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ECE 313/MATH 362
PROBABILITY WITH ENGINEERING APPLICATIONS
Spring 2022
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.
Please e-mail the course e-mail address ece-313-spring22-group@office365.illinois.edu for all course-related correspondence.
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 for office hours (beginning second week, i.e., Jan. 24).
Location of All In-person Office Hours except Teja's tutorial session: 5034 ECEB
| Hours | Monday | Tuesday | Wednesday | Thursday | Friday |
| 9-11am | Teja Gupta | ||||
| 11am -1pm | Seiyun Shin | ||||
| 1-2pm | Vishal Rana | ||||
| 2-3pm | Teja Gupta | ||||
| 3-4pm | Jinhui Song | Jinhui Song | |||
| 4-5pm | Yuechen Wang | Seiyun Shin | |||
| 5-6pm | Teja (Tutorial Session) 3015 ECEB |
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| 6-7pm | |||||
| 8:30-9:30pm | Adarsh (Online) | Adarsh | |||
| 9:30-10:30pm | Adarsh (Online) | ||||
| Section | Meeting time and place | Instructor |
|---|---|---|
|
C |
10:00 AM - 10:50 AM MWF Week 1: Zoom 1015 ECEB (In-person starts 1/24) | Professor Xu Chen e-mail: xuchen1 AT illinois dot edu Office Hours: Thursday 10-11AM, Zoom |
|
D |
11:00 AM - 11:50 AM MWF 3017 ECEB (In-person lectures start from 2/14, live on Echo360) | Professor Naresh Shanbhag email: shanbhag AT illinois dot edu Office Hours: Monday 2-3PM Zoom |
|
F |
1:00 PM - 1:50 PM MWF 1015 ECEB (In-person lectures start from 2/21, live on Echo360) | Professor Venugopal V. Veeravalli e-mail: vvv AT illinois dot edu Office Hours: Wednesday 2-3PM, Zoom |
|
OND |
11:00 AM - 11:50 AM MWF Live streamed on Echo 360 |
Professor Naresh Shanbhag |
|
ONF |
1:00 PM - 1:50 PM MWF Live streamed on Echo 360 |
Professor Venugopal V. Veeravalli |
Echo360: Section D and F will be simulcast , and recordings will be made available here
Mediaspace: for long-term storage purpose, update once a week
| Teja Gupta tejag2 AT illinois dot edu |
Office Hours: Monday 9-11AM, Friday 2-4PM Thursday 5-7PM, 3015 ECEB (Tutorial Session) |
| Seiyun Shin seiyuns2 AT illinois dot edu |
Office Hours: Monday 11AM-1PM, Wednesday 4-6PM |
| Jinhui Song jinhuis2 AT illinois dot edu |
Office Hours: Monday 3-4PM, Thursday 3-4PM |
| Vishal Rana vishalr AT illinois dot edu |
Office Hours: Monday 1-3PM |
| Adarsh Muthuveeru-Subramaniam adarshm2 AT illinois dot edu |
Office Hours: Monday 8:30-9:30PM (Online),
Thursday 9:30-10:30PM (Online) Thursday 8:30-9:30PM (Online Tutorial Session) |
| Yuechen Wang yuechen6 AT illinois dot edu |
Office Hours: Monday 4-6PM |
| Course schedule (subject to change) | |||
| Homework # Deadline |
Lecture dates |
Concepts and assigned reading)[ Short videos] | Recommended Study Problems |
|---|---|---|---|
| - | - |
* the sum of a geometric series and power series for exp(x) * basic calculus: the chain rule for differentiation and use of logarithms |
- |
| 1 Mon, 1.31 11:59:00pm for all HW deadlines below |
1.24-1.28 | * 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] |
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 Mon, 2.7 |
1.31-2.4 | * 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] |
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 Mon, 2.14 |
2.7-2.11 | * 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] |
SAQs (p. 75) for Sections 2.4-2.7 Problems (pp. 81-84) 2.14, 2.18, 2.20, 2.22, 2.24 |
| 4 Mon, 2.21 |
2.14-2.18 | * 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] * law of total probability (Ch 2.10) [deuce] [SAQ 2.10] * Bayes formula (Ch. 2.10) |
SAQs (pp. 75-76) for Sections 2.8-2.10 Problems (pp. 85-88) 2.26, 2.28, 2.30, 2.32, 2.34 |
| 5 Fri, 2.25 |
2.21-2.25 | * 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) |
SAQs (p. 76) for Sections 2.11 & 2.12 Problems (pp. 88-93) 2.36, 2.38, 2.40, 2.42, 2.44, 2.46 |
| 6 Mon, 3.7 |
2.28-3.4 (no class on 2.28: midterm I) |
* 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] | 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 Mon, 3.21 |
3.7-3.11 |
*
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] |
SAQs (p 147) for Sections 3.5 & 3.6 . Problems (p. 152-154) 3.12, 3.14, 3.16, 3.18, 3.20 |
| 3.14-3.18 | Spring break | ||
| 8 Mon, 3.28 |
3.21-3.25 | *
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] | 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 Mon, 4.4 |
3.28-4.1 | * 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] |
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 Fri, 4.8 | 4.4-4.8
(skip EOH 4.8-4.9) |
* 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. 223-224) for Sections 4.1-4.3. Problems (pp. 226-228) 4.2, 4.6, 4.10. |
| 11 Mon, 4.18 |
4.11-4.15 (no class on 4.11: midterm II) |
* 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] |
SAQs (p. 224) for Sections 4.4-4.7. Problems (p. 226-230) 4.4, 4.8, 4.12, 4.14, 4.16. |
| 12 Mon, 4.25 |
4.18-4.22 |
* 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) |
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 Wed, 5.4 |
4.25-5.4 |
* 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] |
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 | |
Optional Reading: D. V. Sarwate, Probability with Engineering Applications, Powerpoint Slides for ECE 313 , Fall 2000
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