Ho10-practicemidterm

Practice Midterm Taken from MS&E 252: Decision Analysis I Midterm Examination 2001-2002 Please read the following instructions carefully! 1. This exam is closed book and closed notes, except for a single sheet (2 sides). You may use a calculator and a foreign language dictionary. Please sit in alternate seats. 2. The answer sheet is stapled to the back of the exam. Please tear it off, print your name, SU ID#, Section TA, and sign the Honor Code and exam agreement. Your exam will not be graded unless you have printed your name and signed this statement. 3. There are three blank pages at the end for you to use as scratch paper. All exam questions carry the same weight. Don’t spend too much time on any one question. 4. Read over each question carefully. You may not need all the information given. 5. At the end of the exam, please make sure your probability assignments are written clearly in the appropriate boxes on the answer sheet. If the teaching team cannot read your probability assignment we will use our best judgment as to what you meant to write down and this decision will be final. You will not be allowed to rewrite your assignment after the exam has been graded. You will be graded solely on the basis of your probability assignments. Turn in your answer sheet ONLY. 6. The exam will end at 12:15 pm. You will have five minutes to turn in your answer sheet. In fairness to all members of the class, we will not accept exams after 12:20 pm. 7. You will receive a photocopy of your answer sheet. You will have until 11:59 pm on Friday November 9, 2001 to enter your responses on the web. Please select “Midterm” from the pulldown menu on the answer sheet page. 8. In the spirit of the Honor Code, the Teaching Team will not remain in the classroom during the exam. If you have questions please ask. Clarifications will be announced to the class. 9. Unless stated otherwise, the characters in the exam prefer more money to less, and follow the Five Rules of Actional Thought. Do not make any additional assumptions. 10. If your probability assignments do not add up to one, the teaching team will normalize them. If you leave boxes blank and your assignments add up to less than one, we will distribute the remaining probability equally among the empty answer boxes. If your assignments add up to more than one and you have left boxes blank, we will normalize the non-blank boxes and place zeroes in the empty boxes. For example, the following assignments: Question Number i j k

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a 0.3

b 0.5

0.9

0.2

c 0.3 0.7

d 0.3

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would become: Question Number i j k

a 0.214 0.1 0.82

b 0.357 0.1 0.18

c 0.214 0.7 0

d 0.214 0.1 0

If you leave a question blank it will be interpreted as an assignment of 0.25 across the board. 10.

Your exam be will graded according to the following scoring function: Question Score =

100 ln p * (1 + ) 15 ln 4

where p is the probability you assign to the correct answer. The graph and table below show the number of points you will receive per question depending on the probability you assign to the correct answer. p 0 0.01 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00

12.

Score −∞ -15.48 -7.74 -4.41 -2.46 -1.07 0.00 0.88 1.62 2.26 2.83 3.33 3.79 4.21 4.60 4.95 5.28 5.59 5.89 6.16 6.42 6.67

7.50 5.00 2.50 0.00 Score(p)

11.

-2.50

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

-5.00 -7.50 -10.00 -12.50 -15.00 -17.50 Probability Assigned to Correct Answer (p)

Relax and make good decisions! !

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1.1

DO NOT TURN THIS PAGE UNTIL INSTRUCTED TO DO SO!

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1.

How many of the following are not among the Five Rules of Actional Thought? I II III IV

a) b) c) d)

Order Rule Value Rule Consistency rule Price Rule

1 2 3 4

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2.

There are two concerts you would like to go to next week: “Back Street Boys” and “New Kids on the Block.” Your PIBPs for each of the concerts individually are $30 and $55 respectively. Later you find out that the tickets are only being sold in the following way: I II

A bundle, both concerts for $85 “Back Street Boys” for $35

Tickets you buy are for your own use only. (You cannot resell them or give them to a friend.) What should you do? a) b) c) d)

Buy only the “Back Street boys” ticket Buy the bundle for both concerts You are indifferent between I and II Cannot be determined from the information given

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3.

