ECE 313/MATH 362
PROBABILITY WITH ENGINEERING APPLICATIONS
Fall 2023
ECE 313 (also crosslisted 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 Homeworks: Written homework assignments will be available on Canvas under "Assignments". Please submit your written homework on Gradescope (accessible through Canvas). Typesetting with LaTeX is allowed, however, no additional credit will be awarded to typeset homework. Written homework solutions will be made available on Canvas (under "Modules").
Text : ECE 313 Course Notes (hardcopy sold through ECE Stores, pdf file available.)
Lecture Notes: Canvas
Office Hour Schedule (Office hours start from the second week of the semester (08/28))
Recitation Friday 910 AM
Hours  Monday  Tuesday  Wednesday  Thursday  Friday  
910 am  Xu Chen [5040 ECEB]  Hongyu Shen [5034 ECEB]  Hongyu Shen [5034 ECEB]  Hongyu Shen [5034 ECEB]  Shitao Liu  Recitation [5034 ECEB]  
1011 am  Shitao Liu [5034 ECEB]  
11 am12 pm  Amogh Pandey [5034 ECEB]  Dimitrios Katselis[3017 ECEB]  
121 pm  Amogh Pandey [5034 ECEB]  Amogh Pandey [5034 ECEB]  
12 pm  Zifei Han [5034 ECEB]  Vishal Rana [5034 ECEB]  Evan Varghese [5034 ECEB]  Melih Bastopcu [368 CSL]  Zifei Han [5034 ECEB]  Eric Chitamber [virtual]  
23 pm  Evan Varghese [5034 ECEB]  Vishal Rana [5034 ECEB]  Zifei Han [5034 ECEB]  
34 pm  Junyeob Lim [5034 ECEB]  Junyeob Lim [5034 ECEB]  
45 pm  
56 pm  Shitao Liu [5034 ECEB]  Amogh Pandey [5034 ECEB]  Evan Varghese [5034 ECEB]  
67 pm 
Section  Meeting time and place  Instructor 

A 
2:00 PM  3:20 PM TR 3013 ECEB 
Professor Xu Chen email: xuchen1 AT illinois dot edu Office Hours: Monday 910 AM, 5040 ECEB 
B 
10:00 AM  10:50 AM MWF 3017 ECEB 
Professor Eric Chitambar email: echitamb AT illinois dot edu Office Hours: Friday 12 PM (virtual) 
C 
11:00 AM  11:50 AM MWF 3017 ECEB 
Professor Dimitrios Katselis email: katselis AT illinois dot edu Office Hours: Tuesday 11 AM12 PM, 3017 ECEB 
D 
1:00 PM  1:50 PM MWF 3017 ECEB 
Professor Lav R Varshney email: varshney AT illinois dot edu Office Hours: , 314 Coordinated Science Lab 
E 
2:00 PM  2:50 PM MWF  
Professor Lav R Varshney email: varshney AT illinois dot edu Office Hours: , 314 Coordinated Science Lab 
F 
5:00 PM  5:50 PM MWF 3017 ECEB 
Dr. Melih Bastopcu email: bastopcu AT illinois dot edu Office Hours: Wednesday 12 PM, 368 Coordinated Science Lab 
Name  Office Hour Time  Office Hour Location 
Vishal Rana vishalr AT illinois dot edu 
Tuesday 13 PM  5034 ECEB 
Thursday 25 PM  5034 ECEB  
Amogh Pandey amoghp3 AT illinois dot edu 
Tuesday 11 AM1 PM; 56 PM 
5034 ECEB 
Thursday 122 PM  5034 ECEB  
Evan Varghese evanjv2 AT illinois dot edu 
Wednesday 13 PM  5034 ECEB 
Thursday 57 PM  5034 ECEB  
Hongyu Shen hongyu2 AT illinois dot edu 
Tuesday 911 AM  5034 ECEB 
Wednesday 9 AM12 PM  5034 ECEB  
Thursday 9 AM11 AM  5034 ECEB  
Junyeob Lim junyeob2 AT illinois dot edu 
Tuesday 35 PM  5034 ECEB 
Wednesday 35 PM  5034 ECEB  
Shitao Liu sl53 AT illinois dot edu 
Monday 57 PM  5034 ECEB 
Friday 910 AM  5034 ECEB Recitation  
Friday 10 AM1 PM  5034 ECEB  
Zifei Han zifeih2 AT illinois dot edu 
Monday 14 PM  5034 ECEB 
Friday 14 PM  5034 ECEB 
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 
Week of August 21   
1 9/1


