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CSE 250A FINAL EXAM
FINAL EXAM
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CSE 250A FINAL EXAM
Question PointsAcademic integrity statement *
1. d-separation 10
2. Polytree inference 10
3. Naı¨ve Bayes vs logistic regression 10
4. Nonnegative random variables 5
5. EM algorithm 10
6. Inference in HMMs 8
Question Points
7. Most likely hidden states 7
8. Gaussian random variables 6
9. Policy improvement 7
10. The simplest MDP 3
11. Noisy parity model 9
12. Gamer rating engine 15
Total: 100
The exam is expected to take one full afternoon, but you may work as long as needed until the deadline. Be sure to
sign and submit the statement of academic integrity with your completed exam. Exams without signed statements
will not be graded.
You are not required to typeset your solutions. We do expect your writing to be legible and your final answers clearly
indicated. Also, please allow sufficient time to upload your solutions.
You are allowed to check your answers with programs in Matlab, Mathematica, Maple, NumPy, etc. But this should
not be necessary, and be aware that these programs may not produce the intermediate steps needed to receive credit.
The later parts of problems often do not depend on the results of earlier ones; therefore it is a good strategy to attempt
all parts of every problem.
An asterisk may indicate the need for a somewhat more laborious calculation. If you do not see the solution quickly,
you may wish to return to these parts later.
If something is unclear, state the assumptions that seem most natural to you and proceed under those assumptions. Out
of fairness, we will not be answering questions about the technical content of the exam on Piazza or by email.
1
Academic Integrity Statement
This take-home, open-book exam represents work that I have completed on my own. In particular,
during the twenty-four hour period of the exam, I hereby affirm1 the following:
(i) I have not communicated with other students in the class about these problems.
(ii) I have not consulted other knowledgeable researchers or acquaintances.
(iii) I have not contracted for help on any parts of the exam over the Internet.
I understand that any of the above actions, if proven, will result in a failing grade on the exam. In
addition, I understand the following:
(i) I am obligated to report any violations of academic integrity by others that come to my
attention during the exam.
(ii) All other students in the course (past and present) are under the same obligation.
Signature Date
1If you do not have a printer, you may simply copy, sign, and date the following statement with your solu-
tions: I affirm the statement of academic integrity on page 2 of the exam.
2
1. d-separation (10 pts)
Consider the following statements of marginal or conditional independence in the belief network
shown below. For each statement, indicate whether it is true or false, and then justify your answer
as shown in the provided examples. Note that credit will only be awarded to answers that are
supported by further explanation.
A
C
B
D
E GF
Examples:
(i) P (F |A,C) ?= P (F |C)
True. There are four paths from node A to node F . They are
A→ C → F ,
A→ E ← C → F ,
A→ C → G← D → F ,
A→ E ← C → G← D → F ,
and each of these paths is blocked by node C. (Some of these paths are also blocked by other
nodes, but the answer is already complete as written.)
(ii) P (C,D|G) ?= P (C|G)P (D|G)
False. The path C → G← D is not blocked.
Problems:
(a) P (B|F ) ?= P (B|E,F )
(b) P (B,E) ?= P (B)P (E)
(c) P (A|B,F ) ?= P (A|F )
(d) P (A,B|E) ?= P (A|E)P (B|E)
(e) P (C|A,E, F,G) ?= P (C|A,B,E, F,G)
3
2. Polytree inference (10 pts)
A B DC
GF H
E
For the belief network shown above, consider how to efficiently compute the conditional probability
P (G|A,C, F,H). This can be done in four consecutive steps in which some later steps rely on the
results from earlier ones.
Complete the procedure below for this inference by showing how to compute the following prob-
abilities. Make each computation as efficient as possible, and briefly justify each step in your
solutions for full credit. Your answers should be expressed in terms of the CPTs of the belief
network and (as needed) the results of previous steps.
(a) Compute P (E|H).
(2 pts)
(b) Compute P (D|H).
(2 pts)
(c) Compute P (B|A,F ).
