ECE 313/MATH 362
PROBABILITY WITH ENGINEERING APPLICATIONS
Fall 2021
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 286 or Math 415
Exam times : See Exam information.
Text : ECE 313 Course Notes (hardcopy sold through ECE Stores, pdf file available.)
Times/locations for guided study sessions and regular office hours (beginning second week, i.e., Aug. 30).
Hours  Monday  Tuesday  Wednesday  Thursday  Friday  
89 am  Online Guided study sessions Reserve here. Zoom/location 
Online Guided study sessions Reserve here. Zoom/location 

12 pm  12:301:30 (regular)  
23 pm  
34 pm  
45 pm  Zoom/location  Zoom/location  Zoom/location  Zoom/location  
56 pm 
Section  Meeting time and place  Instructor 

10 MWF Online (live streamed in Zoom, recordings in Illinois Media Space) 
Professor Yuliy Baryshnikov email: ymb AT illinois dot edu Office Hours: Tuesday 45PM (regular) 

1112:20 TuTh 1015 ECEB (live streamed in Echo 360, recordings in Echo 360) 
Professor Olgica Milenkovic email: milenkov AT illinois dot edu Office Hours: Wednesday 34PM (regular, Weeks 2, 4, 6,...) Wednesday 45PM (regular, Weeks 3, 5, 7,...) location: 2017 ECEB 

D 
1 MWF Online (live streamed in Zoom, recordings in Illinois Media Space) 
Professor Aiguo Han email: han51 AT illinois dot edu Office Hours: Thursday 45PM (guided study) Lecture slides 
Teja Gupta tejag2 AT illinois dot edu 
Office Hours: Monday 45PM (regular, 2017 ECEB) Friday 13PM (guided study, 3015 ECEB) 
Kelly Levick klevick2 AT illinois dot edu 
Office Hours: Friday 45PM (regular) 
Srilakshmi Pattabiraman sp16 AT illinois dot edu 
Office Hours: Thursday 14PM (guided study) 
Vishal Rana vishalr AT illinois dot edu 
Office Hours: Thursday 12:301:30PM (regular), Friday 89AM (guided study) 
Lingda Wang lingdaw2 AT illinois dot edu 
Office Hours: Wednesday 45PM (regular), Friday 36PM (guided study) 
Yuechen Wang yuechen6 AT illinois dot edu 
Office Hours: Monday 34PM (regular, online and inperson 2036 ECEB), Thursday 89AM (guided study) 
Course schedule (subject to change)  
Quiz # Deadline 
Lecture dates 
Concepts and assigned reading)[ Short videos]  Homework problems (not to hand in but similar to quiz questions) 

0 Mon, 8/30 10pm 
  Quiz 0 covers two topics that come up later in the course: * the sum of a geometric series and power series for exp(x) * basic calculus: the chain rule for differentiation and use of logarithms 
Quiz 0 is a practice quiz and carries no course credit. 
1 Mon, 9/6 10pm (All quiz deadlines 10pm) 
8/239/3  * 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] 
SAQs (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] Tip for quiz 1: Make sure you can compute the numerical values of binomial coefficients. See p. 13 of the course notes. 
2 Mon, 9/13 
9/69/10  * 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] 
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 Mon, 9/20 
9/139/17  * 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] 
SAQs (p. 75) for Sections 2.42.7 Problems (pp. 8184) 2.14, 2.18, 2.20, 2.22, 2.24 
4 Mon, 9/27 
9/209/24  * 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] * law of total probability (Ch 2.10) [deuce] [SAQ 2.10] * Bayes formula (Ch. 2.10) 
SAQs (pp. 7576) for Sections 2.82.10 Problems (pp. 8588) 2.26, 2.28, 2.30, 2.32, 2.34 
5 Mon, 10/4 
9/2710/1  * 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) * union bound and its application (Ch 2.12.1) [SAQ 2.12] * network outage probability and distribution of capacity, and more applications of the union bound (Ch 2.12.22.12.4) 
SAQs (p. 76) for Sections 2.11 & 2.12 Problems (pp. 8893) 2.36, 2.38, 2.40, 2.42, 2.44, 2.46 
6 Mon, 10/11 
10/410/8  * 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] * exponential distribution (Ch 3.4) [SAQ 3.4] 
SAQs (p. 146147) for Sections 3.13.4. Problems (pp.149151) 3.2, 3.4, 3.6, 3.8, 3.10. 
7 Mon, 10/18 
10/1110/15  * 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] * 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 3.5 & 3.6 . Problems (p. 152154) 3.12, 3.14, 3.16, 3.18, 3.20 
8 Mon, 10/25 
10/1810/22  * 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) * failure rate functions (Ch 3.9) [SAQ 3.9] * binary hypothesis testing for continuous type random variables (Ch 3.10) [SAQ 3.10] 
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 Mon, 11/1 
10/2510/29  * joint CDFs (Ch 4.1) [SAQ 4.1] * joint pmfs (Ch 4.2) [SAQ 4.2] * joint pdfs (Ch 4.3) [SAQ 4.3] 
SAQs (pp. 223224) for Sections 4.14.3. Problems (pp. 226228) 4.2, 4.6, 4.10. 
10 Mon, 11/15 (skip 11/8) 
11/111/12  * 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] * 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) 
SAQs (p. 224) for Sections 4.44.7. Problems (p. 226230) 4.4, 4.8, 4.12, 4.14, 4.16. 
11 Tue, 11/30 
11/1511/19  * 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) * 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. 224) for Sections 4.84.9. Problems (p. 230233) 4.18, 4.20, 4.22, 4.24, 4.26, 4.28 
11/2211/26  Thanksgiving vacation  
12 Mon, 12/6 
11/2912/3  * 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 4.104.11 Problems (pp.233237) 4.30, 4.32, 4.34, 4.36, 4.38, 4.40, 4.42. 
  12/612/8  wrap up and review 
Optional Reading: D. V. Sarwate, Probability with Engineering Applications, Powerpoint Slides for ECE 313 , Fall 2000
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