ECE 313/MATH 362

PROBABILITY WITH ENGINEERING APPLICATIONS

Fall 2019 - Sections A,C, D, and E

Section	Meeting time and place	Instructor
A	9 MWF 3081 ECE Building	Dr. Donghwan Lee e-mail: donghwan AT illinois dot edu Office Hours: Thursdays 2-3 pm, 5034 ECEB
C	11 MWF 3017 ECE Building	Professor Idoia Ochoa e-mail:idoia AT illinois dot edu Office Hours: Wednesdays 4-5 pm, 4034 ECEB
D	1 MWF 3017 ECE Building	Professor Dimitrios Katselis e-mail: katselis AT illinois dot edu Office Hours: Mondays 4-5 pm, 4034 ECEB
E	2 MWF 3017 ECE Building	Professor Minh Do e-mail: minh do AT illinois dot edu Office Hours: Fridays 3-4 pm, 5034 ECEB

Graduate Teaching Assistants

Anu Gamarallage gamaral2 AT illinois dot edu	Office Hours: Thursdays 1pm (guided study) Fridays 4-5pm (regular) and 5-6pm (guided study)
Liming Wang lwang114 AT illinois dot edu	Office Hours: Fridays 4-5pm (guided study)
Ningkai Wu nwu10 AT illinois dot edu	Office Hours:
Ali Yekkehkhany yekkehk2 AT illinois dot edu	Office Hours: Fridays 1-3pm (guided study)
Mona Zehni mzehni2 AT illinois dot edu	Office Hours: Tuesdays 4-5pm (regular)
Yichi Zhang yichi3 AT illinois dot edu	Office Hours: Thursdays 4-6pm (guided study)
Zeyu Zhou zzhou51 AT illinois dot edu	Office Hours: Thursdays 3-4pm (guided study) and 4-5pm (regular)

Concept constellation

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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 Tue, 9/3	-	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 Mon, 9/9	8/26-9/6	* 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.
2 Mon, 9/16	9/9-9/13	* 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, 9/23	9/16-9/20	* 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, 9/30	9/23-9/27	* 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 Mon, 10/7	9/30-10/4	* 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
6 Mon, 10/14	10/7-10/11	* 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.
7 Mon, 10/21	10/14-10/18	* 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
8 Mon, 10/28	10/21-10/25	* 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
9 Mon, 11/4	10/28-11/1	* 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.
10 Mon, 11/18 (skip 11/11)	11/4-11/15	* 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.
11 Tue, 12/3	11/18-11/22	* 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
	11/25-11/29	Thanksgiving vacation
12 Mon, 12/9	12/2-12/6	* 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.
-	12/10-12/12	wrap up and review

Optional Reading:

• D. V. Sarwate, Probability with Engineering Applications, Powerpoint Slides for ECE 313, Fall 2000