(3 pts)
(d) Compute P (G|A,C, F,H).
(3 pts)
4
3. Naı¨ve Bayes versus logistic regression (10 pts)
Y
X1 X2 X3 Xd...
(a) Naı¨ve Bayes model (2 pts)
Consider the belief network of discrete random variables shown above. Show how to com-
pute the conditional probability
P (y|x1, x2, . . . , xd)
in terms of the belief network’s probability tables for P (y) and P (xi|y). Justify your steps
to receive full credit.
(b) Log-odds (2 pts)
Consider the special case where all the variables in this belief network are binary-valued.
For this special case, compute the log-odds
log
P (Y =1|x1, x2, . . . , xd)
P (Y =0|x1, x2, . . . , xd)
in terms of the belief network’s probability tables. Simplify your answer as much as possible;
this will be helpful for the next parts of the problem.
(c*) Linear decision boundary (3 pts)
Show that the log-odds from part (b) is a linear function of the values of x1, x2, . . . , xn. In
particular, show that it can be written in the form:
log
P (Y =1|x1, x2, . . . , xd)
P (Y =0|x1, x2, . . . , xd) = a0 +
d∑
i=1
aixi
for appropriately chosen values of a0, a1, . . . , ad. Your solution should express these values
in terms of the belief network’s probability tables.
Hint: since each xi is equal to either 0 or 1, it may be a useful notation to write
log
P (xi|Y =1)
P (xi|Y =0) = xi log
P (Xi=1|Y =1)
P (Xi=1|Y =0) + (1−xi) log
P (Xi=0|Y =1)
P (Xi=0|Y =0) .
5
(d) Logistic regression (2 pts)
Consider whether it is possible to express your result for P (Y =1|x1, x2, . . . , xd) in the form
of a logistic regression. In particular, are there parameters w0, w1, . . . , wd such that
P (Y =1|x1, x2, . . . , xd) = σ
(
w0 +
d∑
i=1
wixi
)
,
where σ(z) = (1 + e−z)−1 is the sigmoid function? If yes, show how to choose these
parameters so that this is true. If not, explain why not.
Hint: What is the inverse of the sigmoid function?
6
4. Nonnegative random variables (5 pts)
Let µ > 0. In this problem you will derive some elementary but useful properties of the exponential
distribution
P (z) =
1
µ
exp
(
− z
µ
)
for a continuous, nonegative random variable with mean µ. (You will be exploiting these proper-
ties to solve the last problem on the exam.)
(a) Log-likelihood (1 pt)
Let {z1, z2, . . . , zT} be an i.i.d. data set of nonnegative values. Assuming each value was
drawn from an exponential distribution, compute the log-likelihood
L(µ) =
T∑
t=1
logP (zt)
in terms of the distribution’s parameter µ.
(b) Maximum likelihood estimation (1 pt)
Show that the maximum likelihood estimate for µ is given by the sample mean of the data.
(c) Cumulative distribution (1 pt)
Calculate the cumulative distribution, given by
P (Z
0
dz P (z),
when Z is exponentially distributed with mean µ.
(d) Comparison (2 pts)
Suppose that Z1 and Z2 are independent, exponentially distributed random variables with
means µ1 and µ2, respectively. Show that
P (Z1>Z2) =
µ1
µ1 + µ2
,
where the left side denotes the probability that Z1 exceeds Z2 in value.
Hint: note that P (Z1 > Z2) =
∫∞
0
daP (Z1 = a)P (Z2 < a), and use your result from the
previous part of this problem.
7
5. EM algorithm (10 pts)
A B
F
C
ED
Consider the belief network shown at the right,
with observed nodes {A,B,E, F} and hidden nodes {C,D}.
On the problems below, simplify your answers as much as
possible, and briefly justify your steps to receive full credit.
(a) Hidden node C (2 pts)
Show how to compute the posterior probability P (C|A,B,E, F ) in terms of the conditional
probability tables (CPTs) of the belief network.
