ECE 313/MATH 362
PROBABILITY WITH ENGINEERING APPLICATIONS
Spring 2020
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. Jan. 27).
Hours  Monday  Tuesday  Wednesday  Thursday  Friday  
12 pm  5034 ECEB Guided study sessions Reserve here. 
5034 ECEB Guided study sessions Reserve here. 

23 pm  
34 pm  
45 pm  4034 ECEB  4034 ECEB  4034 ECEB  4034 ECEB  4034 ECEB  
56 pm 
Section  Meeting time and place  Instructor 

C  10 MWF 3017 ECE Building 
Professor Eric Chitamber email: echitamb AT illinois dot edu Office Hours: Thursdays 45 pm, 4034 ECEB 
D  11 MWF 3017 ECE Building 
Professor Ilan Shomorony email:ilans AT illinois dot edu Office Hours: Fridays 56 pm, 5034 ECEB 
F  1 MWF 3017 ECE Building 
Professor Zhizhen Jane Zhao email: zhizhenz AT illinois dot edu Office Hours: Fridays 45 pm, 5034 ECEB 
Kelly Levick klevick2 AT illinois dot edu 
Office Hours: Fridays 45pm (office hour), Thursdays 23pm and Fridays 34pm (guided study) 
Raimi Shah rsshah2 AT illinois dot edu 
Office Hours: Tuesdays 45pm (office hour), Thursdays 12pm (guided study) 
Ningkai Wu nwu10 AT illinois dot edu 
Office Hours: 
Ali Yekkehkhany yekkehk2 AT illinois dot edu 
Office Hours: Wednesdays 45pm (office hour), Thursdays 36pm (guided study) 
Yichi Zhang yichi3 AT illinois dot edu 
Office Hours: Mondays 45pm (office hour), Fridays 13pm (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, 1/27 
  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. 
1/22  1/31  * 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. 

1 Mon, 2/10 
2/32/7  * 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. 
2/102/14  * 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 

2 Mon, 2/24 
2/172/21  * 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 
2/242/28  * 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 

3 Mon, 3/9 
3/2  3/6  * 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. 
3/9  3/13  * 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 

3/163/20  Spring vacation  
4 Mon, 3/30 
3/233/25 (EOH is 3/27)  * 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 
3/304/3  * joint CDFs (Ch 4.1) [SAQ 4.1] * joint pmfs (Ch 4.2) [SAQ 4.2] * joint pdfs (Ch 4.3) [SAQ 4.3] 
SAQs (pp. 223224) for Sections 4.14.3. Problems (pp. 226228) 4.2, 4.6, 4.10. 

5 Mon, 4/20 (skip 4/13) 
4/64/17  * 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. 
4/204/24  * 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 

6 Mon, 5/4 
4/275/1  * 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. 
  5/45/6  wrap up and review 
Optional Reading:
More Information
Grading Policies 
Homework 
Exams 
Piazza 
COMPASS (for grades) 
Previous Web PagesPrevious Exams 
The ECE 313 FAQ 
Reserve Books 
Syllabus 