ECE 313 Spring 2020, University of Illinois at Urbana-Champaign

Image ECE ILLINOIS

 

ECE 313/MATH 362

PROBABILITY WITH ENGINEERING APPLICATIONS

Spring 2020

 


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 286 or Math 415

Exam times : See Exam information.

 


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

 

Lecture Notes

 


Times/locations for guided study sessions and regular office hours (beginning second week -- i.e. Jan. 27).

Hours Monday Tuesday Wednesday Thursday Friday
1-2 pm       5034 ECEB
Guided study
sessions
Reserve here.
  5034 ECEB
Guided study
sessions
Reserve here.
 
2-3 pm
3-4 pm
4-5 pm 4034 ECEB 4034 ECEB 4034 ECEB 4034 ECEB 4034 ECEB
5-6 pm          

 


 

Section Meeting time and place Instructor
C 10 MWF
3017 ECE Building
Professor Eric Chitamber
e-mail: echitamb AT illinois dot edu
Office Hours: Thursdays 4-5 pm, 4034 ECEB
D 11 MWF
3017 ECE Building
Professor Ilan Shomorony
e-mail:ilans AT illinois dot edu
Office Hours: Fridays 5-6 pm, 5034 ECEB
F 1 MWF
3017 ECE Building
Professor Zhizhen Jane Zhao
e-mail: zhizhenz AT illinois dot edu
Office Hours: Fridays 4-5 pm, 5034 ECEB

Lecture Notes

Graduate Teaching Assistants (needs to be updated)

Kelly Levick
klevick2 AT illinois dot edu
Office Hours: Fridays 4-5pm (office hour), Thursdays 2-3pm and Fridays 3-4pm (guided study)
Raimi Shah
rsshah2 AT illinois dot edu
Office Hours: Tuesdays 4-5pm (office hour), Thursdays 1-2pm (guided study)
Ningkai Wu
nwu10 AT illinois dot edu
Office Hours:
Ali Yekkehkhany
yekkehk2 AT illinois dot edu
Office Hours: Wednesdays 4-5pm (office hour), Thursdays 3-6pm (guided study)
Yichi Zhang
yichi3 AT illinois dot edu
Office Hours: Mondays 4-5pm (office hour), Fridays 1-3pm (guided study)

 

Concept constellation

 

Course schedule (subject to change)
Quiz #
Deadline
Lecture
dates
Concepts and assigned reading)[ Short videos] Homework problems (not to hand in but similar to quiz questions)
0

Mon, 1/27
- Quiz 0 covers two topics that come up later in the course:
* the sum of a geometric series and power series for exp(x)
* basic calculus: the chain rule for differentiation and use of logarithms
Quiz 0 is a practice quiz and carries no course credit.
  1/22 - 1/31 * 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 (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]
Tip for quiz 1: Make sure you can compute the numerical values of binomial coefficients. See p. 13 of the course notes.
1

Mon, 2/10
2/3-2/7 * 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.
  2/10-2/14 * 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
2

Mon, 2/24
2/17-2/21 * 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
  2/24-2/28 * 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)
* union bound and its application (Ch 2.12.1) [SAQ 2.12]
* network outage probability and distribution of capacity, and more applications of the union bound (Ch 2.12.2-2.12.4)
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
3

Mon, 3/9
3/2 - 3/6 * 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]
* exponential distribution (Ch 3.4) [SAQ 3.4]
SAQs (p. 146-147) for Sections 3.1-3.4.

Problems (pp.149-151) 3.2, 3.4, 3.6, 3.8, 3.10.
  3/9 - 3/13 * 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]
* 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]
SAQs (p 147) for Sections 3.5 & 3.6 .

Problems (p. 152-154) 3.12, 3.14, 3.16, 3.18, 3.20
  3/16-3/20 Spring vacation  
4

Mon, 3/30
3/23-3/25 (EOH is 3/27) * ML parameter estimation for continuous type random variables (Ch. 3.7) [SAQ 3.7]
* 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)
* failure rate functions (Ch 3.9) [SAQ 3.9]
* 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
  3/30-4/3
* 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.
5

Mon, 4/20
(skip 4/13)
4/6-4/17 * 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]
* 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)
SAQs (p. 224) for Sections 4.4-4.7.

Problems (p. 226-230) 4.4, 4.8, 4.12, 4.14, 4.16.
  4/20-4/24 * 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)
* minimum mean square error unconstrained estimators (Ch 4.9.2)
* minimum mean square error linear estimator (Ch 4.9.3) [SAQ 4.9]
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
6

Mon, 5/4
4/27-5/1 * 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.
- 5/4-5/6 wrap up and review  

Optional Reading:


 

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