ECE ILLINOIS

ECE 313/MATH 362

PROBABILITY WITH ENGINEERING APPLICATIONS

Fall 2015


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.

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.) Corrections to notes.


Summary of office hours times and locations (starting August 26).
  Office hours for Q&A about lectures, SAQs, problems, quizzes, exams. No concept matrix certification.
  Office hours giving priority to concept matrix certification.
Hours Monday Tuesday Wednesday Thursday Friday
1-2pm   3020 ECEB
and
3034 ECEB
3034 ECEB 3034 ECEB 3034 ECEB
2-3pm 3015 ECEB
3-4pm  
4-5pm 335 MEB  
5-6pm  
6-7pm  


Section Meeting time and place Instructor
A 9 MWF
3015 ECE Building
Professor Juan Alvarez
e-mail: alvarez AT illinois dot edu
Office Hours: Thursdays, 1-2pm, 3034 ECEB
figures and notes
B 10 MWF
3015 ECE Building
Professor Yihong Wu
e-mail: yihongwu AT illinois dot edu
Office Hours: Wednesdays, 1-3pm, 3034 ECEB
C 11 MWF
3017 ECE Building
Professor Yihong Wu
e-mail: yihongwu AT illinois dot edu
Office Hours: Wednesdays, 1-3pm, 3034 ECEB
D 1 MWF
3017 ECE Building
Dimitrios Katselis
e-mail: katselis AT illinois dot edu
Office Hours: Thursdays, 3-4pm, 3034 ECEB
E 2 MWF
3017 ECE Building
Peter Kairouz
e-mail: kairouz2 AT illinois dot edu
Office Hours: Thursdays, 2-3pm, 3034 ECEB

Graduate Teaching Assistants
Fardad Raisali
raisali2 AT illinois dot edu
Office Hours: Mondays, 2-4pm (3015 ECEB), Tuesdays, 1-4pm (3020/3034 ECEB), Tuesdays, 4-5pm (335 MEB), Fridays, 1-3pm (3034 ECEB).
Maojing Fu
mfu2 AT illinois dot edu
Office Hours: Mondays, 2-6pm (3015 ECEB), Tuesdays 4-7pm (335 MEB), Fridays, 4-5pm (3034 ECEB).
Ali Yekkehkhany
yekkehk2 AT illinois dot edu
Office Hours: Mondays, 4-6pm (3015 ECEB), Tuesdays 4-7pm (335 MEB), Fridays, 3-4pm (3034 ECEB).
Ge Yu
geyu3 AT illinois dot edu
Office Hours: Tuesdays, 2-4pm (3020/3034 ECEB), Tuesdays, 5-7pm (335 MEB).


Concept constellation

Concept matrix

Course schedule (subject to change)
Week #
Quiz date
Lecture
dates
Concepts (Reading)[ Short videos] Short Answer Questions (SAQ)
and Problems for Quizzes
1

Mon, 8/31
8/24-8/28 * 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]
2

Wed, 9/9
8/31-9/4 * 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 & 2.3

Problems (pp. 77-82) 2.2 (quiz won't ask for mean and variance), 2.4, 2.6 (quiz skips parts (d) & (e)) , 2.12, 2.14, 2.16.

NOTE: the matrix deadline this week is Wednesday, Sept 9 at 6pm.
3

Mon, 9/14
9/9-9/11

No lecture 9/7
* binomial distribution (how it arises, mean, variance, mode) (Ch 2.4.3-2.4.4) [SAQ 2.4] [bestofseven] SAQs (p. 75) for Section 2.4

Problems (pp. 83-84) 2.18, 2.20.
For problems asking for a numerical answer, on a quiz you would only need to indicate how to solve the problems up to the point a calculator is needed.
4

Mon, 9/21
9/14-9/16 * 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]
* Maximum likelihood parameter estimation (definition, how to calculate for continuous and discrete parameters) (Ch 2.8) [SAQ 2.8]
SAQs (p. 75) for Sections 2.5-2.8.

