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C H APTE R 9
I
The Ctlpit,il :Isset ?ri<.i117bio:le!
311
simple version of the expected return-beta relationship holds. But if those distributions change
unprrdictably, or if investors seek to hedge nonmarket

10) Which of the following is not true about the composition of U.S. GDP in 2010? (You may
want to consult the Bureau of Economic Analysis at www.bea.gov)
A) The majority of consumer spending is on nondurable goods.
B) Purchases made by state and local go

Problem 2 (10 Points)
Lamborghini, an Italian sports cars maker, asked you to design a relational database that keeps track of its
part suppliers and the purchases of parts by its departments from these suppliers.
A part is identified by it its PID number

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https:/www.coursehero.com/file/7193411/25BIS-2C-Midterm-1/
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Bis 2c winter midterm 1 answer key
SA1
C1, C2, C4,C5
C1 and C4
C2 and

terminate our computations by computing f1(6). Then we retrace our steps and determine
the amount that should be allocated to each investment (just as we retraced our steps to
determine the optimal production level for each month in Example 4).
Stage 3 Co

FIGURE
8
Time Horizon for
Equipment
Replacement
Year 1
Time
0
Year 2
Time
1
Year 3
Time
2
Year 4
Time
3
Year 5
Time
4
Time
5
1, 2, or 3 years; after i years of use (i 1, 2, 3), it may be traded in for a new one. If an
i-year-old engine analyzer is traded

This often occurs when the stage alone supplies sufcient information to make an optimal decision. We now work through several examples that illustrate the art of formulating dynamic programming recursions.
EXAMPLE
8
A Fishery
The owner of a lake must deci

Chemistry 14D Lecture 1
Fall 2012
Final Exam Part A
Page 3
10. (15) Write the major product(s) for each reaction shown below. If no reaction occurs, write "NR". Assume the
reactants above and below the arrow are present in excess. Do not provide any mecha

Chemistry 14D Lecture 1
Br
Fall 2012
Final Exam Part B Solutions
Page 3
Br
Br
29.
Ph
Free radical chain mechanisms end with a propagation step,
not a termination step.
+ Br
Ph
30. Atom transfer (2nd and 3rd mechanism steps), initiation (1st mechanism step

Total transaction costs=$92,680.
e. What if Grant Hill Associates cash holdings of Asia money are 15 billion Indonesia rupiahs, 18 million
Malaysia ringgits, and 2.4 billion yens, it is not clear how these holdings should be converted back into
dollars, w

Chemistry 14D Lecture 1
Fall 2012
Final Exam Part B Solutions
Page 1
Statistics: High score, average and low score will be posted on the course web site after exam grading is complete.
A note about exam keys: The answers presented here may be significantl

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Bioenergetics: Aerobic Production of ATP Review Sheet
You should read pp. 47-59 (Oxidative System through Oxygen Needs) and refer to lecture notes when
completing

Nathan Li
December 16, 2011
AS.180.261.01
price = C/(1+i) + C/(1+i)2 + + C/(1+i)T-1 + (C+F)/(1 + i)T , where C is a periodic coupon payment,
i is the interest rate, T is the time it takes for the bond to mature, and F is the final face
value that is paid

4. (30 points) Discuss the policies of the U.S. government, the
Federal Reserve, and regulators of financial institutions.
(Suggested length: 1-2 pages for each part.)
A. With hindsight, could policymakers have done things before
2007 to prevent the finan

114.
Did you bubble in your perm number and what color did you write underneath it?
A. For the last time, YES; Blue
B. Ok one more time, YES!, Yellow
C. No more test color questions! Yes! Pink
End of Exam. Please return your test and scantron to your TA.

102. A filter feeder acquires food items by (3 pts)
A. extracting particles suspended in water.
B. ingesting mud and extracting particles.
C. filtering food substances from blood.
D. using claws and jaws to restrain prey.
E. using poison to restrain prey.

Nathan Li
December 16, 2011
AS.180.261.01
C. Today, do policymakers have tools to reverse the increase in
unemployment that occurred during the crisis? What, if anything,
can they do to reduce unemployment beyond what they are already
doing? Are there dra

cj
In terms of benet per unit weight, the best item is the item with the largest value of .
wj
Assume there are n types of items that have been ordered, so that
c1
c2
cn
w1
w2
wn
Thus, Type 1 items are the best, Type 2 items are the second best, and so

Mathematical Methods I, Autumn 2009
61
V (x, t) = E V (Xt+dt , t + dt) | Xt = x .
(5.7)
so that
Next, by Itos lemma (V can be shown to be twice continuously dierentiable),
V
1 2V
(Xt , t) dXt +
(Xt , t)(dXt )2
2
x
2
x
V
(Xt , t)2 2 V
(Xt , t) +
= V (Xt )

Mathematical Methods I, Autumn 2009
67
where we used that dierent components of (Zt )t0 are independent at all times
(possibly dierent for the dierent components). Finally, the third and fourth
properties are immediate consequences of similar properties o

Mathematical Methods I, Autumn 2009
69
Theorem 6.3 (It
os lemma for vector processes). Let Xt = (X1,t , . . . , Xn,t )
be a vector It
o process dened by (6.11). Then
df (Xt , t) =
f
f
1 2f
dt +
dXj,t +
dXj,t dXk,t ,
t
xj
2
xj xk
j
(6.14)
j,k
which can al

Mathematical Methods I, Autumn 2009
=
since
p
ip jp = i2
73
1
j i2 dt +
ij dZj,t ,
2
j
hip hpi = i2 ii = i2 . From there, proceed as before.
Example 6.8 (Weakly coupled Ornstein - Uehlenbeck). The following
example is a 2-dimensional version of the Orn

Mathematical Methods I, Autumn 2009
77
and deduce form this that Yt as variance-covariance matrix
t
T
E Yt Yt =
exp u1 A exp uT AT T ,
0
where T stands for the adjoint of 1 .
Hint. Use
that
the variance-covariance matrix of the stochastic dieren

Mathematical Methods I, Autumn 2009
63
and, for a general European pay-o of f (ST ) at T ,
V (S, T ) = f (S),
(5.12)
f being specied by the derivatives contract.
Now (5.11)(5.12) is precisely the type of problem to which we can apply
our baby FeynmanKac t

Chapter 5
Stochastic processes and
PDEs
There is a close connection between solving an sde and solving boundary value
problems for a certain type of partial dierential equations (pdes) which are
known as parabolic. Parabolic pdes are, roughly speaking, th