(b) Hidden node D (2 pts)
Show how to compute the posterior probability P (D|A,B,E, F ) in terms of the CPTs of
the belief network.
(c) Both hidden nodes (1 pt)
Show how to compute the posterior probability P (C,D|A,B,E, F ) in terms of your previ-
ous results.
(d) Log-likelihood (2 pts)
Consider a data set of T partially labeled examples {at, bt, et, ft}Tt=1 over the observed nodes
of the network. The log-likelihood of the data set is given by:
L =
∑
t
logP (A=at, B=bt, E=et, F =ft)
Compute this expression in terms of the CPTs of the belief network.
(e) EM algorithm (3 pts)
Consider the EM updates for the CPTs of this belief network that maximize the log-likelihood
in part (d). Provide these updates for the following:
(i) P (C=c)
(ii) P (D=d|A=a,B=b)
(iii) P (E=e|B=b, C=c)
For this part of the problem, it is not necessary to justify your steps; it is only necessary to
state the correct updates.
8
6. Inference in HMMs (8 pts)
Consider a discrete HMM with the belief network shown below. As usual, let st ∈ {1, 2, . . . , n}
and ot ∈ {1, 2, . . . ,m} denote, respectively, the hidden state and observation at time t; also, let
pii = P (S1= i),
aij = P (St+1=j|St= i),
bik = P (Ot=k|St= i),
denote the initial distribution over hidden states, the transition matrix, and the emission matrix. In
your answers you may also use bi(k) to denote the matrix element bik.
S1 S2 S3 ST-1 ST
O2 O3 OT-1 OT
...
O1
(a) Inference (4 pts)
Let at denotes the tth power (via matrix multiplication) of the transition matrix, and assume
that a0 denotes the identity matrix. Prove by induction or otherwise that
P (St= i) =
n∑
k=1
pik(a
t−1)ki.
(b) More inference (4 pts)
The forward-backward algorithm in discrete HMMs computes the probabilities
αit = P (o1, o2, . . . , ot, St= i),
βit = P (ot+1, ot+2, . . . , oT |St= i).
In terms of these probabilities (which you may assume to be given) and the parameters
(aij, bik, pii) of the HMM, show how to compute the conditional probability
P (o1, o2, . . . , oT |St= i, St+1=j)
for times 1≤ t
your answer as much as possible. Hint: your result from part (a) may be useful.
9
7. Most likely hidden states (7 pts)
ST-1 ST
OT-1OT-2
S1 S2 S3
O2O1
…
Consider the belief network shown above, where st ∈ {1, 2, . . . , n} and ot ∈ {1, 2, . . . ,m} denote,
respectively, the hidden state and observation at time t. In this problem you will derive an efficient
algorithm for computing the most likely sequence of hidden states
{s∗1, s∗2, . . . , s∗T} = argmax
s1,s2,...,st
P (s1, s2, . . . , st|o1, o2, . . . , ot−1).
Note that this is not a hidden Markov model: in particular, every observation node has two parents,
every hidden node has none, and the joint distribution is given by
P (S1, S2, . . . , ST , O1, O2, . . . , OT−1) =
T∏
t=1
P (St)
T−1∏
t=1
P (Ot|St, St+1).
(a) Forward pass (4 pts)
Given a sequence of T−1 observations, the most likely hidden states are most easily found
by computing the T -column matrix with elements
`∗it = max
s1,s2,...,st−1
logP (s1, s2, . . . , st−1, St= i, o1, o2, . . . , ot−1).
Note that the log probability for `∗it in this network only includes observations up to time t−1.
Give an efficient algorithm to compute these matrix elements for 1 ≤ i ≤ n and 1 ≤ t ≤ T .
(b) Backward pass (3 pts)
Show how to efficiently derive the sequence of most likely hidden states from the results of
the forward pass in part (a).
