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GSOE9210 Engineering Decisions

创建日期：2024-04-22 18:05:41

所属分类：数学mathematics

标签： GSOE9210

Engineering Decisions

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GSOE9210 Engineering Decisions
sample final exam
GSOE9210 Instructions:
• Time allowed: 2 hours
• Reading time: 10 minutes
• This paper has 19 pages
• Total number of questions: 53 (multiple choice)
• Total marks available: 60 (not all questions are of equal value)
• Allowed materials: UNSW approved calculator, pencil (2B), pen, ruler,
language dictionary (paper)
This exam is closed-book. No books, study notes, or other study ma-
terials may be used
• Provided materials: generalised multiple choice answer sheet, graph
paper (1 page), working out booklet
• Answers should be marked in pencil (2B) on the accompanying multiple
choice answer sheet
• The exam paper may not be retained by the candidate
1
Start of exam
Questions 1 to 7 refer to the problem below.
Recall the school fund-raiser example from lectures. There are two options
for the fund-raising activity: a feˆte (F) or a sports day (S). The money raised
by each activity depends on the (unpredictable) weather: on a dry day (d)
a feˆte will make a profit of $150 and a sports day only $120; however, on a
wet day (w) the sports day will earn $85 and the feˆte only $75.
Suppose Alice has no information about the likelihood of whether any given
day will be dry or wet. The fund-raiser is a once-off event; i.e., it will only
be held once on a particular day.
1. (1 mark) On any given day, which of the two activities (S or F) will ensure
the greatest lower bound on profit?
a) S only
b) F only
c) both S and F
d) neither S nor F
e) a mixture of S and F
2. (1 mark) Suppose Alice is more concerned about limiting the maximum
regret—she doesn’t like to miss out on opportunities. Which activity would
Alice prefer?
a) S only
b) F only
c) both S and F
d) neither S nor F
e) a mixture of S and F
For the following questions assume the following:
Suppose now that Alice works for the local branch of the Government’s ed-
ucation department. She is in charge of twelve local schools, and is planning
to hold a single-day fund-raiser in each school on the same day. She can hold
different activities in different schools, if she wishes.
2
3. (1 mark) In how many schools should Alice hold a sports day if she wants
to ensure the greatest minimum profit?
a) in none of them
b) in four of them
c) in six of them
d) in eight of them
e) in all twelve of them
4. (1 mark) In how many schools should a sports day be hosted if limiting the
maximum regret is the main consideration?
a) in none of them
b) in three of them
c) in four of them
d) in six of them
e) in all twelve of them
For the following question, suppose that fund-raising events are held in one
day of each week of every month.
5. (1 mark) Let p = P (d) be the probability that any given day is dry. Which
is the Bayes action for probability p = 1
2
?
a) S only
b) F only
c) both S and F
d) neither S nor F
e) a mixture of S and F
Records kept over the last ten years indicate that, on average, the number
of dry days per month in Alice’s geographic area are as follows:1
Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Dry days 15 13 10 8 6 5 5 7 11 13 14 16
1Note that Alice lives in a very wet area; perhaps a mountain valley.
3
6. (2 marks) Alice holds her fund-raisers every month except the one month
in which she takes her annual holidays. If Alice is concerned with limiting
the maximum regret, which of the options below would be the best time for
Alice to take her holidays?
a) Jan or Feb
b) Feb or Sep
c) June or July
d) Apr or Aug
e) Jan or Dec
7. (1 mark) If Alice were concerned with securing the greatest minimum profit,
in which months should she schedule her holidays?
a) Jan or Feb
b) Feb or Sep
c) June or July
d) Apr or Aug
e) Jan or Dec
Questions 8 to 22 refer to decision table below.
Consider the following decision table for a problem in which the outcomes
are measured in dollars ($).
s1 s2
a1 10 50
a2 40 20
There are two agents, A and B, who are making independent decisions on
which of the possible actions (a1 and a2) to take—note that this is not a
game: both agents are choosing separate decisions at different times.
Consider agent A first. Agent A’s utility function for money is logarithmic
(with base 2); i.e., u(x) = log2(x − a), where a ∈ R is a parameter to be
determined.