* 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 1.31.4) [ILLINI, SAQ 1.3, SAQ 1.4, PokerIntro, PokerFH2P] * using Karnaugh maps for three sets (Ch 1.4) [Karnaughpuzzle, SAQ1.2] 
Week of August 21  SAQs, i.e. Solution Available Question, (on p. 20) for Sections 1.2, 1.3, 1.4. Problems (pp. 2124) 1.2, 1.4, 1.6, 1.8, 1.10, 1.12. Optional: [SAQ 1.5] 
2 9/8 

* 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 2.4.12.4.2) [SimdocIntro] [SimdocMinhash1] 
Week of August 28  SAQs (pp. 7475) for Sections 2.22.4 Problems (pp. 7782) 2.2, 2.4, 2.6, 2.8, 2.10, 2.12, 2.16. 
3 9/15 

* binomial distribution (how it arises, mean, variance, mode) (Ch 2.4.32.4.4) [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] 
Week of September 4  SAQs (p. 75) for Sections 2.42.7 Problems (pp. 8184) 2.14, 2.18, 2.20, 2.22, 2.24 
4 9/22 

* 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,SimdocMinhash2] 
Week of September 11 
SAQs (pp. 7576) for Sections 2.82.9 Problems (pp. 8586) 2.26, 2.28, 2.30 
5 9/29 

* law of total probability (Ch 2.10) [deuce] [SAQ 2.10] * Hypothesis testing  probability of false alarm and probability of miss (Ch. 2.11) 
Week of September 18  SAQs (p. 76) for Sections 2.10, 2.11 & 2.12 Problems (pp. 8693) 2.32, 2.34, 2.36, 2.38, 2.40, 2.42, 2.44, 2.46 
6 10/6 

* 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 25 
SAQs (p. 146147) for Sections 3.13.4. Problems (pp.149151) 3.2, 3.4, 3.6, 3.8, 3.10. 
7 10/13 

* 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] 
Week of October 2  SAQs (p 147) for Sections 3.5 & 3.6 . Problems (p. 152154) 3.12, 3.14, 3.16, 3.18, 3.20 
8 10/20 

* 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] 
Week of October 9  SAQs (pp. 147148) for Sections 3.73.10. Problems (pp. 154159) 3.22, 3.24, 3.26, 3.28, 3.30, 3.32, 3.34, 3.38 
9 10/27 

* 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] 
Week of October 16 
SAQs (pp. 147148) for Sections 3.73.10. Problems (pp. 154159) 3.22, 3.24, 3.26, 3.28, 3.30, 3.32, 3.34, 3.38 
10 11/3 

* joint CDFs (Ch 4.1) [SAQ 4.1] * joint pmfs (Ch 4.2) [SAQ 4.2] * joint pdfs (Ch 4.3) [SAQ 4.3] 
Week of October 23 
SAQs (pp. 223224) for Sections 4.14.3. Problems (pp. 226228) 4.2, 4.6, 4.10. 
11 11/10 

* 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] 
Week of October 30 
SAQs (p. 224) for Sections 4.44.7. Problems (p. 226230) 4.4, 4.8, 4.12, 4.14, 4.16. 
12 11/17 

* 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) 
Week of November 6  SAQs (p. 224) for Sections 4.84.9. Problems (p. 230233) 4.18, 4.20, 4.22, 4.24, 4.26, 4.28 
13 12/1 

* 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] 
Week of November 13  SAQs (p.225) for Sections 4.104.11 Problems (pp.233237) 4.30, 4.32, 4.34, 4.36, 4.38, 4.40, 4.42. 
  wrap up and review  Week of November 27 
More Information
Grading Policies 
Written Homework 
Exams 
Gradescope (via Canvas) 
Canvas 
Previous Web PagesPrevious Exams 
The ECE 313 FAQ 
Reserve Books 
Syllabus 