10
8. Gaussian random variables (6 pts)
z x
z ∼ N (0, I) x ∼ N (Λz, I)
Consider the belief network of multivariate Gaussian random variables shown above, where z ∈
1
(2pi)d/2
exp
{
− 1
2
z>z
}
,
P (x|z) = 1
(2pi)D/2
exp
{
− 1
2
(x−Λz)>(x−Λz)
}
.
Here, the parameter Λ is a D × d matrix. Note that both these multivariate Gaussian distributions
have an identity covariance matrix.
(a) Posterior mode (2 pts)
Let z∗ = argmaxz P (z|x) denote the mode of the posterior distribution (i.e., the location of
its global maximum). Prove that we may also compute this mode from
z∗ = argmax
z
log
[
P (z)P (x|z)].
(b*) Maximization (3 pts)
Compute z∗ by explicitly maximizing log
[
P (z)P (x|z)] as suggested in part (a). Your an-
swer should express z∗ in terms of the observed value of x and the matrix parameter Λ.
(c) Posterior mean (1 pt)
Consider the following assertion:
The posterior mean E[z|x], defined by the multidimensional integral
E[z|x] =
∫
z∈
is equal to the posterior mode z∗ = argmaxz P (z|x) that was obtained
(much more simply) by differentiation in part (b).
Is the above statement true or false? If true, explain by appealing to the properties of normal
distributions; if false, provide a counterexample. (You are not meant to evaluate the integral.)
11
9. Policy improvement (7 pts)
Consider the Markov decision process (MDP) with two states s ∈ {0, 1}, two actions a ∈ {↓, ↑},
discount factor γ= 2
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COMS30034
DTSC 71
AcF 702
AcF702
DTSC71
MAT021
ELE8083
ACFI213
EG-127J
127J
FIT5163
FIT2001
ELE00113M
CMT310
CS 245
ENGL 1101
MTH6115
EE497
CS 325
Math 124A
MTH5130
MBA502
MGT 5380
ARCH 1261
F033800
20LLP109
ELE4009
FINANCIAL
COMP3331
Computer
ECE4179
20T3 COMP9311
COMP9311
UNSW MFIN6210
ACCT 5930
EE590
ENG2029
ECO100
SIT315
ACCT3610
COMP3600
STK2100
FIT2004
COMP30020
ACTL1101
Stat 101B
BANA 200
COSC2473
ENGG1400
AI
COMP90043
MMF 1914H
PHYS 127
CS584
CIVL2010
ECMT2150
CS 333
CP1406
KIT308
Economics 701
ECON3740
ECE 5759
BFC3340
FINC2012
COMP4500
MATH3871
FIT3080
18-819C
Economic
ECO202Y5Y
PHY100
FINC-780
Econ 100B
EC602
IE582
EE450
COMP9517
WRDS 150B
ECON 570
LECTURE 2
ECA5101
ECE 4420
ADAD9311
FIT3031
CS 544
MF 703
CS 6140
KIT501
ENGSCI 344
CSC171
IE 332
FINM8007
21S2
COSC 1114
FE545
E471
SIT102
CSC108
MAT301
IAE 101
COP3503
STAT2004
EC 303
CS1026
STAT1203
MATH3171
ISOM5160
IFN657
FIT2014
ACCT2102
DSCI550
STATS 330