4
8. (1 mark) If u(10) = 0, which alternative below best describes the utility
function u(x)?
a) log(x)
b) log(x− 1)
c) log(x + 9)
d) log(x− 9)
e) none of the above
9. (1 mark) Let p = P (s1). If p =
1
2
, which of the following statements is
correct?
a) a1 has greater expected dollar value than a2
b) a2 has greater expected dollar value than a1
c) both actions have the same expected dollar value
d) a1 is dominated
e) none of the above
10. (2 marks) For p = 1
2
, which of the following statements is true?
a) A prefers a1 to a2
b) A prefers a2 to a1
c) A is indifferent between the two actions
d) A prefers neither action
e) none of the above
11. (1 mark) For which value(s) of p would A be indifferent between the two
actions?
a) p = 0
b) 0 < p 6 1
4
c) 1
4
< p 6 1
2
d) 1
2
< p < 3
4
e) 3
4
6 p
5
12. (1 mark) For p = 1
2
, the certainty equivalent of a1 is closest to . . .
a) $0
b) $10
c) $15
d) $25
e) $45
13. (1 mark) For p = 1
2
, the certainty equivalent of a2 is closest to . . .
a) $0
b) $10
c) $15
d) $25
e) $45
14. (1 mark) For p = 1
2
, what is the approximate value of the risk premium of
a1?
a) $0
b) −$10
c) −$6
d) $15
e) $20
15. (1 mark) For p = 1
2
, what is the approximate value of the risk premium of
a2?
a) $0
b) −$10
c) −$3
d) $3
e) $10
For agent B all we know is that she is indifferent between a certain $20 and
10% chance of $50 and 90% of $10. She is also indifferent between $40 and
the lottery [ 6
10
: $50| 4
10
: $10].
Assume in the following questions that p = P (s1) =
1
2
.
6
16. (1 mark) Which of the following statements is true?
a) B prefers a1 to a2
b) B prefers a2 to a1
c) B is indifferent between the two actions
d) B prefers neither action
e) none of the above
17. (2 marks) Assume that utilities for dollar values other than those given
can be linearly interpolated. For a utility scale in the range [0, 10], which
expression below best represents u(x) for $20 6 x 6 $40?
a) x− 10
b) 1
10
x− 1
c) 2
5
x− 10
d) 4− 4x
e) 1
4
x− 4
18. (1 mark) The certainty equivalent of a1 is closest to . . .
a) $20
b) $25
c) $30
d) $35
e) $40
19. (1 mark) The certainty equivalent of a2 is closest to . . .
a) $0
b) $10
c) $15
d) $25
e) $45
7
20. (1 mark) What is the approximate value of the risk premium of a1?
a) $0
b) −$10
c) −$6
d) $15
e) $20
21. (1 mark) What is the approximate value of the risk premium of a2?
a) $0
b) −$10
c) −$3
d) $3
e) $10
22. (1 mark) For which value of p = P (s1) would B be indifferent between the
two actions?
a) 1
10
b) 1
5
c) 2
5
d) 3
5
e) 7
10
Questions 23 to 26 refer to the problem below.
Two friends agree to “meet at the park”, but subsequently each realises
that there are two identical parks (A and B) nearby. Each friend has to
decide, independently, to which park to go to meet their friend. The game
is modelled by the matrix below.
A B
A 1, 1 0, 0
B 0, 0 1, 1
11
00
8
23. (1 mark) How many plays survive simplification by elimination of dominated
strategies?
a) none
b) one
c) two
d) three
e) four
24. (1 mark) How many equilibrium points does this game have?
a) none
b) one
c) two
d) three
e) four
25. (1 mark) How many Pareto optimal plays are there in this game?
a) none
b) one
c) two
d) three
e) four
26. (1 mark) Suppose Alice believes that the probability of Bob going to park A
is p = PB(A). Which value of p would leave Alice indifferent between going
to either park?
a) p = 0
b) p = 1
4
c) p = 1
3
d) p = 1
2
e) for any p ∈ [0, 1]
Questions 27 to 30 refer to problem below.
Alice and Bob have agreed to meet for lunch. Alice prefers restaurant A
and Bob prefers restaurant B. Unfortunately, they didn’t specify at which
9
restaurant they were to meet. This ‘game’ is modelled by the following game
matrix.
a b
A 2, 1 0, 0
B 0, 0 1, 2
21
00
27. (1 mark) How many plays survive simplification by elimination of dominated
strategies?
a) none
b) one
c) two
d) three
e) four
28. (1 mark) How many equilibrium points does this game have?
a) none
b) one
c) two
d) three
e) four
29. (1 mark) How many Pareto optimal plays are there in this game?
a) none
b) one
c) two
d) three
e) four
10
30. (1 mark) Suppose Alice believes that the probability of Bob going to restau-
rant A is p = PB(a). Which value of p would leave Alice indifferent between
going to either restaurant?

