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ECE 313/MATH 362

PROBABILITY WITH ENGINEERING APPLICATIONS

Spring 2025, Sections A,B,C

Link to website for Section G

 

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.

Homeworks : Homeworks will be issued weekly on Fridays and will be due the next Friday at 7pm, through Gradescope (enrollment code KZ2VJY). On each homework, we will randomly select about half the problems to be fully graded. Homework assignments and solutions will be posted here. Typesetting with LaTeX is allowed, however, no additional credit will be awarded to typeset homework.

Quizzes : Every third week of the semester, there will be an in-class quiz covering one problem. You will have 15 min to solve the problem, and will be provided with a shortlist of problems to prepare for. The shortlist will be provided at least one week before the quiz. One quiz with the lowest score will be dropped from your final grade calculation. If you have a valid excuse for missing a quiz (see Student code), you may request to take the quiz the following week.

 

Campuswire: We encourage you to use Campuswire for online discussions related to the class. The course staff will try to answer any question within 48 hours during weekdays. Online questions and emails will not be answered during weekends. Questions during the weekends before exams can be answered during regular office hours. Self-enrollment code for Campuswire is 7123.

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

Lecture Notes : Section B


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

Before attending office hours, students are strongly encouraged to read the homework problems and lecture material and formulate their questions for the instructors/TAs. This will facilitate a more productive discussion and allow more students to get detailed feedback.

Hours Monday Tuesday Wednesday Thursday Friday
9 am-10 am         Zifei [ECEB 4034]
10 am-11 am       Vishal [ECEB 5034]
11 am-12 pm        
12 pm-1 pm Aris [ECEB 2036]      
1 pm-2 pm        
2 pm-3 pm Dimitris [ECEB 2013]
(2:00 pm - 2:30 pm)
  Dimitris [ECEB 3017]
(2:00 pm - 2:30 pm)
Shitao [ECEB 4034]    
3 pm-4 pm Shitao [ECEB 3013]   Shitao [ECEB 4034] Olgica [CSL 311]
(3:30 pm - 4:30 pm)
Zifei [ECEB 4034]
4 pm-5 pm   Adarsh [ECEB 4034](Cancelled for 02/05)
5 pm-6 pm   Evan [ECEB 4034] Evan [ECEB 5034]  
6 pm-7 pm    
7 pm-8 pm          

Meeting Details

Section Meeting time and place Instructor

A

2:00 PM - 3:15 PM TR
1015 ECEB
Professor Olgica Milenkovic
e-mail: milenkov AT illinois dot edu
Office Hours:  Thursday 3:30 PM - 4:30 PM, CSL 311

B

11:00 AM - 11:50 AM MWF
3017 ECEB
Dr. Aristomenis Tsopelakos
e-mail: tsopela2 AT illinois dot edu
Office Hours:  Monday 12:00 - 1:00 PM, ECEB 2036

C

1:00 PM - 1:50 PM MWF
1013 ECEB
Professor Dimitrios Katselis
e-mail: katselis AT illinois dot edu
Office Hours: Monday 2:00 - 2:30 PM ECEB 2013; Wednesday 2:00 - 2:30 PM ECEB 3017

 

Graduate Teaching Assistants

Name Office Hour Time Office Hour Location
Adarsh Muthuveeru-Subramaniam
adarshm2 AT illinois dot edu
Wednesday 4pm-6pm ECEB 4034
Evan Varghese
evanjv2 AT illinois dot edu
Tuesday 5pm-7pm ECEB 4034
Thursday 5pm-7pm ECEB 5034
Shitao Liu
sl53 AT illinois dot edu
Monday 3pm-5pm ECEB 3013
Wednesday 2pm-4pm ECEB 4034
Vishal Rana
vishalr AT illinois dot edu
Thursday 10am-1pm ECEB 5034
Zifei Han
zifeih2 AT illinois dot edu
Friday 9am-11am ECEB 4034
Friday 3pm-5pm ECEB 4034

Concept constellation

 

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

SAQs - Solution Available Questions

Problems at the end of each chapter

Examples within each chapter

Week of January 20

0

HW 0 will not be graded

7:00:00pm 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) (Ch 1.2)