ELEC421
COMP3670
QBUS6840
MEES:698B
MAST30027
MIET1077
Economics
IFT 6758
FIT5122
BUSN5101
CptS 111
HRMT5502
Math2018
PP 312
INFS3200
CZ3005
CSSE1001
SENG 2011
MKTG 553Q
BUFN 640
COMP507
ETF5952
DATA 311
ECE4043
BANK3011
finance
M3H623544
HW1
INFS 7410
AI6103
STAT3888
INFS3208
ACCT7103
ECOS3013
PSYCH 20B
F79MA
STAT3006
ENGG952
2X
MGSC 7000
ECE4132
MSF 526
MATH 3033
CDS 511
EEEE4120
EEET2465
ECA5103
MATH2070
ELEC3104
BU51019
EEE8147
ENGR20003
COSC 1107
ETF3200
FNCE 435
MSFI 435
ISyE6420
GENG4405
HW
ETC5523
IE 7315
MOEC0021
STA 106
ENGG 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 534
Elec4430
MATS3001
MGT6047
FINS5514
MIS602
ATS1279
ECMM445
2F
CS262
EFIMM0097
FINM2002
ECMT3150
FINC5090
WACC1000
MECH4620
ECOS 2002
SEESGS79
STAT
COMP3007
BUSB200F
ACST8040
CAES9920
STAT0020
INFR11205
PHYS2111
FINM7402
STAT 428
SOFT3202
ME220
ACC-ACF2100
EC9410
CSE 120
COMP90042
SEE5211
ECON0048
BUSN2036
MKT2010
3SMFE4
EFIMM0117
ECON3034
MTH5120
EFIMM0120
X0
W19186
MATH 034
COMP2100
COMS4104
CS1210
MENG10005
ACCT 5906
ECMT1020
MGTS7607
MATH3090
CIV4100
CSYS5020
ELE2019
PHS4200
ACS6124
MSIN0225
PHAS0061
6CCS3BIM
FINM7403
COMP8410
PY406
COMP2620
CS226
SDEV2004
COMP6080
BFF1001
HR410
MCEN30017
AMS3328
ML3
ELE8059
FINC3017
ACAD001
FTEC2101
ES480 3D
ELECTENG 734
MTH731U
MATH-UA 251
CSCI-UA 9473
A2
MSDM5058
FIT5047
COM6012
1FIN B386F
MPHY202P
ACCT6003
ECE 6913
HMB312H1
AC1025
MTH6105
Math6168
FINM 3003
CS24320
PHYS2134
ACCT3011
MECH1400
COMP30024
ENGGEN 121
COMP3721
MCD2080
ECON 7002
MAS439
COMP6216
ECON2011
M23367
CSC597
COMP6247
BRIEF
QBUS6180
EENG22000
FN1024
MATH0094
MANG 6554
ECOS3003
ELEC6252
C2511C
PHY328
EC1060
ECON32202
COMP4002-E1
MATH3063
EFIMM0124
QBUS2310
ECON4411
FUNDAMENTALS
ACCT20001
18YX RPM
COMP 2711
QBUS6600
BUSS5221
ST3189
FIT1047
MAT344
EGB375
MATH60013
MATH96011
COMP3557
MAST20029
ECM159
EAE1011
ENSCEN 105
SECTION A
STA 141C
SOSE 2022
PAM006
COMP0048
M40007
ISOM2500
CMPE 142
A06472
MCC150
ACST 8083
GEOG6087
ECON920
FINM7008
ENVENG 4110
COMPSCI 361
ENGRCEE 21
PHYS 1112
ACF2100
ECMM108
COMPS267F
MAT00050M
MAST30025
CSIT970
MSCI 224
INT202
PUBL0054
MSDM5004
BMAN 21020
BMAN21020
MGMT1002
MATH11150
LAWS7023
ACTL30002
CIVL3340
MATH1002
ECON 8069
COMPSCI 351
IBUS7302
STAT4528
CHEM1101
STAT3925
BUSN 7008
Comp 3120
ECOS2040
SWEN90010
ENGN6528
ECM158
ECON20022
COMP6452
Calculation
CITS1401
S1889112
BUS 351
ACTL30008
FIT2091
ECON6002
IBUS6020
PHI 001
ECON30290