Problems (pp. 84-85) 2.22, 2.24, 2.26
5

Mon, 9/28
9/18-9/23
(one lecture to be cancelled this week)
* 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 2.9-2.10

Problems (pp. 86-88) 2.28, 2.30, 2.32, 2.34
6

Mon, 10/12
(skip 10/5)
9/25-9/30 * 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 (Ch 2.12.1) [SAQ 2.12]
* network outage probability and distribution of capacity (Ch 2.12.2-2.12.3)
* probability of undetected error for coded system (Ch 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 (For 2.38 on quiz, you should realize the intervals overlap, even though you don't have a calculator.)

Exam 1: Wednesday, October 7, 7-8.15pm
(no quiz October 5)
7

Mon, 10/12
(week 6 too)
10/2-10/7 * 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. 145-146) for Sections 3.1-3.4.

Problems (pp.148-150) 3.2, 3.4, 3.6, 3.8, 3.10.
8

Mon, 10/19
10/9-10/14 * 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 146) for Sections 3.5 & 3.6.

Problems (pp. 151-153) 3.12, 3.14, 3.16, 3.18, 3.20.
9

Mon, 10/26
10/16-10/21
(one lecture to be cancelled this week)
* 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)
SAQs (pp. 146-147) for Sections 3.7-3.8.

Problems (pp. 154-156) 3.22, 3.24, 3.26, 3.28, 3.30, 3.32.
10

Mon, 11/2
10/23-10/28 * the area rule for expectation based on CDF (Ch 3.8.3)
* failure rate functions (Ch 3.9) [SAQ 3.9]
* binary hypothesis testing for continuous type random variables (Ch 3.10) [SAQ 3.10]
* joint CDFs (Ch 4.1) [SAQ 4.1]
* joint pmfs (Ch 4.2) [SAQ 4.2]
SAQs (p. 147) for Sections 3.9-3.10
SAQs (p. 220-221) for Sections 4.1-4.2.

Problems (pp. 157-159) 3.34, 3.38.
11

Mon, 11/16
(skip 11/9)
10/30-11/4 * joint pdfs (Ch 4.3) [SAQ 4.3]
* joint pdfs of independent random variables (Ch 4.4) [SAQ 4.4]
* distribution of sums of random variables (Ch 4.5) [SAQ 4.5]
SAQs (p. 221) for Sections 4.3-4.5.

Problems (p. 223-226) 4.2, 4.4, 4.6, 4.8, 4.10.
To shorten the problems on quizzes, Parts 4.2(c), 4.4(c), 4.6(c), 4.10(e) will not be included.

Exam 2: Wednesday, November 11, 7-8.15pm
(no quiz November 9)
12

Mon, 11/16
(week 11 too)
11/6-11/11 * more problems involving joint densities (Ch 4.6) [SAQ 4.6]
* joint pdfs of functions of random variables (Ch 4.7) [SAQ 4.7]
SAQs (pp. 221-222) for Sections 4.6-4.7.

Problems (pp. 226-227) 4.12, 4.14, 4.16.
To shorten the problems on quizzes, Part 4.12(d) will not be included.
13

Mon, 11/30
11/13-11/20
(one lecture to be cancelled between 11/20-12/9)
* correlation and covariance (e.g. scaling properties) (Ch 4.8) [SAQ 4.8]
* 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. 222) for Sections 4.8-4.9.

Problems (p. 227-230) 4.18, 4.20, 4.22, 4.24, 4.26, 4.28.
11/23-11/27 Thanksgiving vacation
14

Mon, 12/7
or
Wed, 12/9
11/30-12/4
(one lecture to be cancelled between 11/20-12/9)
* 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]
SAQs (p.222) for Sections 4.10-4.11

Problems (pp.230-235) 4.30, 4.32, 4.34, 4.36, 4.38, 4.40, 4.42.
15 12/7-12/9
(one lecture to be cancelled between 11/20-12/9)
wrap up and review

Optional Reading:



More Detailed Information

The ECE 313 FAQ

About the Concept Matrix

Homework

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