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ECE 313/MATH 362
PROBABILITY WITH ENGINEERING APPLICATIONS
Spring 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.
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. Typesetting with LaTeX is allowed, however, no additional credit will be awarded to typeset homework.
Campuswire: Self-enrollment code for Campuswire is 2941.
Text : ECE 313 Course Notes (hardcopy sold through ECE Stores, pdf file available.)
Recitation: Tuesday 1-2 pm [Vishal Rana 4036 ECEB]; Thursday 11-12 pm [Shitao Liu 4034 ECEB]
Office Hour Schedule (Office hours start from the second week of the semester (01/22))
| Hours | Monday | Tuesday | Wednesday | Thursday | Friday | |||
| 9 am-10 am | Mosbah Aouad [4036 ECEB] | Shitao Liu [4034 ECEB] | ||||||
| 10 am-11 am | ||||||||
| 11 am-12 pm | Olgica Milenkovic [311 CSL] | Shitao Liu [4034 ECEB] Recitation | ||||||
| 12 pm-1 pm |
Shitao Liu [4034 ECEB] Melih Bastopcu [368 CSL] |
Junyeob Lim [4034 ECEB] | ||||||
| 1 pm-2 pm | Vishal Rana [4036 ECEB] Recitation | |||||||
| 2 pm-3 pm | Naresh R Shanbhag [414 CSL] | Vishal Rana [4036 ECEB] | Vishal Rana [4034 ECEB] | |||||
| 3 pm-4 pm | Zifei Han [4034 ECEB] | Junyeob Lim [4036 ECEB] | Dimitrios K. [3013 ECEB] (3:20-4:20 pm) | Junyeob Lim [4034 ECEB] | Zifei Han [4034 ECEB] | |||
| 4 pm-5 pm | ||||||||
| 5 pm-6 pm | Evan Varghese [4036 ECEB] | Mosbah Aouad [4034 ECEB] | Evan Varghese [4034 ECEB] | Shitao Liu [4034 ECEB] | ||||
| 6 pm-7 pm | Evan Varghese [4034 ECEB] | |||||||
| Section | Meeting time and place | Instructor |
|---|---|---|
|
A |
10:00 AM - 10:50 AM MWF 1015 ECEB |
Professor Olgica Milenkovic e-mail: milenkov AT illinois dot edu Office Hours: Monday 11 AM-12 PM, 311 CSL |
|
B |
11:00 AM - 11:50 AM MWF 3017 ECEB |
Professor Dimitrios Katselis e-mail: katselis AT illinois dot edu Office Hours: Tuesday 3:20 - 4:20 PM, 3013 ECEB |
|
C |
1:00 PM - 1:50 PM MWF 1013 ECEB |
Professor Naresh R Shanbhag email: shanbhag AT illinois dot edu Office Hours: Monday 2 - 3 PM, 414 CSL |
|
D |
2:00 PM - 2:50 PM MWF 3013 ECEB |
Dr. Melih Bastopcu e-mail: bastopcu AT illinois dot edu Office Hours: Wednesday, 12-1 PM 368 CSL |
| Name | Office Hour Time | Office Hour Location |
| Vishal Rana vishalr AT illinois dot edu |
Tuesday 1-2 PM | 4036 ECEB Recitation |
| Tuesday 2-3 PM | 4036 ECEB | |
| Thursday 2-5 PM | 4034 ECEB | |
| Evan Varghese evanjv2 AT illinois dot edu |
Monday 6-7 PM | 4034 ECEB |
| Tuesday 5-7 PM | 4036 ECEB | |
| Thursday 5-7 PM | 4034 ECEB | |
| Junyeob Lim junyeob2 AT illinois dot edu |
Tuesday 3-5 PM | 4036 ECEB |
| Wednesday 3-5 PM | 4034 ECEB | |
| Friday 1-2 PM | 4034 ECEB | |
| Mosbah Aouad maouad2 AT illinois dot edu |
Tuesday 9 AM-12 PM | 4036 ECEB |
| Wednesday 5-7 PM | 4034 ECEB | |
| Shitao Liu sl53 AT illinois dot edu |
Wednesday 12 PM-1 PM | 4034 ECEB |
| Thursday 11 AM-12 PM | 4034 ECEB Recitation | |
| Friday 9 AM-10 AM | 4034 ECEB | |
| Friday 5 PM-6 PM | 4034 ECEB | |
| Zifei Han zifeih2 AT illinois dot edu |
Monday 3-6 PM | 4034 ECEB |
| Friday 3-5 PM | 4034 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 January 15 | - |
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1 1/26
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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 January 15 | 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 2/2 |
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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 January 22 | 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 2/9 |
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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 January 29 | 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 2/16 |
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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 February 5 |
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 2/23 |
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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 February 12 | 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 3/1 |
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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 February 19 |
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 3/8 |
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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 February 26 | 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 3/22 |
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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 March 4 | 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 3/29 |
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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 March 18 |
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 4/5 |
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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 March 25 |
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 4/12 |
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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 April 1 |
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 4/19 |
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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 April 8 | 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 4/26 |
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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] |
Weeks of April 15 and 22 | 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 April 29 | ||
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