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1300A ENGG 1300 OLET1139 STAT 3503 STAT 206 FEM11149 ELEN 4720 COMP20003 SOLA1070 CS574 C11CS LINB29H3 MAST90083 ECON7200 STAT 610 LINB29 DSM-5 COMP3161 EEEN40010 MATH 4431 K353 STA 3386 IERG4300 COMS W4167 ENG5298 AMME 2302 CS3910 COMPSCI 320 STATS 369 GR5242 COSC 328 CSCI435 MGTS1301 INFS2200 COMP3900 CIS 375 Module AE03 COMP3121 CS260 HAM503 MGMT5050 INT3075 COSC 285 GEOL0029 GEGE2X01 STAT1201 MATH1061 MMF1941H STAT 5060 CS 520 COMP 4320 MSIN0104 000T FINS3648 ECMT2160 ECON4003 Phys 129L CSE 142 CS 3130 MGEB01 EECS 340 Finance (20443/20444) ECMM149 COMP5310 EEEN60180 CSC 111 AT2 CSCI 4430 STAB57 MA/CSC 427 MATH322 D100 CSCI544 CITS3004 CI6227 CSE 565 APCO 1P01 852L1 ELEC S411F COMP3207 STATS330 ECON7530 FIT5149 CSI4104 CMPT 371 COMP201 SEHS4696 FI4003 MATH6182 CG1 WS MATH401 MGT 205 QTM 110 COMP 0137 MACE12201 FIT5210 ECE 544 BISM7206 HUDM 6055 ECON3203 STATS 210 MSCI 570 MATH6173 COMPSCI4039 Accounting COM3503 AOE2024 ECON213 PSYC10004 Control Data 100/200A PHIL2617 PHYS3116 MIE250 BCPM0008 ECN 620 QBUS6830 ECSE-415 ECON5102 MGMT20005 MAT 653 ECO 480 COMP 5/600 CSSE 5600 ME 571 7CCMMS61 CS 550 COMP2865 MATH3075 STATS 506 QTM 220 ISYS2120 FIT5106 STAT 153 MKTG3112 ECON2102 ELE2018 COMP3031 MSIN0010 SCC461 MATH237 CS246 CSC3065 CSE 101 ICTWEB411 COMP9313 ECOS 2025 FN620 MATH11111 MATH 3018 KE1068 FINA 6112 C++ MISM 6202 MSIN0105 CSC8631 MECO6935 COMP4121 ACCT2011 DPBS1150 EEL 3701C F19PL OPM 661 CSE 310 CS918 BIOL30001 ACCT3563 BANK3600 MET CS622 MATH367 ACCT5907 Continuing COMP5048 COMP61021 CS3334 GSOE9210 CSCI-570 COMP 5322 HW 2 ALY-6020 IEOR 4706 DATA 200 EBUS504 CGE12412 COMP4108 7SSMM800 ECMM171P MATE50002 CS225 RS 6003 BH2274 ELEC3111 MAT6669 ECON-UA 227 PHIL 1012 7SSMM603 TB028A P6 ECS708 CSC 427 CS6476 CSE 250A A1A2 ITS61504 EECS 376 model HW6 UV0010 ECON 6074 MG4F7 CMP-7030Y INFO3008 BFIP013 ECON 5068 MATH6002 CS3483 PSTAT 131 C31FM CSOR W4246 AAEC 5307 DATA ELEC362 COMSM0047 ECN6006 MA20224 BST351 MATH 323 MATH323 AA2021 COMP3811 COMP2013 IB9X60 INVP001 EMATM0051 COMP220 BLAW1002 E20 TCP8001 ECON61001 EART40005 ECONM1022 MATH 365 MATH 367 ELEC6218 COMP 5812M EDUC 5061M ELEC ENG 1101 equation MATH6174 ST334 C4 EC9570 A33648 EBUS603 ECON47815 stata WFMS0001 PEM102 INF6060 ionically ELECTRICAL MATH 375 MMW 12 MKTG860 ECON60401 ALY6010 SOST20131 Introduction COM3524 MME2 GGR305 JNB 538 EECS101 COMM5030 IEOR E4601 2B CSC336 EN2315 LAW 432 CSC263 MATH2001 OLET1143 CSCB63 SIT772 COMM1170 STAT 441 MS930 INFT3050 GLBH0030 Stat 120B MAST10007 MGEC61 