ECE 313 Spring 2023, University of Illinois at Urbana-Champaign

Image ECE ILLINOIS

 

ECE 313/MATH 362

PROBABILITY WITH ENGINEERING APPLICATIONS

Spring 2023

 

ECE 313 (also cross-listed as MATH 362) is an undergraduate course on probability theory and statistics with applications to engineering problems primarily chosen from the areas of communications, control, signal processing, and computer engineering. Students taking ECE 313 might consider taking ECE 314, Probability Lab, at the same time.

EE and CompE students must complete one of the two courses ECE 313 or Stat 410.


Prerequisite : Math 257 or Math 416

Exam times : See Exam information.

Written HomeworksWritten homework assignments would be available on Canvas (under "files") and GradescopePlease submit your written homework on GradescopeWritten homework solutions would be available on Canvas (under "files").

Prairielearn Homeworks: Prairielearn homeworks are due every Sunday at 5:00:00pm.

Course Communications: Please email: ece-313-spring23-group@office365.illinois.edu instead of emailing instructors/TAs individually.

Campuswire: All questions regarding homework should be posted and discussed on Campuswire. Students should NOT send ece-313-spring23-group@office365.illinois.edu questions about homework or other general issues that other students in the class should be aware of as well.


Text : ECE 313 Course Notes (hardcopy sold through ECE Stores, pdf file available.)

Lecture Recordings: Section C    Section D

Lecture Notes: Section C    Section D


Office Hour Schedule (Office hours start from the second week of the semester (01/23)) 

Hours Monday Tuesday Wednesday Thursday Friday
9-10am   Vishal Rana [3034 ECEB]   Jinyao Yang [5034 ECEB]  
10-11am      
11am-12pm     Kayvon Amir Mazooji [5034 ECEB]  
12-1pm   Teja Gupta [5034 ECEB]  
1-2pm   Kayvon Amir Mazooji [5034 ECEB]    
2-3pm Adi Pasic [5034 ECEB]   Prof. Ilan Shomorony [313 CSL] Teja Gupta [5034 ECEB] Prof. Minh N Do [113 CSL]
3-4pm Prof. Xu Chen [5040 ECEB] Junyeob Lim [5034 ECEB] Teja Gupta [4034 ECEB] Adi Pasic [5034 ECEB]  
4-5pm Jinyao Yang [5034 ECEB]    
5-6pm   Adi Pasic [5034 ECEB]    
6-7pm Adi Pasic (Recitation Session) [3020 ECEB]   Adi Pasic [5034 ECEB] Junyeob Lim [Zoom]    

Meeting Details

Section Meeting time and place Instructor

C

10:00 AM - 10:50 AM MWF
1015 ECEB
Professor Ilan Shomorony
e-mail: ilans AT illinois dot edu
Office Hours:  Wednesday 2-3PM, 313 Coordinated Science Lab

D

11:00 AM - 11:50 AM MWF
3017 ECEB
Professor Minh Do
email: minhdo AT illinois dot edu
Office Hours: Friday 2-3PM, 113 Coordinated Science Lab

F

1:00 PM - 1:50 PM MWF
1013 ECEB
Professor Xu Chen
e-mail: xuchen1 AT illinois dot edu
Office Hours: Monday 3-4PM, 5040 ECEB

 

Graduate Teaching Assistants

 

Name Office Hour Time Office Hour Location
Kayvon Amir Mazooji
mazooji2 AT illinois dot edu
Tuesday 1-2 pm; Thursday 11am-2pm
5034 ECEB
Teja Gupta
tejag2 AT illinois dot edu
Wednesday 12-1pm; Thursday 2-3pm 5034 ECEB
Wednesday 3-5pm 4034 ECEB
Adi Pasic
pasic2 AT illinois dot edu

Office Hours: Monday 2-3pm; Wednesday 5-7pm; Thursday 3-4pm

5034 ECEB
Recitation Session: Monday 6-7pm 3020 ECEB
Jinyao Yang
jinyaoy2 AT illinois dot edu
Monday 4-6pm; Thursday 9-11am 5034 ECEB
Junyeob Lim
junyeob AT illinois dot edu
Tuesday 3-5pm 5034 ECEB
Wednesday 6-7pm Online (Zoom Link)
Vishal Rana
vishalr AT illinois dot edu

