ECE 313/MATH 362

PROBABILITY WITH ENGINEERING APPLICATIONS

Fall 2024

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.

Communication : Please email ece-313-fall24-group@office365.illinois.edu instead of contacting instructors or TAs directly.

Prerequisite : Math 257 or Math 416

Exam times : See Exam information.

Homeworks : Homework assignments and solutions will be posted here. Please submit your written homework on Gradescope (enrollment code 2B2Y8R). Typesetting with LaTeX is allowed, however, no additional credit will be awarded to typeset homework.

Campuswire: Self-enrollment code for Campuswire is 0479.

Text : ECE 313 Course Notes (hardcopy sold through ECE Stores, pdf file available.)(alt link)

Lecture Notes : Section B

Office Hour Schedule (TA Office hours start from the second week of the semester)

Hours	Monday	Tuesday	Wednesday		Thursday		Friday
9 am-10 am			Adarsh [4034 ECEB]
10 am-11 am					Jonah [3001 ECEB]	Vishal [2034 ECEB]
11 am-12 pm			Zifei [4034 ECEB]	Dimitris [1015 ECEB] (11:20 am- 11:50 am)			Dimitris [1015 ECEB] (11:20 am- 11:50 am)
12 pm-1 pm					Jonah [3001 ECEB]	Junyeob [2034 ECEB]
1 pm-2 pm			Xu [5040 ECEB]			Vishal [2034 ECEB]
2 pm-3 pm	Aris [2036 ECEB]		Junyeob [4034 ECEB]		Shitao [3001 ECEB]
3 pm-4 pm	Evan [4036 ECEB]	Venu [Zoom] (3:30-4:30 pm)	Evan [4034 ECEB]		Adarsh [3001 ECEB]	Junyeob [2034 ECEB]
4 pm-5 pm			Evan [4034 ECEB]	Junyeob [3003 ECEB]	Zifei [3001 ECEB]
5 pm-6 pm			Shitao [4034 ECEB]
6 pm-7 pm
7 pm-8 pm

Meeting Details

Section	Meeting time and place	Instructor
A	2:00 PM - 3:15 PM TR 3013 ECEB	Professor Venugopal V. Veeravalli e-mail: vvv AT illinois dot edu Office Hours: Tuesday 3:30 PM - 4:30 PM, Zoom
B	10:00 AM - 10:50 AM MWF 3017 ECEB	Dr. Aristomenis Tsopelakos e-mail: tsopela2 AT illinois dot edu Office Hours: Monday 2:00 - 3:00 PM, 2036 ECEB
C	11:00 AM - 11:50 AM MWF 3017 ECEB	Professor Xu Chen email: xuchen1 AT illinois dot edu Office Hours: Wednesday 1:00 - 2:00 PM, 5040 ECEB
D	1:00 PM - 1:50 PM MWF 3017 ECEB	Professor Dimitrios Katselis e-mail: katselis AT illinois dot edu Office Hours: Wednesday, Friday, 11:20 AM - 11:50 AM, 1015 ECEB

Graduate Teaching Assistants

Name	Office Hour Time	Office Hour Location
Shitao Liu sl53 AT illinois dot edu	Thursday 2-3 PM	3001 ECEB
Shitao Liu sl53 AT illinois dot edu	Wednesday 5-8 PM	4034 ECEB
Adarsh Muthuveeru-Subramaniam adarshm2 AT illinois dot edu	Wednesday 9-10 AM	4034 ECEB
Adarsh Muthuveeru-Subramaniam adarshm2 AT illinois dot edu	Thursday 3-4 PM	3001 ECEB
Evan Varghese evanjv2 AT illinois dot edu	Monday 3-5 PM	4036 ECEB
Evan Varghese evanjv2 AT illinois dot edu	Wednesday 3-5 PM	4034 ECEB
Jonah Jesus Cadena-Perena jonahjc2 AT illinois dot edu	Thursday 10 AM-2 PM	3001 ECEB
Junyeob Lim junyeob2 AT illinois dot edu	Wednesday 2-3 PM	4034 ECEB
	Wednesday 4-5 PM	3003 ECEB
	Thursday 12-1 PM	2034 ECEB
	Thursday 3-4 PM	2034 ECEB
Vishal Rana vishalr AT illinois dot edu	Thursday 10 AM-12 PM	2034 ECEB
Vishal Rana vishalr AT illinois dot edu	Thursday 1 PM-3 PM	2034 ECEB
Zifei Han zifeih2 AT illinois dot edu	Wednesday 11 AM-1 PM	4034 ECEB
Zifei Han zifeih2 AT illinois dot edu	Thursday 4-6 PM	3001 ECEB