The ula-ula is a very rare bird that lives only on the island of Dia-Tia. Until recently, only two types of ula-ula were known: the blue ula-ula, and the red ula-ula. Logically, the scientific community used a perfectly clear distinction, “Color of the Ula-Ula” with two degrees, “Blue” and “Red.” A promising young researcher, A. Carver, recently discovered a third type of ula-ula in a remote area of the island: the yellow ula-ula. Assuming that there is no mixed-color ulaula, why would it be a problem to use the distinction “Color of the Ula-Ula” with only two degrees “Blue” and “Red”?

a) b) c) d)

The degrees would be mutually exclusive, but not collectively exhaustive The degrees would be collectively exhaustive, but not mutually exclusive The degrees would be neither mutually exclusive nor collectively exhaustive There is no problem: the degrees are mutually exclusive and collectively exhaustive

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4.

Which of the following statements represent a decision? I II III IV

a) b) c) d)

After careful thought, Armando says he prefers vanilla ice cream to chocolate ice cream. After careful thought, Ali buys a red Ferrari. After careful thought, Mathias goes for a run. After careful thought, Andy claims there is a 50% chance that someone will get a negative infinity on the midterm.

II only I and II II and III III and IV

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5.

Given the choice between hiring The Clairvoyant and hiring The Wizard to help you with a decision problem, which should you hire?

a) b) c)

The Clairvoyant The Wizard You need more information about the decision problem and the fees charged by The Clairvoyant and The Wizard before you can answer this question. You should be indifferent between hiring The Clairvoyant and hiring The Wizard.

d)

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6.

Consider the following relevance diagram.

A

B

C

D

How many of the following operations can be performed directly on the diagram above, without having to make other arrow manipulations beforehand? I II III IV a) b) c) d)

Adding an arrow from D to C Adding an arrow from B to C Removing the arrow from A to B Reversing the arrow from B to D

Only one of the above Two of the above Three of the above None of the above

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7.

Consider the following relevance diagram.

A

B

C

D

After performing any necessary manipulations, how many of the following statements must be true? I II III a) b) c) d)

A is relevant to B, given & C is irrelevant to D, given B and & We can reverse the arrow between B and D

Only one of the above Two of the above All three of the above None of the above

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8.

DA Industries Inc., a risk-neutral corporation, is ready to launch its new product, the “Gizmo.” Given the current market uncertainty, the CEO thinks three cases are possible: • Gizmo could be a “Hit” and result in $200 million in profit (probability = 0.3) • Gizmo could be “OK” and result in $30 million in profit (probability = 0.4) • Gizmo could be a “Flop” and result in a $240 million loss (probability = 0.3) A clairvoyant proposes the following deals: I Full perfect information for $75 million II A discounted offer: for $10 million, the Clairvoyant will reveal whether Gizmo will be “OK” or not. However, if Gizmo is not “OK,” the Clairvoyant will not reveal whether the product will be a “Hit” or a “Flop.” What should DA Industries Inc. do?

a) b) c) d)

Buy neither I not II Buy I only Buy II only Buy both I and II

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9.

Joanna is risk neutral, and last week was considering the decision situation depicted below.

Decision

Uncertainty X

Uncertainty Y Y1

X1

Alternative 1

0.25 X2

0.6

Y2

0.4

0.75 Alternative 2

$20

$80 $20 $30

Joanna decided to go with Alternative 1. As it happened, uncertainty “X” turned out to be X1 and Uncertainty “Y” turned out to be Y2. Which of the following is true? a) b) c) d)

Joanna made a good decision and had a good outcome Joanna made a good decision, but had a bad outcome Joanna made a bad decision, but had a good outcome Joanna made a bad decision and had a bad outcome

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10.

Last year, Decisions Inc. had to choose between two projects. The “Agro” project was to cost $50 million, and would return $80 million in one year. The “Bio” project was to cost $40 million, would return $60 million in one year. The firm could not finance both projects, and chose to invest in the Agro only. Now, one year later, the Agro project has already cost $90 million, and has not yet generated any return. The Agro manager is asking for $10 million in addition, and admits there is just a 50% probability of generating $80 million, and a 50% probability of generating only $20 million. The R&D budget is $50 million, and the Bio project is still available. Assume the firm is risk-neutral and there is no discounting. What should Decisions Inc. do?

a) b) c) d)

Invest in neither project Invest the $10 additional million in Agro, but do not invest in Bio Invest the $40 million in Bio, but do not invest further in Agro Invest both the $10 million in Agro and the $40 million in Bio

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11.