MATH7501
ECON10004
MFIN7017
ISYS90043
LAWS7012
ECON30025
COMP30023
COMM1190
ECOM20001
GSBS6009
STAT 337
EMET8002
ECOM90001
ECOM30001
FINC 2012
BUSINESS
ENGCV512
ECO 101H1
IB9520
FINM 3008
ECON7310
FIT 1006
MANAGEMENT
MATH3821
MTHM504
CS975
COMM1100
ELEC2133
MMAI 5500
MIS611
ELEC3114
CS 173
ELEC 3105
ISO 9001
IDSC10 Rural livelihoods and globalisati
IDSC10
K17 202
CS823
MAST90007
SPG8024
MAT246
EG-264
CVEN2303
INFS1603
3PR3
MN-2508
4CCE1MCP
SPG8030
CMT224
Inflation
consumption
Applying
MAT137
CSE 111
DPBS1110
FINS5530
ELEC4613
GSBS6200
COMP4336
Math W54
DIFFERENTIAL
7PAVMALM
ACC 1110
ME 3210
MATH2801
MGMT20001
ECON 6202
PSTAT 120B
COMP9024
ENG5027
comp3219
ELE00107M
ECON20003
ECON2103
FINA2209
MAST20018
LUBS5308M01
MATH2023
Computation
COMP1600
CHEM 3X23
BBMM506
FNCE20003
BMET2922
BISM7216
financial
ECMT5001
ACST3059
MAST30012
COMP3511
ECOS 2201
MKTG7512
ECON2540
MTH1010
MAT1841
COMP4600
ECON7740
PAPER C331
CAP 6617
ECON2420
ACCT7107
HLTH 7001
ECOS3002
CVEN30010
MAST30021
MATH1014
BIOL1007
ECOS 3010
SWEN90016
BISM7202
ACCT90012
INFO3315
DSCI 553
INFO90002
COMP3419
CITS 3001
EE5731
FINA3326
NFS 284
COMM2501
FIT2104
PHYS3035
RSM260
MAN3080
CHEM30028
MATH2088
ELEC0144
MECM10006
2D
AE 202
ENG5022
CHEM3121
FINM7006
CS5340
CSE 594
FIT9136
FINS3633
RSM222
STAT3017
CS 8395
MAST10005
AMA546
ETC2410
FINM 7406
MSBA 7004
BUSS6002
CHEN 90038
PSYC20007
ACTL 3162
DIGITAL
COSC 2670
PROGRAMMING
ECON 5007
FNCE90045
PSTAT 126
MATH2307
STAT7055
SOC 360
BINF2010
WSTA01
AMME2200
ECO 204
BIO773P
BU 312
AERO2598
ENGG 5103
ECON1010
ECON3031
MATH3078
HPS319H1
COMP26020
COMP42215
ACCT7106
COMP3271
MKTG10001
ECOS2025
MATH36031
CSE 402
ACCT1110
ECON 20005
MTH319
COMP 3711
PHYS1160
COMP3601
MSIN0026
ECON1202
ARCL0103
PHYS5033
PSYC 171
QBUS1040
ATOC10001
1ENVS222
COMP9032
CIVL2812
JURD7152
CS 449
ECON 7073
INFS6015
INFS7203
MATH2521
ECON7073
CSE101
COMP2121A
DSC 40A
MGT3009
COMP4161
FINM8006
BUSM054
COM6503
ST443
P 500
DPBS1190
ELEC5101
STA457H1
MATH3411
COMP5216
PLAN30081
STAT7203
MTHS3003
37T37T
BLAW30002
GY7702
MATH580
ME 3057
PHYS 2012
ACCT13
ECON 3210
EE7207
ECOS3005
EC 502
MATH1004
CC0675
PHYS 4315
FINS 3636
COMP1012
economy
ISE 562
MACS 30121
ML4ENG
ECOS2201
ECOS3008
ECON312
PPGA 503
COMP26120
COMP2511
COM00111M
CMPU4021
HP435
ELEC1111
ACS61013
MAE 8
ECOS3007
ENGG5103
FINS5568
PHYS40001
CS 0002
IB9W00
CSCI 141
ACCT5942
FINC6015
CSCI 3150
ELEC1200
CSC236
CSC236H5
CIT 593