Concept constellation

Written Homework # Deadline	Concepts and assigned reading [ Short videos]	Lecture Dates	Recommended Study Problems
Course schedule (subject to change)
-	* the sum of a geometric series and power series for exp(x) * basic calculus: the chain rule for differentiation and use of logarithms	-	-
1 9/5 6:00:00pm for all HW deadlines below	* 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]	Week of August 26	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 9/12	* 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]	Week of September 2	SAQs (pp. 74-75) for Sections 2.2-2.3 Problems (pp. 77-82) 2.2, 2.4, 2.6, 2.8, 2.10, 2.12, 2.16.
3 9/19	* law of total probability (Ch 2.10) [deuce] [SAQ 2.10] * Bayes formula (Ch. 2.10) * independence of events and random variables (Ch 2.4.1-2.4.2) [SimdocIntro] [Simdoc-Minhash1] * binomial distribution (how it arises, mean, variance, mode) (Ch 2.4.3-2.4.4) [SAQ 2.4] [bestofseven]	Week of September 9	SAQs (p. 75-76) for Sections 2.4, 2.10 Problems (pp. 81-84, 86-87) 2.14, 2.18, 2.20, 2.22, 2.24, 2.32, 2.34.
4 9/26	* 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] * Markov and Chebychev inequalities (Ch 2.9)	Week of September 16	SAQs (pp. 75) for Section 2.5-2.7, 2.9 Problems (pp. 86) 2.30a-b
5 10/3	* confidence intervals (definitions, meaning of confidence level) (Ch 2.9) [SAQ 2.9,Simdoc-Minhash2] * 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)	Week of September 23	SAQs (p. 75-76) for Sections 2.9, 2.11 & 2.12 Problems (pp. 85, 88-93) 2.28, 2.36, 2.38, 2.40, 2.42, 2.44, 2.46
6 10/10	* 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 30	SAQs (p. 146) for Sections 3.1-3.3. Problems (pp.149-151) 3.2, 3.4, 3.6, 3.8, 3.10.
7 10/17	* 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)	Week of October 7	SAQs (p 147) for Sections 3.4-3.5 & 3.6 . Problems (p. 151-152) 3.10, 3.12, 3.14
8 10/24	* 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] * the distribution of a function of a random variable (Ch 3.8.1) [SAQ 3.8]	Week of October 14	SAQs (pp. 147) for Sections 3.6, 3.8 Problems (pp. 152-159) 3.16, 3.18, 3.20, 3.26, 3.28, 3.30, 3.32, 3.34a, 3.38a-b,d
9 10/31	* 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] * joint CDFs (Ch 4.1) [SAQ 4.1]	Week of October 21	SAQs (pp. 147-148, 223) for Sections 3.8, 3.10, 4.1 Problems (pp. 154-159, 226) 3.22, 3.24, 3.26, 3.28, 3.30, 3.32, 3.34a, 3.38a-b,d, 4.2
10 11/7	* joint pmfs (Ch 4.2) [SAQ 4.2] * joint pdfs (Ch 4.3) [SAQ 4.3] * joint pdfs of independent random variables (Ch 4.4) [SAQ 4.4]	Week of October 28	SAQs (pp. 223-224) for Sections 4.2-4.4. Problems (pp. 226-229) 4.4, 4.6, 4.8, 4.10, 4.12.
11 11/14	* 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)	Week of November 4	SAQs (p. 224) for Sections 4.5-4.7. Problems (p. 229-230) 4.14, 4.16.
12 11/21	* 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 11	SAQs (p. 224) for Sections 4.7-4.8 Problems (p. 230-231) 4.18, 4.20, 4.22
13 12/5	* minimum mean square error unconstrained estimators (Ch 4.9.2) * minimum mean square error linear estimator (Ch 4.9.3) [SAQ 4.9]	Week of November 18	SAQs (pp.225) for Sections 4.9 Problems (pp. 231-233) 4.24, 4.26, 4.28
Fall Break
14 --	* 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 December 2	SAQs (pp.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	Week of December 9

More Information

Meeting Details

Graduate Teaching Assistants

Concept constellation

Grading Policies

Written Homework

Exams

Gradescope

Campuswire

Previous Web Pages

Previous Exams

The ECE 313 FAQ

Reserve Books

Syllabus