ECE 313/MATH 362
PROBABILITY WITH ENGINEERING APPLICATIONS
Spring 2024
ECE 313 (also crosslisted 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: Selfenrollment code for Campuswire is 2941.
Text : ECE 313 Course Notes (hardcopy sold through ECE Stores, pdf file available.)
Recitation: Tuesday 12 pm [Vishal Rana 4036 ECEB]; Thursday 1112 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 am10 am  Mosbah Aouad [4036 ECEB]  Shitao Liu [4034 ECEB]  
10 am11 am  
11 am12 pm  Olgica Milenkovic [311 CSL]  Shitao Liu [4034 ECEB] Recitation  
12 pm1 pm 
Shitao Liu [4034 ECEB] Melih Bastopcu [368 CSL] 
Junyeob Lim [4034 ECEB]  
1 pm2 pm  Vishal Rana [4036 ECEB] Recitation  
2 pm3 pm  Naresh R Shanbhag [414 CSL]  Vishal Rana [4036 ECEB]  Vishal Rana [4034 ECEB]  
3 pm4 pm  Zifei Han [4034 ECEB]  Junyeob Lim [4036 ECEB]  Dimitrios K. [3013 ECEB] (3:204:20 pm)  Junyeob Lim [4034 ECEB]  Zifei Han [4034 ECEB]  
4 pm5 pm  
5 pm6 pm  Evan Varghese [4036 ECEB]  Mosbah Aouad [4034 ECEB]  Evan Varghese [4034 ECEB]  Shitao Liu [4034 ECEB]  
6 pm7 pm  Evan Varghese [4034 ECEB] 
Section  Meeting time and place  Instructor 

A 
10:00 AM  10:50 AM MWF 1015 ECEB 
Professor Olgica Milenkovic email: milenkov AT illinois dot edu Office Hours: Monday 11 AM12 PM, 311 CSL 
B 
11:00 AM  11:50 AM MWF 3017 ECEB 
Professor Dimitrios Katselis email: 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 email: bastopcu AT illinois dot edu Office Hours: Wednesday, 121 PM 368 CSL 
Name  Office Hour Time  Office Hour Location 
Vishal Rana vishalr AT illinois dot edu 
Tuesday 12 PM  4036 ECEB Recitation 
Tuesday 23 PM  4036 ECEB  
Thursday 25 PM  4034 ECEB  
Evan Varghese evanjv2 AT illinois dot edu 
Monday 67 PM  4034 ECEB 
Tuesday 57 PM  4036 ECEB  
Thursday 57 PM  4034 ECEB  
Junyeob Lim junyeob2 AT illinois dot edu 
Tuesday 35 PM  4036 ECEB 
Wednesday 35 PM  4034 ECEB  
Friday 12 PM  4034 ECEB  
Mosbah Aouad maouad2 AT illinois dot edu 
Tuesday 9 AM12 PM  4036 ECEB 
Wednesday 57 PM  4034 ECEB  
Shitao Liu sl53 AT illinois dot edu 
Wednesday 12 PM1 PM  4034 ECEB 
Thursday 11 AM12 PM  4034 ECEB Recitation  
Friday 9 AM10 AM  4034 ECEB  
Friday 5 PM6 PM  4034 ECEB  
Zifei Han zifeih2 AT illinois dot edu 
Monday 36 PM  4034 ECEB 
Friday 35 PM  4034 ECEB 
Course schedule (subject to change)  
Written Homework # Deadline 
Concepts and assigned reading [ Short videos]  Lecture Dates  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 
Week of January 15   
1 1/26


* 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 1.31.4) [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. 2124) 1.2, 1.4, 1.6, 1.8, 1.10, 1.12. Optional: [SAQ 1.5] 
2 2/2 

* 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 2.4.12.4.2) [SimdocIntro] [SimdocMinhash1] 
Week of January 22  SAQs (pp. 7475) for Sections 2.22.4 Problems (pp. 7782) 2.2, 2.4, 2.6, 2.8, 2.10, 2.12, 2.16. 
3 2/9 

* binomial distribution (how it arises, mean, variance, mode) (Ch 2.4.32.4.4) [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 2.42.7 Problems (pp. 8184) 2.14, 2.18, 2.20, 2.22, 2.24 
4 2/16 

* 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,SimdocMinhash2] 
Week of February 5 
SAQs (pp. 7576) for Sections 2.82.9 Problems (pp. 8586) 2.26, 2.28, 2.30 
5 2/23 

* 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. 8693) 2.32, 2.34, 2.36, 2.38, 2.40, 2.42, 2.44, 2.46 
6 3/1 

* 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. 146147) for Sections 3.13.4. Problems (pp.149151) 3.2, 3.4, 3.6, 3.8, 3.10. 
7 3/8 

* 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. 152154) 3.12, 3.14, 3.16, 3.18, 3.20 
8 3/22 

* 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. 147148) for Sections 3.73.10. Problems (pp. 154159) 3.22, 3.24, 3.26, 3.28, 3.30, 3.32, 3.34, 3.38 
9 3/29 

* 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. 147148) for Sections 3.73.10. Problems (pp. 154159) 3.22, 3.24, 3.26, 3.28, 3.30, 3.32, 3.34, 3.38 
10 4/5 

* 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. 223224) for Sections 4.14.3. Problems (pp. 226228) 4.2, 4.6, 4.10. 
11 4/12 

* 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 4.44.7. Problems (p. 226230) 4.4, 4.8, 4.12, 4.14, 4.16. 
12 4/19 

* 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 4.84.9. Problems (p. 230233) 4.18, 4.20, 4.22, 4.24, 4.26, 4.28 
13 4/26 

* 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 4.104.11 Problems (pp.233237) 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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