ECE ILLINOIS

ECE 313/MATH 362

PROBABILITY WITH ENGINEERING APPLICATIONS

Spring 2014


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 410

Exam times : See Exam information.

In an effort to serve you better, this semester we will use a new teaching format, similar to that used in ECE 310 in Spring 2013. Click on Concept Matrix, Quizzes and exams, and Grading Policies below for more information.

Office Hours Summary: Mondays 1-3, 4-6, Tuesdays 1-3, Wednesdays 11-12, 1-7, Thursdays 2-6, Fridays 1-5


Section Meeting time and place Instructor
E 9 MWF
163 Everitt Laboratory
Professor Dominguez-Garcia
e-mail: aledan AT illinois dot edu
Office Hours: Wednesdays, 3-4 pm in 170 EL, or by appointment

C 10 MWF
163 Everitt Laboratory
Professor Yi Lu
e-mail: yilu4 AT illinois dot edu
Office Hours: Wednesdays, 11 am - noon in 369 EL

D11 MWF
163 Everitt Laboratory
Professor Yihong Wu
e-mail: yihongwu AT illinois dot edu
Office Hours: Wednesdays, 1-2 pm in 369 EL

F 1 MWF
218 Mechanical Engineering
Professor Bruce Hajek
e-mail: b-hajek AT illinois dot edu
Office Hours: Wednesdays, 2-3 pm in 369 EL

Bussaba Amnueypornsakul (amnueyp1 AT illinois dot edu) Office Hours: Monday 1-3PM in EL 368, Tuesday 1-3PM in EL 368, Wednesday 3.00-7.00PM in EL 170
Xichen Jiang (xjiang4 AT illinois dot edu) Office Hours: Friday 1-5 PM in 369 EL
Ding Liu (dingliu2 AT illinois dot edu) Office Hours: Monday 4-6 PM in 168 EL, Wednesday 4-6 PM in 170 EL, Thursday 2-6 PM in 369 EL


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


Concept constellation Concept matrix
# Week Concepts (Reading)[ Short videos] Short Answer Questions
and Problems for Quizzes
1 & 2 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, SAQ1.3, PokerIntro, PokerFH2P]
*using Karnaugh maps for three sets (Ch 1.4)[Karnaughpuzzle, SAQ1.2]
*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]
SAQs (on p. 20) for Sections 1.2, 1.3, 1.4.
Problems (pp. 21-23, 77-78) 1.2, 1.4, 1.6, 1.8, 1.10, 1.12, 2.2 (skip part about variance), 2.4.
Quiz 1: 1/31
3 2/3-2/7 *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]
*binomial distribution (how it arises, mean, variance, mode) (Ch 2.4.3-2.4.4)[SAQ 2.4][bestofseven]
SAQs (pp. 73-74) for Sections 2.2, 2.3, 2.4.
Problems (pp. 77-82) 2.6, 2.12, 2.14, 2.16, 2.18, 2.20.
Quiz 2: 2/7
4 2/10 - 2/14 *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)
*Poisson distribution (how it arises, mean, variance) (Ch 2.7)
*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)[Simdoc-Minhash2]
SAQs (p. 74) for Sections 2.5-2.9.
Problems (pp. 82-84) 2.22, 2.24, 2.26, 2.28.
If appearing on a quiz, numerical answers are not required for problems SAQ 2.5.1 or 2.7, or Problems 2.26(b) or 2.28(a). As usual, you would need to indicate how to solve the problems up to the point a calculator is needed.
Quiz 3: 2/14
5 2/17-2/21 *law of total probability (Ch 2.10) [deuce] [SAQ 2.10]
*Bayes formula (Ch. 2.10)
*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)
SAQs (p. 75) for Sections 2.10, 2.11.
Problems (pp. 85-88) 2.30, 2.32, 2.34, 2.36, 2.38. (For 2.34 on quiz, you should realize the intervals overlap, even though you don't have a calculator.)
Quiz 4: 2/21
6 2/24-2/28 *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)
*cumulative distribution functions (Ch 3.1)
SAQs (p. 75, 143) for Sections 2.12, 3.1.
Problems (pp. 89-90, 145-146) 2.40, 2.42, 2.44, 3.2.
Quiz 5: 2/28
Exam 1: Monday, March 3
7 3/3-3/7 *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]
*Poisson processes (Ch 3.5) [SAQ 3.5]
*Erlang distribution (Ch 3.5.3)
SAQs (p. 143-144) for Sections 3.2-3.5.
Problems (pp.146-148) 3.4, 3.6, 3.8, 3.10, 3.12.
Quiz 6: Monday 3/10
8 3/10-3/14 *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 144) for Section 3.6.
Problems (pp. 149-150) 3.14, 3.16, 3.18.
No class Friday (EOH!)
Quiz 7: Monday 3/17
9 3/17-3/21 *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)
*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]
SAQs (pp. 144-145) for Sections 3.7-3.10.
Problems (pp. 150-155) 3.20, 3.22, 3.24, 3.26, 3.28, 3.30, 3.32, 3.36
Quiz 8: Monday 3/31
SPRING BREAK
10 3/31 - 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]
*joint pdfs of independent random variables (Ch 4.4)[SAQ 4.4]
SAQs (p. 215-216) for Sections 4.1-4.4.
Problems (p. 218-221) 4.2, 4.4, 4.6, 4.8, 4.10, 4.12.
To shorten the problems on quizzes, Parts 4.2(c), 4.4(c), 4.6(c), 4.10(e), 4.12(d) will not be included.
Quiz 9: Monday 4/7
11 & 12 4/7-4/18 *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]
SAQs (pp. 216-217) for Sections 4.5, 4.6, 4.7.
Problems (pp. 221-222) 4.14, 4.16.
NO QUIZ 4/14
Exam 2: Monday, April 14
Quiz 10: Monday 4/21
13 4/21-4/25 *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. 217) for Sections 4.8, 4.9.
Problems (p. 222-225) 4.18, 4.20, 4.22, 4.24, 4.26, 4.28.
(Problem 4.26 refers back to problem 4.24.)
Quiz 11: Monday 4/28
14 4/28-5/1 *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.217) for Sections 4.10-4.11
Problems (pp.225-230) 4.30, 4.32, 4.34, 4.36, 4.38, 4.40, 4.42
Quiz 12: Monday 5/5
15 5/5-5/7 wrap up and review

Optional Reading:



More Detailed Information

The ECE 313 FAQ

About the Concept Matrix

Homework

Previous Web Pages

Reserve Books

Quizzes and exams

Piazza

COMPASS (for grades)

Grading Policies

Powerpoint slides