In Italy, one person in 400 carries a harmful virus. A diagnostic test can detect this virus with 99% sensitivity; that is, for those who carry the virus, the probability of the test reporting that the virus is present (a “positive” test result) is 99%. The specificity of the test is also 99%; that is, for those who do not carry the virus, the probability of the test reporting the virus is not present (a “negative” test result) is also 99%. Valentina, an Italian, just received a “positive” test result. Which of the following is closest to the probability you should assign to her carrying the virus?

a) b) c) d)

0.20 0.50 0.99 0.999

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12.

Consider the certificate below:

B

EARER MAY FIRST CHOOSE ONE OF THE

FOLLOWING DEALS, AND THEN SPIN THE SPINNER:

DEAL DEAL“X” X: Black = Win $100 White = Win $400

50%

DEAL DEAL“Y” Y: Black = Win $500 White = Win $0

50%

R

W B

EDEEM AT ANY

IZARD

ANK BRANCH OFFICE

* VOID IF TRADED OR SOLD *

Quincy, a risk-neutral decision maker, has just acquired this certificate for $190 at an auction. A clairvoyant offers to reveal the spinner outcome before Quincy chooses his deal. Which of the following is closest to the most Quincy should be willing to pay for this information? a) b) c) d)

$10 $200 $450 Cannot be determined from the information given

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13.

Hubert has hired you to help him get control of a complex situation. You decide to draw a relevance diagram for him. There are 4 uncertainties, and Hubert tells you the following facts about them: A is relevant to B, given & B is relevant to C, given & C is relevant to D, given & However if he knew D, A would no longer be relevant to B. Which of the following diagrams best describes this situation?

a)

b)

A

D

A

D

B

C

B

C

A

D

B

C

c)

d)

The situation cannot be logically represented with a relevance diagram

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14.

Josephine is about to receive a $2000 check, and is contemplating using it to buy stock in a company for a 1-year investment. In researching the firm, Josephine read an analyst report claiming there is a 20% chance that it will acquire a major competitor. Josephine further believes that the GNP growth in one year is relevant to the final stock price. She draws the following tree: GNP “Well” 0.3

$3000

Acquisition 0.2 GNP “Badly” 0.7

$2000

Buy Stock GNP “Well” 0.8

$1000

No Acquisition 0.8 GNP “Badly” 0.2 Do Nothing

$0

$2000

Although risk-neutral, Josephine is somewhat baffled by the two uncertainties. Luckily, Josephine’s friend Claire is a clairvoyant. How much should Josephine pay for joint clairvoyance on both uncertainties? a) b) c) d)

$0 $60 The sum of the value of clairvoyance on the acquisition, plus the value of clairvoyance on the GNP None of the above

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15.

Corina has an unknown risk attitude and the following certain equivalents:

0.9

$200

$100 ~

0.4

$80

$30 ~ 0.1

0.6

$30

$20

If presented with a choice between the following two deals, which would she prefer? Deal I 0.5

0.1

0.4

a) b) c) d)

Deal II $200

$80

$20

0.6

0.2

0.2

$100

$30

$20

Deal I Deal II Corina is indifferent between Deal I and Deal II Cannot be determined from the information given

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MS&E 252: DECISION ANALYSIS I Midterm Answer Sheet Name (print) _________________________________________

SU ID# ________________

TA: (circle one)

Mathias

Ali

John

Andy

Armando

In recognition and in the spirit of the Honor Code, I certify that I will neither receive nor give unpermitted aid on this exam and that I will report, to the best of my ability, all Honor Code violations observed. I also understand that obtaining a score of negative infinity on this exam will result in failing this course. If I assign a zero probability to any answer, I declare that it is done consciously and against the advice of the teaching team. Signature ________________________________________

a

Question Number 1

b

Date ______________

c

d

2 3 4 5 6 7 8 9 10 11 12 13 14 15

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