3. (2 points) What is the estimated variance of the error disturbance u? (You need not simplify
your answer if it has a fraction or exponent.)
4. (3 points) Does the R-squared value (0.1104) tell you anything about the correlation between
sleep and totwrk

ECO 341K
University of Texas
Introduction to Econometrics
In-Class Exam #1 Solutions (Practice)
1.
An hour increase in amount worked per week is associated with an expected decrease in sleep of
8.97 minutes per week (or 0.149 hours per week), holding educ

38. Name a compound/drug that specifically affects actin-based motility in a
cell:_Cytochalasin D, phalloidin
39. This type of kinetics is characteristic of channels and passive transporters (e.g., for
glucose):_saturation_
40. When a normal cell becomes

Version 097 EXAM02 gilbert (56690)
4
2
2
4
4
F (u, v) du dv
u =
4. I = 2
F (u, v) du dv
0
1
2
5. I =
To compute a, b, c, d rst solve for u, v in
terms of x, y:
4
3. I = 2
2
0
1
(x y) ,
2
v =
1
(x + y) .
2
Thus
4
4
F (u, v) du dv
4
2
T : (u, v) ( u + v, v

2. Subspaces and FTLA (20 pts.)
Let A Rmn , and let B Rnn so that its left null space N (BT ) = cfw_0. Provide short proofs
(mostly 1 or 2 line, but no more than 3 lines) to the following statements. You may use the
Fundamental Theorem of Linear Algebra (

Name:
c) In order to save energy, it is advised that you let the dishes in the dishwasher air-
energy is needed to evaporate 0.5 L of water at 25 °C and latm?
new -——")° 5H3”
16°C, \asmn 15°C., \W
AH: L TAM“—
ww Auvg gm
\oooc ‘ubm \oo cum A “I 27. cg Md
A

Version 097 EXAM02 gilbert (56690)
4
Evaluate the double integral
I =
D
006
8y
dxdy
2+1
x
10.0 points
Evaluate the iterated integral
2
4y
2
when D is the region
(x, y) : 0 x 1,
0y
3xy dxdy
I =
0
0
x
by converting to polar coordinates.
in the xy-plane.
1.

Version 074 EXAM02 gilbert (56690)
1
To compute a, b, c, d rst solve for u, v in
terms of x, y:
1
4. I = 2
F (u, v) du dv correct
0
0
u =
2
2
5. I = 2
F (u, v) du dv
0
v =
1
(x + y) .
2
T : (u, v) ( u + v, v u )
1
1
1
(x y) ,
2
Thus
0
1
1
6. I =
2
6
1
F (

Version 114 EXAM02 gilbert (56690)
i.e., tan = 1, or, in other words, as = /4.
Since = 0 at the North Pole, W consists of
all points (, , ) such that
0 1, 0 2, 0 .
4
On the other hand, the Jacobian for spherical coordinates is 2 sin . Thus, in spherical
c

CAAM 335: Matrix Analysis
Solutions to Practice Examination 1
Posted Friday February 8, 2013.
1. Multiplication, Inverse, Rank (15 pts.)
1 0 0
1 0 0
1 0 0
Let A1 = a 1 0 0 1 0 0 1 0 ,
0 0 1
b 0 1
0 c 1
where a, b, c R. Let I be the 3 by 3 identity matrix.

ECO 341K
University of Texas
Introduction to Econometrics
In-Class Exam #1 (Practice)
NAME:
_
EID:
_
There are a total of 35 points on this exam. The exam is closed book. You may only refer
to the exam and the provided cheat sheet. Do not spend too much t

Version 114 EXAM02 gilbert (56690)
9
shows that E consists of all points (x, y, z) in
3-space satisfying both the inequalities
x, y, z 0,
as well as
0 z 1x2 , 0 y 1x , 0 x 1 .
Consequently, as a repeated integral,
1
1x2
1x
I =
f (x, y, z) dz dy dx .
0
0
0

Version 097 EXAM02 gilbert (56690)
10
y
Explanation:
To nd the Regression line for the given
data set we have to minimize the expression
edge 3
It will occur at the critical point of E, i.e., at
the solution of the equations
edge 4
edge 2
E(m, b) = (4m+b)

Version 074 EXAM02 gilbert (56690)
2
Use spherical coordinates to evaluate the
triple integral
6. I = 2
Explanation:
As an iterated integral, integrating rst
with respect to y, we see that
1
I =
0
0
x
4y
dy
+1
x2
I =
4z dV .
W
1. I = 4 2
dx .
2. I = 8 2
N

