ECE 313 Spring 2023, University of Illinois at Urbana-Champaign

ECE 313/MATH 362

PROBABILITY WITH ENGINEERING APPLICATIONS

Spring 2023

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.

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: ece-313-spring23-group@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 ece-313-spring23-group@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
9-10am		Vishal Rana [3034 ECEB]			Jinyao Yang [5034 ECEB]
10-11am					Jinyao Yang [5034 ECEB]
11am-12pm					Kayvon Amir Mazooji [5034 ECEB]
12-1pm			Teja Gupta [5034 ECEB]
1-2pm		Kayvon Amir Mazooji [3036 ECEB]
2-3pm	Adi Pasic [5034 ECEB]		Prof. Ilan Shomorony [313 CSL]		Teja Gupta [5034 ECEB]	Prof. Minh N Do [113 CSL]
3-4pm	Prof. Xu Chen [5040 ECEB]	Junyeob Lim [5034 ECEB]	Teja Gupta [4034 ECEB]		Adi Pasic [5034 ECEB]
4-5pm	Jinyao Yang [5034 ECEB]	Junyeob Lim [5034 ECEB]	Teja Gupta [4034 ECEB]
5-6pm	Jinyao Yang [5034 ECEB]		Adi Pasic [5034 ECEB]
6-7pm	Adi Pasic (Recitation Session) [3020 ECEB]		Adi Pasic [5034 ECEB]	Junyeob Lim [Zoom]

Meeting Details

Section	Meeting time and place	Instructor
C	10:00 AM - 10:50 AM MWF 1015 ECEB	Professor Ilan Shomorony e-mail: ilans AT illinois dot edu Office Hours: Wednesday 2-3PM, 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 2-3PM, 113 Coordinated Science Lab
F	1:00 PM - 1:50 PM MWF 1013 ECEB	Professor Xu Chen e-mail: xuchen1 AT illinois dot edu Office Hours: Monday 3-4PM, 5040 ECEB

Graduate Teaching Assistants

Name	Office Hour Time	Office Hour Location
Kayvon Amir Mazooji mazooji2 AT illinois dot edu	Tuesday 1-2 pm	3036 ECEB
Kayvon Amir Mazooji mazooji2 AT illinois dot edu	Thursday 11am-2pm	5034 ECEB
Teja Gupta tejag2 AT illinois dot edu	Wednesday 12-1pm; Thursday 2-3pm	5034 ECEB
Teja Gupta tejag2 AT illinois dot edu	Wednesday 3-5pm	4034 ECEB
Adi Pasic pasic2 AT illinois dot edu	Office Hours: Monday 2-3pm; Wednesday 5-7pm; Thursday 3-4pm	5034 ECEB
Adi Pasic pasic2 AT illinois dot edu	Recitation Session: Monday 6-7pm	3020 ECEB
Jinyao Yang jinyaoy2 AT illinois dot edu	Monday 4-6pm; Thursday 9-11am	5034 ECEB
Junyeob Lim junyeob AT illinois dot edu	Tuesday 3-5pm	5034 ECEB
Junyeob Lim junyeob AT illinois dot edu	Wednesday 6-7pm	Online (Zoom Link)
Vishal Rana vishalr AT illinois dot edu	Tuesday 9am-1pm	3034 ECEB

Concept constellation

Written Homework # Deadline	Prairielearn Homework # Deadline	Concepts and assigned reading)[ Short videos]	Lecture Dates	Recommended Study Problems
Course schedule (subject to change)
-	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 5:00:00pm for all HW deadlines below	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 1.3-1.4) [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. 21-24) 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 2.4.1-2.4.2) [SimdocIntro] [Simdoc-Minhash1]	Jan 27 30; Feb 1	SAQs (pp. 74-75) for Sections 2.2-2.4 Problems (pp. 77-82) 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 2.4.3-2.4.4) [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]	Feb 3 6 8	SAQs (p. 75) for Sections 2.4-2.7 Problems (pp. 81-84) 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,Simdoc-Minhash2]	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. 75-76) for Sections 2.8-2.9 Problems (pp. 85-86) 2.26, 2.28, 2.30
5 02/23	5 02/26	* law of total probability (Ch 2.10) [deuce] [SAQ 2.10] * Bayes formula (Ch. 2.10) * 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 2.10, 2.11 & 2.12 Problems (pp. 86-93) 2.32, 2.34, 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. 146-147) for Sections 3.1-3.4. Problems (pp.149-151) 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. 152-154) 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. 147-148) for Sections 3.7-3.10. Problems (pp. 154-159) 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. 147-148) for Sections 3.7-3.10. Problems (pp. 154-159) 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. 223-224) for Sections 4.1-4.3. Problems (pp. 226-228) 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 4.4-4.7. Problems (p. 226-230) 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 4.8-4.9. Problems (p. 230-233) 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 4.10-4.11 Problems (pp.233-237) 4.30, 4.32, 4.34, 4.36, 4.38, 4.40, 4.42.
-		wrap up and review	Apr 28; May 1 3

More Information

Grading Policies	Written Homework	Exams
Gradescope	Canvas	Previous Web Pages Previous Exams
The ECE 313 FAQ	Reserve Books	Syllabus
Prairielearn Homework	Campuswire