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ECE 313/MATH 362
PROBABILITY WITH ENGINEERING APPLICATIONS
Fall 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 will be available on Canvas under "Assignments". Please submit your written homework on Gradescope (accessible through Canvas). Typesetting with LaTeX is allowed, however, no additional credit will be awarded to typeset homework. Written homework solutions will be made available on Canvas (under "Modules").
Text : ECE 313 Course Notes (hardcopy sold through ECE Stores, pdf file available.)
Lecture Notes: Canvas
Office Hour Schedule (Office hours start from the second week of the semester (08/28))
Recitation Friday 9-10 AM
| Hours | Monday | Tuesday | Wednesday | Thursday | Friday | |||
| 9-10 am | Xu Chen [5040 ECEB] | Hongyu Shen [5034 ECEB] | Hongyu Shen [5034 ECEB] | Hongyu Shen [5034 ECEB] | Shitao Liu - Recitation [5034 ECEB] | |||
| 10-11 am | Shitao Liu [5034 ECEB] | |||||||
| 11 am-12 pm | Amogh Pandey [5034 ECEB] | Dimitrios Katselis[3017 ECEB] | ||||||
| 12-1 pm | Amogh Pandey [5034 ECEB] | Amogh Pandey [5034 ECEB] | ||||||
| 1-2 pm | Zifei Han [5034 ECEB] | Vishal Rana [5034 ECEB] | Evan Varghese [5034 ECEB] | Melih Bastopcu [368- CSL] | Zifei Han [5034 ECEB] | Eric Chitamber [virtual] | ||
| 2-3 pm | Evan Varghese [5034 ECEB] | Vishal Rana [5034 ECEB] | Zifei Han [5034 ECEB] | |||||
| 3-4 pm | Junyeob Lim [5034 ECEB] | Junyeob Lim [5034 ECEB] | ||||||
| 4-5 pm | ||||||||
| 5-6 pm | Shitao Liu [5034 ECEB] | Amogh Pandey [5034 ECEB] | Evan Varghese [5034 ECEB] | |||||
| 6-7 pm | ||||||||
| Section | Meeting time and place | Instructor |
|---|---|---|
|
A |
2:00 PM - 3:20 PM TR 3013 ECEB |
Professor Xu Chen e-mail: xuchen1 AT illinois dot edu Office Hours: Monday 9-10 AM, 5040 ECEB |
|
B |
10:00 AM - 10:50 AM MWF 3017 ECEB |
Professor Eric Chitambar e-mail: echitamb AT illinois dot edu Office Hours: Friday 1-2 PM (virtual) |
|
C |
11:00 AM - 11:50 AM MWF 3017 ECEB |
Professor Dimitrios Katselis e-mail: katselis AT illinois dot edu Office Hours: Tuesday 11 AM-12 PM, 3017 ECEB |
|
D |
1:00 PM - 1:50 PM MWF 3017 ECEB |
Professor Lav R Varshney email: varshney AT illinois dot edu Office Hours: -, 314 Coordinated Science Lab |
|
E |
2:00 PM - 2:50 PM MWF - |
Professor Lav R Varshney email: varshney AT illinois dot edu Office Hours: -, 314 Coordinated Science Lab |
|
F |
5:00 PM - 5:50 PM MWF 3017 ECEB |
Dr. Melih Bastopcu e-mail: bastopcu AT illinois dot edu Office Hours: Wednesday 1-2 PM, 368 Coordinated Science Lab |
| Name | Office Hour Time | Office Hour Location |
| Vishal Rana vishalr AT illinois dot edu |
Tuesday 1-3 PM | 5034 ECEB |
| Thursday 2-5 PM | 5034 ECEB | |
| Amogh Pandey amoghp3 AT illinois dot edu |
Tuesday 11 AM-1 PM; 5-6 PM |
5034 ECEB |
| Thursday 12-2 PM | 5034 ECEB | |
| Evan Varghese evanjv2 AT illinois dot edu |
Wednesday 1-3 PM | 5034 ECEB |
| Thursday 5-7 PM | 5034 ECEB | |
| Hongyu Shen hongyu2 AT illinois dot edu |
Tuesday 9-11 AM | 5034 ECEB |
| Wednesday 9 AM-12 PM | 5034 ECEB | |
| Thursday 9 AM-11 AM | 5034 ECEB | |
| Junyeob Lim junyeob2 AT illinois dot edu |
Tuesday 3-5 PM | 5034 ECEB |
| Wednesday 3-5 PM | 5034 ECEB | |
| Shitao Liu sl53 AT illinois dot edu |
Monday 5-7 PM | 5034 ECEB |
| Friday 9-10 AM | 5034 ECEB Recitation | |
| Friday 10 AM-1 PM | 5034 ECEB | |
| Zifei Han zifeih2 AT illinois dot edu |
Monday 1-4 PM | 5034 ECEB |
| Friday 1-4 PM | 5034 ECEB |
| Course schedule (subject to change) | ||||
| Written Homework # Deadline |
Concepts and assigned reading [ Short videos] | Lecture Dates | Recommended Study Problems | |
|---|---|---|---|---|
| - |
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* the sum of a geometric series and power series for exp(x) * basic calculus: the chain rule for differentiation and use of logarithms |
Week of August 21 | - |
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1 9/1
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* 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 21 | 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] |
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2 9/8 |
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* 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] |
Week of August 28 | 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. |
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3 9/15 |
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* 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] |
Week of September 4 | SAQs (p. 75) for Sections 2.4-2.7 Problems (pp. 81-84) 2.14, 2.18, 2.20, 2.22, 2.24 |
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4 9/22 |
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* 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] |
Week of September 11 |
SAQs (pp. 75-76) for Sections 2.8-2.9 Problems (pp. 85-86) 2.26, 2.28, 2.30 |
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5 9/29 |
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* law of total probability (Ch 2.10) [deuce] [SAQ 2.10] * Hypothesis testing -- probability of false alarm and probability of miss (Ch. 2.11) |
Week of September 18 | 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 |
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6 10/6 |
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* 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 25 |
SAQs (p. 146-147) for Sections 3.1-3.4. Problems (pp.149-151) 3.2, 3.4, 3.6, 3.8, 3.10. |
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7 10/13 |
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* 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] |
Week of October 2 | SAQs (p 147) for Sections 3.5 & 3.6 . Problems (p. 152-154) 3.12, 3.14, 3.16, 3.18, 3.20 |
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8 10/20 |
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* 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] |
Week of October 9 | 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 |
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9 10/27 |
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* 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] |
Week of October 16 |
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 |
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10 11/3 |
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* joint CDFs (Ch 4.1) [SAQ 4.1] * joint pmfs (Ch 4.2) [SAQ 4.2] * joint pdfs (Ch 4.3) [SAQ 4.3] |
Week of October 23 |
SAQs (pp. 223-224) for Sections 4.1-4.3. Problems (pp. 226-228) 4.2, 4.6, 4.10. |
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11 11/10 |
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* 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] |
Week of October 30 |
SAQs (p. 224) for Sections 4.4-4.7. Problems (p. 226-230) 4.4, 4.8, 4.12, 4.14, 4.16. |
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12 11/17 |
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* 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) |
Week of November 6 | 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 |
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13 12/1 |
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* 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] |
Week of November 13 | 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 | Week of November 27 | ||
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