Image ECE ILLINOIS

 

ECE 313/MATH 362

PROBABILITY WITH ENGINEERING APPLICATIONS

Fall 2024

 

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.


Communication : Please email ece-313-fall24-group@office365.illinois.edu instead of contacting instructors or TAs directly.

Prerequisite : Math 257 or Math 416

Exam times : See Exam information.

Homeworks : Homework assignments and solutions will be posted here. Please submit your written homework on Gradescope (enrollment code 2B2Y8R). Typesetting with LaTeX is allowed, however, no additional credit will be awarded to typeset homework.

Campuswire: Self-enrollment code for Campuswire is 0479.

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

Lecture Notes : Section B


Office Hour Schedule (TA Office hours start from the second week of the semester) 

Hours Monday Tuesday Wednesday Thursday Friday
9 am-10 am     Adarsh [4034 ECEB]    
10 am-11 am       Jonah [3001 ECEB] Vishal [2034 ECEB]  
11 am-12 pm Vishal (11/04 only)[Zoom]   Zifei [4034 ECEB] Dimitris [1015 ECEB]
(11:20 am- 11:50 am)
Dimitris [1015 ECEB]
(11:20 am- 11:50 am)
12 pm-1 pm   Jonah [3001 ECEB] Junyeob [2034 ECEB]  
1 pm-2 pm     Xu [5040 ECEB] Vishal [2034 ECEB]
2 pm-3 pm Aris [2036 ECEB]   Junyeob [4034 ECEB] Shitao [3001 ECEB]
3 pm-4 pm Evan [4036 ECEB] Venu [Zoom]
(3:30-4:30 pm)
Evan [4034 ECEB] Adarsh [3001 ECEB] Junyeob [2034 ECEB]
4 pm-5 pm Evan [4034 ECEB] Junyeob [3003 ECEB] Zifei [3001 ECEB]  
5 pm-6 pm     Shitao [4034 ECEB]  
6 pm-7 pm        
7 pm-8 pm        

Meeting Details

Section Meeting time and place Instructor

A

2:00 PM - 3:15 PM TR
3013 ECEB
Professor Venugopal V. Veeravalli
e-mail: vvv AT illinois dot edu
Office Hours:  Tuesday 3:30 PM - 4:30 PM, 
Zoom

B

10:00 AM - 10:50 AM MWF
3017 ECEB
Dr. Aristomenis Tsopelakos
e-mail: tsopela2 AT illinois dot edu
Office Hours:  Monday 2:00 - 3:00 PM, 2036 ECEB

C

11:00 AM - 11:50 AM MWF
3017 ECEB
Professor Xu Chen
email: xuchen1 AT illinois dot edu
Office Hours: Wednesday 1:00 - 2:00 PM, 5040 ECEB

D

1:00 PM - 1:50 PM MWF
3017 ECEB
Professor Dimitrios Katselis
e-mail: katselis AT illinois dot edu
Office Hours: Wednesday, Friday, 11:20 AM - 11:50 AM, 1015 ECEB

 

Graduate Teaching Assistants

 

Name Office Hour Time Office Hour Location
Shitao Liu
sl53 AT illinois dot edu
Thursday 2-3 PM 3001 ECEB
Wednesday 5-8 PM 4034 ECEB
Adarsh Muthuveeru-Subramaniam
adarshm2 AT illinois dot edu
Wednesday 9-10 AM 4034 ECEB
Thursday 3-4 PM 3001 ECEB
Evan Varghese
evanjv2 AT illinois dot edu
Monday 3-5 PM 4036 ECEB
Wednesday 3-5 PM 4034 ECEB
Jonah Jesus Cadena-Perena
jonahjc2 AT illinois dot edu
Thursday 10 AM-2 PM 3001 ECEB
Junyeob Lim
junyeob2 AT illinois dot edu
Wednesday 2-3 PM 4034 ECEB
Wednesday 4-5 PM 3003 ECEB
Thursday 12-1 PM 2034 ECEB
Thursday 3-4 PM 2034 ECEB
Vishal Rana
vishalr AT illinois dot edu
Thursday 10 AM-12 PM 2034 ECEB
Thursday 1 PM-3 PM 2034 ECEB
Zifei Han
zifeih2 AT illinois dot edu
Wednesday 11 AM-1 PM 4034 ECEB
Thursday 4-6 PM 3001 ECEB

