Problem 3.2 An electron in a hydrogen atom is in the 2p1 state.
a) Calculate the orbital energy, the angular momentum L and the z component of the
angular momentum. You may give your angular momentum calculations in units of
.
Solution:
2.18 1018 J
=
= 5.

P=(0.9*110)/1.04
10. At the beginning of time t, Company X paid a dividend per share of $2 and it is projected to keep a dividend
growth rate of 4%. If the required return on this equity is 10%, what is the price
(i) at the end of time t:
P_t = 2*(1.04)/(

BICD110 Midterm (Prof. Yimin Zou)
4. Experiments (10%)
1) FRAP
a) Briefly explain what is a FRAP experiment and what it is used for.
FRAP is Fluorescence recovery after photobleaching. An area of a cell membrane
containing fluorescent markers/labels on sp

Y? Y!
2. (15 points) You are given that the row reduced echelon form of the matrix
2 1 1 -2 2 1 0 1 1 0
A: 3 2 1 3 1 isB= 0 I 1 0 0 .Youdonotneedto
1 1 0 "1 1 0 0 0 0 1
verifyit.
G7? (3) Write the general solution of the system Aif = 6 in parametric form

Eco 171 Industrial Organization
First Midterm Exarn
Name:
Section:
Instructions
There are 5 short questions and 2 problems, each worth 1/3 of the total
points. Answer in the space provided (no ne (:1 to use it al .) If necessary use
the back of the page.

1
1
3
4
2
0
5
8
2
1
2
2
e i / 2
sin
( 3cos 1)
1/ 2
15
4
sin cos
e i / 2
15
16
sin 2
e i 2 / 2
2
Useful Integrals
Definite and Indefinite Integrals that MAY be useful. In the integrals below a is a
constant and a0 is the Bohr radius. The function Rn ( r

Math 235 section 1 r Midterm 1 Spring 2014
psi/WU
Your Name:
Student ID:
This is a 90 minutes exam. This exam paper consists of 6 questions. It has 7 pages.
The useof calculators is not allowed on this exam. You may use one letter size page of
notes (bo

ECO380: Term Test
8
Since two firms are symmetric, firm 2s best-response function is
p2 (p1 ) =
6 1
+ p1 .
5 5
(4)
2. Find the differentiated Bertrand Nash equilibrium outcome. What are the profits of each firm? Is this outcome efficient? Explain your ans

Economics 151A
Professor David Neumark
Final Exam
Tuesday, November 6
Please place all materials on the sides of the room, away from your desks. You may not use any
materials or calculators for this exam. You will have 1 hour and 20 minutes to complete th

Problems
1. There are two rms in an industry. Suppone n of those rms have
marginal cost zero and 2 n have marginal cost c = 30: Demand is
given by p = 90 Q:
(a) Solve the Cournot equilibrium for n = 0; 1; 2:
(b) Calculate the Herndahl index for each of th

2. There are two groups of consumers to which a monopolist can sell. The
first group has aggregate demand function:
p = 10 q/20.
The second group has demand function:
p = 5 q/10.
The monopolist has zero marginal cost.
(a) If the monopolist can perfectly d

3. There are two rms in a market that have one unit to sell each. With
probability 1/2 only one consumer will come to purchase and with probability 1/2 two consumers will show up. Both consumers are willing
to pay up to a dollar for the good but will buy

BIS 104 Form D
Midterm 2 March 4, 2011
Instructions:
Be sure to mark the version of your test on the scantron. This is FORM D.
There are 9 pages and 33 questions to this exam. Each question is worth 3 points, and
you get 1 point for filling in your studen

2. There are two groups of firms in a competitive market. Each firm in the
first group has constant marginal cost $10 up to 10 units and constant
marginal cost $30 from 10 to 20 units. Each firm in the second group
has constant marginal cost $20 and can p

Problem 2.4. The molecule HBr rotates as a three dimensional rigid rotor. The bond
length of 1H79Br is 0.14 nm. Calculate the energy, the angular momentum L, and the z
component of the angular momentum LZ if the wave function is
21 ( , ) = 21 ( ) 1 ( ) .

