean-zero with variance:
2
i
=
2
exp( xi ).
Use the information above to ans
ECON 5350 Final Exam Fall 2011
Consider the following cross-sectional regression model:
yi =
1
+
2 xi
+
i
where i = 1; :; N . The error terms are independent and mean-zero with variance:
2
i
=
2
exp( xi ).
Use the information above to answer the following
ECON 5340 Final Exam Fall 2008
The Taylor rule for monetary policy describes how central bank authorities set interest rates in response to output
and in
ation. A simple Taylor rule is
rt =
1
+
2 yt
+
3t
+
(1)
t
where rt is the interest rate, yt is the ou
ECON 5350 Solutions to the Final Exam Fall 2012
Consider the Keynesian consumption function
Ct =
+ Yt +
t
where Ct is aggregate consumption, Yt is disposable income, and t = 1; :; T .
1. (20 pts) Under what condition is the OLS estimate of
unbiased? consi
ECON 5350 Final Exam Fall 2012
Consider the Keynesian consumption function
Ct =
+ Yt +
t
where Ct is aggregate consumption, Yt is disposable income, and t = 1; :; T .
1. (20 pts) Under what condition is the OLS estimate of
unbiased? consistent? e cient? A
ECON 5340 Solutions to the Midterm Exam Fall 2008
Consider the following regression model without a constant
yi =
1 x1i
+
2 x2i
+ i ; i = 1; :; n
where the error terms are i.i.d., x1 = x2 = 0 and corr(x1i ; x2i ) = 0. Use this information to answer the
fo
ECON 5340 Midterm Exam Fall 2008
Consider the following regression model without a constant
yi =
1 x1i
+
2 x2i
+ i ; i = 1; :; n
where the error terms are i.i.d., x1 = x2 = 0 and corr(x1i ; x2i ) = 0. Use this information to answer the
following equally w
ECON 5350 Solutions to the Midterm Exam Fall 2010
1. (70 pts) Use the multivariate regression model:
yi =
where i = 1; :; n,
i
iid(0;
2
1
+
2 xi
+
3 zi
+
i
), and x = z = 0 to answer the following questions:
(a) Write the regression model in matrix form.
ECON 5350 Midterm Exam Fall 2010
1. (70 pts) Use the multivariate regression model:
yi =
where i = 1; :; n,
i
iid(0;
2
1
+
2 xi
+
3 zi
+
i
), and x = z = 0 to answer the following questions:
(a) Write the regression model in matrix form. Clearly dene all
ECON 5350 Solutions to the Midterm Exam Fall 2012
1. Probability and Statistics (50 pts). Let X have a Pareto cdf where F (x; ) = 1
and zero elsewhere;
(1=x) for x
1
> 3.
(a) Find the pdf for X , f (x), and verify it is a valid pdf.
Solution. The pdf is
d
EIN 4401
LEAN PRODUCTION
HW # 4
DUE November 5, 2010
1.
Consider the data provided below for three products.
Product
A
B
C
Selling
price
($)
Unit direct
material
($)
Unit
direct
labor
($)
Unit
outsourcin
g cost ($)
Unit
overhead
($)
125
250
200
25
100
110