Tuesday 9am-1pm

3034 ECEB

Concept constellation

 

Course schedule (subject to change)
Written Homework #
Deadline
Prairielearn Homework # Deadline Concepts and assigned reading)[ Short videos] Lecture Dates Recommended Study Problems
-

0

01/22

5:00:00pm for all HW deadlines below

* the sum of a geometric series and power series for exp(x)
* basic calculus: the chain rule for differentiation and use of logarithms
Jan 18 -

1

01/26


5:00:00pm for all HW deadlines below

1

01/29

* How to specify a set of outcomes, events, and probabilities for a given experiment (Ch 1.2)
* set theory (e.g. de Morgan's law, Karnaugh maps for two sets) (Ch 1.2)
* using principles of counting and over counting; binomial coefficients (Ch 1.3-1.4) [ILLINI, SAQ 1.3, SAQ 1.4, PokerIntro, PokerFH2P]
* using Karnaugh maps for three sets (Ch 1.4) [Karnaughpuzzle, SAQ1.2]
Jan 20 23 25 SAQs, i.e. Solution Available Question, (on p. 20) for Sections 1.2, 1.3, 1.4.

Problems (pp. 21-24) 1.2, 1.4, 1.6, 1.8, 1.10, 1.12.

Optional: [SAQ 1.5]

2

02/02

2

02/05

* random variables, probability mass functions, and mean of a function of a random variable (LOTUS) (Ch 2.1, first two pages of Ch 2.2) [pmfmean]
* scaling of expectation, variance, and standard deviation (Ch 2.2) [SAQ 2.2]
* conditional probability (Ch 2.3) [team selection] [SAQ 2.3]
* independence of events and random variables (Ch 2.4.1-2.4.2) [SimdocIntro] [Simdoc-Minhash1]
Jan 27 30; Feb 1 SAQs (pp. 74-75) for Sections 2.2-2.4

Problems (pp. 77-82) 2.2, 2.4, 2.6, 2.8, 2.10, 2.12, 2.16.

3

02/09

3

02/12

* binomial distribution (how it arises, mean, variance, mode) (Ch 2.4.3-2.4.4) [SAQ 2.4] [bestofseven]
* geometric distribution (how it arises, mean, variance, memoryless property) (Ch. 2.5) [SAQ 2.5]
* Bernoulli process (definition, connection to binomial and geometric distributions) (Ch 2.6) [SAQ 2.6]
* Poisson distribution (how it arises, mean, variance) (Ch 2.7) [SAQ 2.7]
Feb 3 6 8 SAQs (p. 75) for Sections 2.4-2.7

Problems (pp. 81-84) 2.14, 2.18, 2.20, 2.22, 2.24

4

02/16

4

02/19

* Maximum likelihood parameter estimation (definition, how to calculate for continuous and discrete parameters) (Ch 2.8) [SAQ 2.8]
* Markov and Chebychev inequalities (Ch 2.9)
* confidence intervals (definitions, meaning of confidence level) (Ch 2.9) [SAQ 2.9,Simdoc-Minhash2]
* law of total probability (Ch 2.10) [deuce] [SAQ 2.10]
* Bayes formula (Ch. 2.10)

Feb 10 13

(No class on Feb 15 due to unavailability of professors)

(To compensate, there would be class on the date of MT 1: Feb 27)

SAQs (pp. 75-76) for Sections 2.8-2.10

Problems (pp. 85-88) 2.26, 2.28, 2.30, 2.32, 2.34

5

02/23

5

02/26

* Hypothesis testing -- probability of false alarm and probability of miss (Ch. 2.11)
* ML decision rule and likelihood ratio tests (Ch 2.11) [SAQ 2.11]
* MAP decision rules (Ch 2.11)
Feb 17 20 22 SAQs (p. 76) for Sections 2.11 & 2.12

Problems (pp. 88-93) 2.36, 2.38, 2.40, 2.42, 2.44, 2.46

6

03/02

6

03/05

* union bound and its application (Ch 2.12.1) [SAQ 2.12]
* cumulative distribution functions (Ch 3.1) [SAQ 3.1]
* probability density functions (Ch 3.2) [SAQ 3.2] [simplepdf]
* uniform distribution (Ch 3.3) [SAQ 3.3]

Feb 24 27; Mar 1

(There would be class on Feb 27)

SAQs (p. 146-147) for Sections 3.1-3.4.