SAQs, (on p. 20) for Sections 1.2

Problems (p. 21-22) 1.2, 1.4, 1.6b, 1.8

Week of January 27

1

2/7

* using principles of counting and over counting; binomial coefficients (Ch 1.3-1.4) [ILLINI, SAQ 1.3, SAQ 1.4, PokerIntro, PokerFH2P]

* 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]

SAQs (p. 20, 74) for Sections 1.3-1.4, 2.2

Problems (p. 23-24, 77-80) 1.10, 1.12, 2.2, 2.4, 2.6, 2.8, 2.10

Optional: [SAQ 1.5]

Week of February 3

Quiz 1

2

2/14

* conditional probability (Ch 2.3) [team selection] [SAQ 2.3]

*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]

SAQs (p. 74-76) for Sections 2.3, 2.10

Problems (p. 81-82, 86-87) , 2.12, 2.14, 2.16, 2.32, 2.34

Week of February 10

3

2/21

* 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]

SAQs (p. 74-75) for Section 2.4-2.7

Problems (p. 82-84) 2.18, 2.20, 2.22, 2.24

Week of February 17

4

2/28

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]

* 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]

SAQs (p. 75-76) for Sections 2.8, 2.9, 2.11

Problems (p. 85-86, 88-90) 2.26, 2.28, 2.30, 2.36a-b, 2.38, 2.40a

Week of February 24

Quiz 2

5

3/7

MAP decision rules (Ch 2.11)

* 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]

SAQs (p. 76, 146) for Sections 2.11, 2.12, 3.1-3.2

Problems (p. 88-92, 149-151) 2.36, 2.40, 2.42, 2.44, 2.46, 3.2, 3.4, 3.6, 3.8

Week of March 3

6

3/14

uniform distribution (Ch 3.3) [SAQ 3.3]

* exponential distribution (Ch 3.4) [SAQ 3.4]

* Poisson processes (Ch 3.5) [SAQ 3.5]

* Erlang distribution (Ch 3.5.3)

SAQs (p 147) for Sections 3.3-3.5

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

Week of March 10

7

3/28

scaling rule for pdfs (Ch. 3.6.1)

* 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]

SAQs (p. 147) for Sections 3.6

Problems (p. 152-154) 3.16, 3.18, 3.20

Spring Break

Week of March 24

Quiz 3

8

4/4

ML parameter estimation for continuous type random variables (Ch. 3.7) [SAQ 3.7]

* 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)

SAQs (pp. 147) for Sections 3.7, 3.8

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

Week of March 31

9

4/11

binary hypothesis testing for continuous type random variables (Ch 3.10) [SAQ 3.10]

* joint CDFs (Ch 4.1) [SAQ 4.1]

* joint pmfs (Ch 4.2) [SAQ 4.2]

 

SAQs (p. 148, 223) for Sections 3.10, 4.1-4.2

Problems (p. 226) 4.2

Week of April 7

10

4/18

joint pdfs (Ch 4.3) [SAQ 4.3]

joint pdfs of independent random variables (Ch 4.4) [SAQ 4.4]

* distribution of sums of random variables (Ch 4.5) [SAQ 4.5]

SAQs (p. 223-224) for Sections 4.3-4.5

Problems (p. 226-229) 4.4, 4.6, 4.8, 4.10, 4.12, 4.14

Week of April 14

Quiz 4

11

4/25

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)

* correlation and covariance: scaling properties and covariances of sums (Ch 4.8) [SAQ 4.8]

SAQs (p. 224) for Sections 4.6-4.8

Problems (p. 229-231) 4.16, 4.18, 4.20, 4.22

Week of April 21

12

5/2

sample mean and variance of a data set, unbiased estimators (Ch 4.8, Example 4.8.7)

* minimum mean square error unconstrained estimators (Ch 4.9.2)

* minimum mean square error linear estimator (Ch 4.9.3) [SAQ 4.9]

SAQs (p.225) for Sections 4.9

Problems (p. 231-233) 4.24, 4.26, 4.28

Week of April 28

13

5/7

* 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]

SAQs (p.225) for Sections 4.10-4.11

Problems (p. 233-237) 4.30, 4.32, 4.34, 4.36, 4.38, 4.40, 4.42

Week of May 5 - wrap up and review -

More Information

 

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