Concept constellation

 

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

 

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

1

9/5


6:00:00pm for all HW deadlines below

 

* 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]
Week of August 26 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

9/12

 

* 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]
Week of September 2 SAQs (pp. 74-75) for Sections 2.2-2.3

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

3

9/19

 

law of total probability (Ch 2.10) [deuce] [SAQ 2.10]
Bayes formula (Ch. 2.10)

* independence of events and random variables (Ch 2.4.1-2.4.2) [SimdocIntro] [Simdoc-Minhash1]
* binomial distribution (how it arises, mean, variance, mode) (Ch 2.4.3-2.4.4) [SAQ 2.4] [bestofseven]
Week of September 9 SAQs (p. 75-76) for Sections 2.4, 2.10

Problems (pp. 81-84, 86-87) 2.14, 2.18, 2.20, 2.22, 2.24, 2.32, 2.34.

4

9/26

 

* 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]
* Markov and Chebychev inequalities (Ch 2.9)

Week of September 16

SAQs (pp. 75) for Section 2.5-2.7, 2.9

Problems (pp. 86) 2.30a-b

5

10/3

 

* confidence intervals (definitions, meaning of confidence level) (Ch 2.9) [SAQ 2.9,Simdoc-Minhash2]
* 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)

Week of September 23 SAQs (p. 75-76) for Sections 2.9, 2.11 & 2.12

Problems (pp. 85, 88-93)
 2.28, 2.36, 2.38, 2.40, 2.42, 2.44, 2.46

6

10/10

 

* 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]

Week of September 30

SAQs (p. 146) for Sections 3.1-3.3.

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

7

10/17

 

* 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)
Week of October 7 SAQs (p 147) for Sections 3.4-3.5 & 3.6 .

Problems (p. 151-152) 3.10, 3.12, 3.14

8

10/24

 

* 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]
the distribution of a function of a random variable (Ch 3.8.1) [SAQ 3.8]

 

Week of October 14 SAQs (pp. 147) for Sections 3.6, 3.8

Problems (pp. 152-159) 3.16, 3.18, 3.20, 3.26, 3.28, 3.30, 3.32, 3.34a, 3.38a-b,d

9

10/31

 

* 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]
joint CDFs (Ch 4.1) [SAQ 4.1]

Week of October 21

SAQs (pp. 147-148, 223) for Sections 3.8, 3.10, 4.1

Problems (pp. 154-159, 226) 3.22, 3.24, 3.26, 3.28, 3.30, 3.32, 3.34a, 3.38a-b,d, 4.2

10

11/7

 

* joint pmfs (Ch 4.2) [SAQ 4.2]
* joint pdfs (Ch 4.3) [SAQ 4.3]
joint pdfs of independent random variables (Ch 4.4) [SAQ 4.4]

Week of October 28


SAQs (pp. 223-224) for Sections 4.2-4.4.

Problems (pp. 226-229) 4.4, 4.6, 4.8, 4.10, 4.12.

11

11/14

 

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

Week of November 4

SAQs (p. 224) for Sections 4.5-4.7.

Problems (p. 229-230) 4.14, 4.16.

12

11/21

 

* 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)
Maximum likelihood parameter estimation (definition, how to calculate for discrete and 
continuous parameters) (Ch 2.8) [SAQ 2.8]

Week of November 11 SAQs (p. 224, 75) for Sections 4.7-4.8, 2.8

Problems (p. 230-231, 85) 4.18, 4.20, 4.22, 2.26

13

12/5

 

* ML parameter estimation for continuous type random variables (Ch. 3.7) [SAQ 3.7]
* minimum mean square error unconstrained estimators (Ch 4.9.2)
* minimum mean square error linear estimator (Ch 4.9.3) [SAQ 4.9]
Week of November 18  SAQs (pp.147, 225) for Sections 3.7, 4.9

Problems (pp. 154-155, 231-233) 3.22, 3.24, 4.24, 4.26, 4.28
Fall Break

14

--

 


* 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]
Week of  December 2 SAQs (pp.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 Week of December 9  

More Information

 

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