ECE ILLINOIS

ECE 313/MATH 362

PROBABILITY WITH ENGINEERING APPLICATIONS

Spring 2016


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 January 25).
  Office hours with priority for Q&A about lectures, SAQs, problems, quizzes, exams.
  Office hours with priority to concept matrix certification.
Hours Monday Tuesday Wednesday Thursday Friday
10-11am 3034 ECEB        
11am-1pm  
1-2pm 3020 ECEB 4034 ECEB 4034 ECEB
2-3pm 3013 ECEB 3034 ECEB
3-4pm 3034 ECEB
4-5pm 3017 ECEB
except*:
Feb. 16
March 15
April 19
  4034 ECEB
5-6pm    
6-7pm  
* These dates, office hours in this slot will be in rooms 4070 and 3020.


Section Meeting time and place Instructor
E 9 MWF
3015 ECE Building
Professor Naresh Shanbhag
e-mail: shanbhag illinois dot edu
Office Hours: Mondays 10-11am, ECEB 3034.
C 10 MWF
3017 ECE Building
Professor Bruce Hajek
e-mail: b-hajek AT illinois dot edu
Office Hours: Fridays 1-2pm, ECEB 4034.
D 11 MWF
3017 ECE Building
Professor Juan Alvarez
e-mail: alvarez AT illinois dot edu
Office Hours: Thursdays, 2-3pm, ECEB 3034.
figures and notes
F 1 MWF
3017 ECE Building
Professor Pramod Viswanath
e-mail: pramodv AT illinois dot edu
Office Hours: Fridays, 2-3pm, ECEB 4034.
B 2 MWF
3015 ECE Building
Professor Yi Lu
e-mail: yilu4 AT illinois dot edu
Office Hours: Fridays, 3-4pm, ECEB 4034.

Graduate Teaching Assistants
Maojing Fu
mfu2 AT illinois dot edu
Office Hours: M 4-5pm, T 3-7pm, Th 3-5pm.
Ali Yekkehkhany
yekkehk2 AT illinois dot edu
Office Hours: M 2-4pm, T 1-4pm, W 1-4pm.
Cheng Chen
cchen130 AT illinois dot edu
Office Hours: M 2-3pm, T 2-5pm.
Fardad Raisali
raisali2 AT illinois dot edu
Office Hours: M 3-6pm, T 1-3pm and 4-7pm.
Weihao Gao
wgao9 AT illinois dot edu
Office Hours: M 5-6pm, T 5-7pm, F 4-5pm.


Concept constellation

Concept matrix

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

Mon, 2/1
1/20-1/29 * 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

Mon, 2/7
2/1-2/5 * 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.
3

Mon, 2/15
2/8-2/12 * 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 Section 2.4-2.7.

Problems (pp. 83-85) 2.18, 2.20, 2.22, 2.24.
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, 2/22
2/15-2/19 * 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, 2/29
2/22-2/26 * 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 (For 2.38 on quiz, you should realize the intervals overlap, even though you don't have a calculator.)

Exam 1: Wednesday, March 2, 7-8.15pm
6

Mon, 3/7
2/29-3/4 * 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.
7

Mon, 3/14
No Lecture 3/11, EOH
3/7-3/9 * 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]
SAQs (p 146) for Sections 3.5 & 3.6 (#1-3).

Problems (pp. 151-152) 3.12, 3.14, 3.16.
8

Mon, 3/28
3/14-3/18 * 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]
* 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. 146-147) for Sections 3.6 (#4)-3.10.

Problems (pp. 152-156) 3.18, 3.20, 3.22, 3.24, 3.26, 3.28, 3.30, 3.32, 3.34, 3.38.
3/21-3/25 Spring vacation
9

Mon, 4/4
3/28-4/1
* 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. 220-221) for Sections 4.1-4.3.

Problems (pp. 155-156) 4.2, 4.4, 4.6.
To shorten the problems on quizzes, Parts 4.2(c), 4.4(c), 4.6(c) will not be included.
10

Mon, 4/18
(skip 4/11)
4/4-4/15 * 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 will not be tested for concept certification nor in the exams)
SAQs (p. 221) for Sections 4.4-4.6 (not 4.7).

Problems (p. 223-227) 4.8, 4.10, 4.12, 4.14, 4.16.
To shorten the problems on quizzes, Parts 4.10(e), and 4.12(d) will not be included.

Exam 2: Wednesday, April 13, 7-8.15pm
(no quiz April 11, no matrix certification deadline this week)
11

Mon, 4/25
4/18-4/22 * 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. 222) for Sections 4.8-4.9.

Problems (p. 227-230) 4.18, 4.20, 4.22, 4.24, 4.26, 4.28.
12

Mon, 5/2
4/25-4/29 * 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.
- 5/2-5/4 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