CSCI3170
ACCT5908
CCIT4076
COMM5011
MGEB11H3
MGEB11
MATH42715
CSC236H5F
ELEC1703
CS4203
MGTS 7603
MANG6529
MUSI08076
EGA366
EIE4432
1EECS 261A
CS-521
FIN 708
MN50374
MSBA7027
STA 4373
MGEB06
PHYS4291
Model
HW 3
MCIT 593
MSBA7021
CS5010
ST326
COMP0043
ECON-371
ENGF0004
INFS1602
MAT6679
ECON1020
STAT40830
CSGY 6923
CS280
Stat GR5204
CIV6115
POLS0012
ACS6127
MKTG1001
MTH305
CRICOS 00099F
SBSD 2063
BE332
ELEC3201W1
EC320
SOC100
COMP 1405
ST 311
COMP 4337
COMP4337
ECE 380
MATH1013
EENG35010
IHSS1200
CSCI1200
ECS 189A
ECON4010
ECE 368
EGA324
SCC462
ECTB61
COMPSCI 589
N2
COMM1120
STA 313
ELEC 301
COMM3030
ECE368
ECO204
ECOS3020
MAT 246
STAT4620
GSOE9820
CCT110
MGTS7303
ACCT11
STAT3010
FIN6108
EE 6225
STAT 3450
BUSS2000
STAT0024
CSC 240
COMP6741
MATH5975
CMT316
ISE 535
210FIN316
MGMT10002
COMP0050
EC306
FIT 5124
59PM ET
S2098367
CAD
MMGT6001
COVID-19
COMP5940M
ARC181H1S
SCC 312
ECO102
MATH4061
ELEC 3848
DATA3888
MECH0024
STA302H1
CSE 510
LAWS8214
WORK6108
E2
ECON 7310
COMP3211
FIT5216
A4
MATH 110
IBUS 1101
CS355
SWEN90004
MATH1023
BEEM012
COMP3311
ACCT90013
EES A06
EC 504
ISE 580
ENG4701
CAS CS538
ELE3040
6013B0506Y
BENV0115
ECON3104
CSCI-1200
COMP27112
IEOR4703
ELEC271
ECE-GY
Math 412
BUSS1000
PP208
BCPM000028
7QQMM316
BISM7209
DASC7606
HW 4
STAT 4620
ECON8026
INFS3202
COMMGMT 3506
COMU1002
ECON 20003
MATH 348
BUSN7008
BENV0113
STATISTICS
Function
STAT2001
ECE6483
MATH1115
MGMT20002
CONSUMPTION
ECO00003I
LAWS6997
APMA 4300
ECON 7030
STAT 413
802G5
GEOG0051
LINA02
ECON 3208
GOVT 1621
ECOS2001
ECON 7520
MGTS7301
ECMT 6002
MATH4321
EIBS7300
MARK5813
BH50A0220
OFFICE280
ECON1012
CIS273
CIS 273
ELEC3106
ACCT3013
EC831
MMAN3400
EC365
MAST20006
ECON7520
ENGM030
CSC148H1S
COMP5125M
CMPSC 497
ST5188
MAST 90082
CSSE3010
ECON7040
GEOM3000
GEOM30009
ACCT5910
ECON7001
CPEN400D
AMME3500
IDSB07H3
Management
BUSN7050
ECON1003
7QQMM312
CIT 5930
MARK2012
ECE 466
STA 365
MIE1621
IB98A0
COMP3278
PHYS3888
BUSN7036
GEOS2121
MATH 368
ECON2020
COMP2111
ECON7110
MATH260
INMT5518
PM 410
mktg3110
econ6021
ACCT867
CS4182
PP 202
COMM5000
ECON1101
ACCT90030
MAST30013
00025B
FINM2416
ECON7300
FINC6001
SOST30012
ASTR1001
ELEC 4510
COMP5206
POL200Y1
PSYM204
EMET1001
MARK5820
Math 9B
ECON7070
PSYC3001
COMP2212
ST117
ECOS3997
BISM7255
MSIN0068
MAST90045
MCD6110
ELEC 5516
MANG 6563
AIML427
CS3402
PHYS3152
PHYS 3152
AMME2500
PSYCH 727
CHAPTER 6
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