L9, Name:
/ CHEM 452
MIDTERM 2, November 14, 2012
Name: (please print)
Student ID number:
Do not open this test booklet until instructed to do so. This is a closed-
book exam. You are allowed to use a 1 sided, letter-sized sheet of notes.
Please sit a

Version 097 EXAM02 gilbert (56690)
6
In spherical coordinates (, , ),
keywords: surface, 3Dgraph, linear equation,
plane, intercepts, intercept form, tetrahedron,
volume, triple integral
008
x = cos sin ,
and
z = cos ,
10.0 points
The solid W consists of

Version 114 EXAM02 gilbert (56690)
while
y
= 3er sin ,
r
y
= 3er cos .
In this case,
4er cos
(x, y)
=
(r, )
3er sin
4er sin
3er cos
= 12er er (sin2 cos2 ) .
Consequently,
7
Explanation:
The region of integration is the set of all
points
(x, y) : 0 y 2

Version 097 EXAM02 gilbert (56690)
6.
8
(x, y)
= 4 cos 2
(r, )
Explanation:
For general functions the Jacobian of the
transformation
T : (u, v) (x(u, v), y(u, v)
is dened by
(x, y)
=
(u, v)
x
u
y
u
x
v
.
y
v
But when
x = er cos ,
y = 4er sin .
is bounded

Version 114 EXAM02 gilbert (56690)
11
while
z
0 y 4 1
x
,
5
0 x 5.
Thus
y
4(1x/5)
5
3(1x/5y/4)
I =
1 dz dy dx .
0
0
0
Now
3(1x/5y/4)
1 dz =
3(1x/5y/4)
z
0
0
x
lies in the rst octant, has one vertex at the
origin and three of its faces in the the coordinat

Version 114 EXAM02 gilbert (56690)
in the xy-plane, use the transformation
T : (u, v) (x(u, v), y(u, v)
Thus by the change of variables formula for
double integrals, if T maps the rectangle
D = [a, b] [c, d]
with
x = u+v,
y = vu
to express the integral
I

9. You decide to focus upon the subsample of individuals with college education (or, more
precisely, those with educ values of 16 and higher). You re-run the regression of sleep on
totwrk and educ on this subsample, which has 180 observations.
a. (2 point

28. How is Ras activity turned off?
a. It is turned off by phosphorylation.
b. It is turned off by hydrolysis of its bound GTP to GDP.
c. It is turned off by hydrolysis of its bound GDP to GTP.
d. It is turned off by an allosteric inhibitor.
e. It is turn

5. Electrical Circuit (20 pts.)
R2
x1
R1
x2
R3
x2
R4
i0
+
V0
Consider the circuit shown above. Note: For plotting purposes the node labeled x2 is split into two
nodes which are connected together by a wire (not a resistor!). The two nodes labeled x2 shoul

Version 074 EXAM02 gilbert (56690)
4
y
Consequently,
r
I = 4 .
006
4
5
x
10.0 points
A cylindrical drill with radius 4 inches is
used to bore a hole through the center of a
sphere of radius 5 inches to produce a solid
similar to the one shown in
In Cartes

Version 074 EXAM02 gilbert (56690)
to (y/2, y) for xed y, and then from y = 0 to
y = 8.
The volume of the tetrahedon E is given by
the triple integral
Consequently, after changing the order of
integration,
y/2
8
I =
f (x, y) dx dy
0
.
0
keywords: double i

Version 114 EXAM02 gilbert (56690)
This print-out should have 15 questions.
Multiple-choice questions may continue on
the next column or page nd all choices
before answering.
001
10.0 points
Use cylindrical coordinates to evaluate the
integral
2x2 dV
I =

4. Mechanical Truss (25 pts.) Consider the truss
4
1
1
3
2
2
5
The gray masses are xed and the others, labeled 1and 2, are free. The springs and the nodes are
numbered as shown.
(a) [5 pts] Compute A so that e = Ax.
Recall that sin(/4) = 2/2, cos(/4) = 2/

Name:
b) 1 kg of water evaporates at 100 °F and 1 atm. Name:
Problem 2 (a-c) (20 points)
Thermodynamics and your dishwasher
a) An energy efﬁcient dishwasher uses energy in the amount of 573 kWh/year assuming that you
run 264 loads of dirty dishes annually