ECE 313/MATH 362
PROBABILITY WITH ENGINEERING APPLICATIONS
Spring 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 would be available on Canvas (under "files") and Gradescope. Please submit your written homework on Gradescope. Written homework solutions would be available on Canvas (under "files").
Prairielearn Homeworks: Prairielearn homeworks are due every Sunday at 5:00:00pm.
Course Communications: Please email: ece313spring23group@office365.illinois.edu instead of emailing instructors/TAs individually.
Campuswire: All questions regarding homework should be posted and discussed on Campuswire. Students should NOT send ece313spring23group@office365.illinois.edu questions about homework or other general issues that other students in the class should be aware of as well.
Text : ECE 313 Course Notes (hardcopy sold through ECE Stores, pdf file available.)
Lecture Recordings: Section C Section D
Lecture Notes: Section C Section D
Office Hour Schedule (Office hours start from the second week of the semester (01/23))
Hours  Monday  Tuesday  Wednesday  Thursday  Friday  
910am  Vishal Rana [3034 ECEB]  Jinyao Yang [5034 ECEB]  
1011am  
11am12pm  Kayvon Amir Mazooji [5034 ECEB]  
121pm  Teja Gupta [5034 ECEB]  
12pm  Kayvon Amir Mazooji [5034 ECEB]  
23pm  Adi Pasic [5034 ECEB]  Prof. Ilan Shomorony [313 CSL]  Teja Gupta [5034 ECEB]  Prof. Minh N Do [113 CSL]  
34pm  Prof. Xu Chen [5040 ECEB]  Junyeob Lim [5034 ECEB]  Teja Gupta [4034 ECEB]  Adi Pasic [5034 ECEB]  
45pm  Jinyao Yang [5034 ECEB]  
56pm  Adi Pasic [5034 ECEB]  
67pm  Adi Pasic (Recitation Session) [3020 ECEB]  Adi Pasic [5034 ECEB]  Junyeob Lim [Zoom] 
Section  Meeting time and place  Instructor 

C 
10:00 AM  10:50 AM MWF 1015 ECEB 
Professor Ilan Shomorony email: ilans AT illinois dot edu Office Hours: Wednesday 23PM, 313 Coordinated Science Lab 
D 
11:00 AM  11:50 AM MWF 3017 ECEB 
Professor Minh Do email: minhdo AT illinois dot edu Office Hours: Friday 23PM, 113 Coordinated Science Lab 
F 
1:00 PM  1:50 PM MWF 1013 ECEB 
Professor Xu Chen email: xuchen1 AT illinois dot edu Office Hours: Monday 34PM, 5040 ECEB 
Name  Office Hour Time  Office Hour Location 
Kayvon Amir Mazooji mazooji2 AT illinois dot edu 
Tuesday 12 pm; Thursday 11am2pm 
5034 ECEB 
Teja Gupta tejag2 AT illinois dot edu 
Wednesday 121pm; Thursday 23pm  5034 ECEB 
Wednesday 35pm  4034 ECEB  
Adi Pasic pasic2 AT illinois dot edu 
Office Hours: Monday 23pm; Wednesday 57pm; Thursday 34pm 
5034 ECEB 
Recitation Session: Monday 67pm  3020 ECEB  
Jinyao Yang jinyaoy2 AT illinois dot edu 
Monday 46pm; Thursday 911am  5034 ECEB 
Junyeob Lim junyeob AT illinois dot edu 
Tuesday 35pm  5034 ECEB 
Wednesday 67pm  Online (Zoom Link)  
Vishal Rana vishalr AT illinois dot edu 
Tuesday 9am1pm 
3034 ECEB 
Course schedule (subject to change)  
Written Homework # Deadline 
Prairielearn Homework # Deadline  Concepts and assigned reading)[ Short videos]  Lecture Dates  Recommended Study Problems 

 
0 01/22 5:00:00pm for all HW deadlines below 
* the sum of a geometric series and power series for exp(x) * basic calculus: the chain rule for differentiation and use of logarithms 
Jan 18   
1 01/26

1 01/29 
* 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] 
Jan 20 23 25  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 02/02 
2 02/05 
* 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] 
Jan 27 30; Feb 1  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 02/09 
3 02/12 
* 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] 
Feb 3 6 8  SAQs (p. 75) for Sections 2.42.7 Problems (pp. 8184) 2.14, 2.18, 2.20, 2.22, 2.24 
4 02/16 
4 02/19 
* 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) 
Feb 10 13 (No class on Feb 15 due to unavailability of professors) (To compensate, there would be class on the date of MT 1: Feb 27) 
SAQs (pp. 7576) for Sections 2.82.10 Problems (pp. 8588) 2.26, 2.28, 2.30, 2.32, 2.34 
5 02/23 
5 02/26 
* 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) 
Feb 17 20 22  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 03/02 
6 03/05 
* 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] 
Feb 24 27; Mar 1 (There would be class on Feb 27) 
SAQs (p. 146147) for Sections 3.13.4. Problems (pp.149151) 3.2, 3.4, 3.6, 3.8, 3.10. 
7 03/09 
7 03/19 
* 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] 
Mar 3 6 8  SAQs (p 147) for Sections 3.5 & 3.6 . Problems (p. 152154) 3.12, 3.14, 3.16, 3.18, 3.20 
Spring Break  
8 03/23 
8 03/26 
* 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] 
Mar 10 20 22  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 03/30 
9 04/02 
* 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] 
Mar 24 27 29 
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 04/06 
10 04/09 
* joint CDFs (Ch 4.1) [SAQ 4.1] * joint pmfs (Ch 4.2) [SAQ 4.2] * joint pdfs (Ch 4.3) [SAQ 4.3] 
Apr 3 5 (No Class on Friday, Mar 31 due to EOH) 
SAQs (pp. 223224) for Sections 4.14.3. Problems (pp. 226228) 4.2, 4.6, 4.10. 
11 04/13 
11 04/16 
* 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] 
Apr 7 12 (No class on Monday, Apr 10 due to MT2) 
SAQs (p. 224) for Sections 4.44.7. Problems (p. 226230) 4.4, 4.8, 4.12, 4.14, 4.16. 
12 04/20 
12 04/23 
* 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) 
Apr 14 17 19  SAQs (p. 224) for Sections 4.84.9. Problems (p. 230233) 4.18, 4.20, 4.22, 4.24, 4.26, 4.28 
13 04/27 

* 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] 
Apr 21 24 26  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  Apr 28; May 1 3 
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