EECS 70B
Spring 2011
Total Points: 105 pts
Name: _
Midterm Exam (8:30 to 9:50 am, 5/6/11)
Problem 1:
10 pts
Problem 2:
10 pts
Problem 3:
10 pts
Problem 4:
25 pts
Problem 5:
20 pts
Problem 6:
20 pts
Problem 7:
10 pts
1. (10 pts) Consider the following Op A

Econ 171 - Industrial Organization
Second Midterm Exam - 2009
Name:
Section:
Instructions
There are 6 short questions and 2 problems. Short questions are worth a
total of 40 points and the problems a total of 60 points. Answer in the space
provided (no ne

Part II. Problems.
1. Company x produces copy machines and leases them to two customers:
firm 1 and firm 2. Besides leasing the machines, it supplies the special
paper required by its machines.
The demand function for copies of both firms are:
q1 = 8 p1
q

4. A monopolist can sel in two markets (one with a higher demand function
than the other) and is able to price discriminate ful y in each of them (rst
degre price discrimination.) Which of the following statements is true?
Explain.
(a) Only consumers in t

ECO380: Term Test
4
1. Write both firms profits as a function of their quantities. That is, what are
a (qa , qb ) and b (qa , qb )?
Solution.
a (qa , qb ) = (74 (qa + qb )qa (5 + 2qa )
= qa2 + (72 qb )qa 5.
b (qa , qb ) = (74 (qa + qb )qb (5 + 2qb )
= qb2

BIS 104 Form D
Midterm 2 March 4, 2011
30. A variety of important model organisms have elucidated different aspects of the cell
cycle. The molecular nature of cyclins and the fact that their levels oscillate in the cell
cycle was discovered using _.
A. Bi

ECO380: Term Test
6
Solution. The utility of purchasing the low ABV beer is
Uxl = 10 pl 1 (x 5)
where pl is the price of the light beer.
2. What is the utility of purchasing the high ABV beer for a consumer whose
preferred beer contains x ABV?
Solution. T

vtit
10
5
1
2
3
4
5
6
ts
-5
- 10
6. (20 pts) (a) (15 pts) Sketch the Magnitude (M) of Bode plot for H ( )
2000
.
(10 j )(100 j )
Label the ticks for x-and y axes in your plot.
Magnitude dB
(b) (5 pts). Find the slope of M for > 100 radian/s.
w
7. (10 pt

c) (5 points) Let A, B C, D be 11 x n matrices, with A and B invertible which
satisfy the equation ABC B 1 A 1_D. Express C in terms of A, B, and D. Show gig
AW? botfl youimk 39; A1 3: m'LM- W A on 70%? mff
m A DA _ 8 7, Wu
Rtpegf WH) 731w 10? W W _
id: [

ii . Answer the fol owing question without making any calculations:
Has welfare -measured by total surplus- increased with price dis-
crimination? Explain.
T-a vow-cu. Maw- 9- lh" 45
05% w+ Men-c41-
(b) Answer the previous three questions assuming margina

For the rest of the problem, suppose rms can invest to increase their
quality and if they do so they raise the utility of consumers that purchase their product by and equivalent of v = 1 dollars.
(b) Suppose only one rm (say L) chooses to provide this imp

1/11/06 3:54 PM C:\Dan\CSU\Book\Problems\Nonlinear\pdepprox.m 2 of 2
m
end
x0=(a+b)/2:
% Plot the final solution and compute the RMS error.
subplot(3,1,k);
ErrRMS = f(xO, M, true)
end
end
%
function ErrRMS = f(sigma, M, PlotFlag}
global muGauss NumPts dx

1/11/06 6:15 PM C:\Dan\CSU\Book\Problems\Unscented\TrackUKF.m 1 of 3
N
function TrackUKF(tf);
% Optimal State Estimation Solution Manual, by Dan Simon
Problem 14.14
do
0V1
UKF simulation of land vehicle tracking system.
INPUTS:
tf = simulation length
n:\‘

1/11/06 3:52 PM C:\Dan\CSU\Book\Prob1ems\Nonlinear\Henl.m 3 of 3
EstZErr
EstiErr
sqrt{(norm(xArray — xhatZArray)‘2/length(xArray)};
sqrt{(norm(xArray — xhatiArray)AZ/length(xArray);
if ~PlotFlag
return;
end
close all;
k = 0 : kf;
figure; hold;
plot(k, xAr