Machine GGR 252H1S ECON7030 Financial Marketing MGMT30019 ECON5120 SDSC 8009 CSC165H1S DSCI 551 3081W ACM41000 ECA 5304 MATH 1064 ECSE444 DATA 604 COMP7105 MIE1615 ECON4004 ENV200H1S EC481 MKT 306 EC1B1 MATH08051 ALY6140 CS260C CSE30 MSIN0226 CS4103 CSC3064 AM16 COMP11212 CSE4101 PSTAT 174 Math 380W CNT 5106C STAT 310 FIN2028 CS5014 STAT 425 COMP 4102A ELEC2140 MANF9544 QRM 9 QRM 8 ECON 457 COMPSCI 4091 MATH 523 DNSC-4211 PEAS 6000 MSIN0180 COMP2119 A2A HT 2022 IB93F0 MAS316/414 ACCT2522 MSIN0181 ATMS 201 COMP3425 MATH7861 SOLA2060 MA 325 7CCEMCTH ECON 432 INFT2051 SOLA 2060 ECOS2002 Stats141XP BIOA02H3 S2022 MA4601 K5 COMP5329 EG 284 IB3A70 WECO1020 COMP3027 Energy ACS61011 MAST20026 STAT 533 MATA31 ENVS257 BEM2031 EC 486 COMP0172 CS3214 EECE5644 IB2B20 COSC2536 COSC1147 COMP6214 5CCM242A COMP0130 AMME2000 MTMG50: EG238 ACF6006 QBUS2810 COSC2391 ECON7560 MATH377 STA305 CS 486 COMP1117B EL648 ELEC3909 ECON 241 COMP 4901W BUSI4428 ENEN20002 ENGN4524 ELEC3115 CSC 413 PSYC 100B ECON1002 MATH256 ANSC20005 MTHS2008 MATH40082 COSC 2406 FIT3174 STA 238 CMT202 Differential Equations MTHM017 GARCH 101 MATH2069 CSC336S ACSC12 ETF2121 CEME 2001 DB B474F ARHT1001 EECS 3311 3220 STATS 786 CS 484 COMP20008 MATH4091 ECE 455 CSCI 204 BUS B200F BA 875 BU5562 COSC 1147 X11 GEOG 101 IMM250F CSE 584A MATH38172 LAB 4 ELEC5882M FINS5523 EE 430 COMP 465 6CCS3PRE 7CCSMNSE FINANCE ACMB02H3 ENGG2112 ELEC5616 SCM B371 CHEM3120 CS22 ECMT2130 MAST30011 ADSPBF706 CENG0013 ACCOUNTING BUSS1040 CHEM 181 MAT136H1 GY 6183 COMP3170 AGRI90089 PHYSICS 1002 ECON10003 IEOR E4004 ACS61012 MATH 40550 MKTG2113 TELE4653 ENSC1004 ECE 232E MK726 MTRX2700 SHEET 3 CSCA08 COMP30027 Math 2XX3 statistic MMAN3200 BISM7213 ECMM109 ECON 2022 FNCE 20005 GR5067 CSCB09 ME 3017 CS 5100 PHYS 2903 COMS 4771 COMP222 COMP 1046 CSC148H1 ISYS2038 FINS2615 OT5206 COMP2048 A6 MECH5770M MA826/20 CMPT 726 STA457 INFS6071 INFS588 integral ECON 216 IRDR 0017 MA323 PA 15213 PSYC2001 ENV222 Statistics ACCT5930 ACCT12 LAND2121 ME 5405 COMM1180 TELE3113 A7 ECE 568 ACCT2019 INFS1200 ENGG1340 CS 1400 ASST3 FINM7409 SWEN30006 INFO2222 FIN20150 SOSS1000 CSSE7231 FINS5513 COMS3200 CECN 702 ECON4060H MN3515 HW2 PSYA02H3 ECON 2112 COMP90051 CS 1652 MA30059 AF1605 MKTG7501 ECO-6003B COM4521 CTM ECON3350 COMP 3804 ELEC9762 BISM 7255 ST22 MATH20014 MNE3122 COMP343 MATH5165 ELE7029 ENGR30002 SEEM3500 ECON7350 RISK5002 FINM7405 COMP90059 MOS 3320B STAT 431 BISM7221 MATH3014 MTH783P EBA 35302 ACS133 BUS2206 IE5600 ECOS 3997 EDST2003 FIN 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