Problems (pp.149-151) 3.2, 3.4, 3.6, 3.8, 3.10.

7

03/09

7

03/19

* exponential distribution (Ch 3.4) [SAQ 3.4]
* Poisson processes (Ch 3.5) [SAQ 3.5]
* Erlang distribution (Ch 3.5.3)
* scaling rule for pdfs (Ch. 3.6.1) [SAQ 3.6]
Mar 3 6 8 SAQs (p 147) for Sections 3.5 & 3.6 .

Problems (p. 152-154) 3.12, 3.14, 3.16, 3.18, 3.20
Spring Break

8

03/23

8

03/26

* Gaussian (normal) distribution (e.g. using Q and Phi functions) (Ch. 3.6.2) [SAQ 3.6] [matlab help including Qfunction.m]
* the central limit theorem and Gaussian approximation (Ch. 3.6.3) [SAQ 3.6]
* ML parameter estimation for continuous type random variables (Ch. 3.7) [SAQ 3.7]
Mar 10 20 22 SAQs (pp. 147-148) for Sections 3.7-3.10.

Problems (pp. 154-159) 3.22, 3.24, 3.26, 3.28, 3.30, 3.32, 3.34, 3.38

9

03/30

9

04/02


* the distribution of a function of a random variable (Ch 3.8.1) [SAQ 3.8]
* generating random variables with a specified distribution (Ch 3.8.2)
* binary hypothesis testing for continuous type random variables (Ch 3.10) [SAQ 3.10]

Mar 24 27 29

SAQs (pp. 147-148) for Sections 3.7-3.10.

Problems (pp. 154-159) 3.22, 3.24, 3.26, 3.28, 3.30, 3.32, 3.34, 3.38

10

04/06

10

04/09

* joint CDFs (Ch 4.1) [SAQ 4.1]
* joint pmfs (Ch 4.2) [SAQ 4.2]
* joint pdfs (Ch 4.3) [SAQ 4.3]

Apr 3 5

(No Class on Friday, Mar 31 due to EOH)


SAQs (pp. 223-224) for Sections 4.1-4.3.

Problems (pp. 226-228) 4.2, 4.6, 4.10.

11

04/13

11

04/16

* joint pdfs of independent random variables (Ch 4.4) [SAQ 4.4]
* distribution of sums of random variables (Ch 4.5) [SAQ 4.5]
* more problems involving joint densities (Ch 4.6) [SAQ 4.6]

Apr 7 12

(No class on Monday, Apr 10 due to MT2)

SAQs (p. 224) for Sections 4.4-4.7.

Problems (p. 226-230) 4.4, 4.8, 4.12, 4.14, 4.16.

12

04/20

12

04/23

* joint pdfs of functions of random variables (Ch 4.7) [SAQ 4.7] (Section 4.7.2 and 4.7.3 will not be tested in the exams)
* correlation and covariance: scaling properties and covariances of sums (Ch 4.8) [SAQ 4.8]
* sample mean and variance of a data set, unbiased estimators (Ch 4.8, Example 4.8.7)
Apr 14 17 19 SAQs (p. 224) for Sections 4.8-4.9.

Problems (p. 230-233) 4.18, 4.20, 4.22, 4.24, 4.26, 4.28

13

04/27

 

* minimum mean square error unconstrained estimators (Ch 4.9.2)
* minimum mean square error linear estimator (Ch 4.9.3) [SAQ 4.9]
* law of large numbers (Ch 4.10.1)
* central limit theorem (Ch 4.10.2) [SAQ 4.10]
* joint Gaussian distribution (Ch 4.11) (e.g. five dimensional characterizations) [SAQ 4.11]
Apr 21 24 26 SAQs (p.225) for Sections 4.10-4.11

Problems (pp.233-237) 4.30, 4.32, 4.34, 4.36, 4.38, 4.40, 4.42.
-   wrap up and review Apr 28; May 1 3  

More Information

 

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