ECE ILLINOIS

ECE 313/MATH 362

PROBABILITY WITH ENGINEERING APPLICATIONS

Summer 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, from June 13 to August 4.
  Office hours giving priority to Q&A about lectures and homework (i.e. problems on quizzes).
  Office hours giving priority to concept matrix certification.
Hours Monday Tuesday Wednesday Thursday Friday
1-1.30pm   3034 ECEB     3034 ECEB
1.30-2pm 3034 ECEB 3034 ECEB
2-2.30pm
2.30-3pm    
3-4pm 3034 ECEB
4-5pm


Section Meeting time and place Instructor
X 10 MTWRF
3017 ECE Building
Professor Juan Alvarez
e-mail: alvarez AT illinois dot edu
Office Hours: Mondays and Thursdays, 1.30-2.30pm, 3034 ECEB.
figures and notes

Graduate Teaching Assistants
Ali Yekkehkhany (yekkehk2 AT illinois dot edu) Office Hours: Tuesday 1-4pm (3034 ECEB),
Wednesday 3-5pm (3034 ECEB),
Friday 1-4pm (3034 ECEB).


Concept constellation
Concept matrix
Quiz # Quiz date
(tentative)
Concepts (Notes sections)[Short videos] Short Answer Questions (SAQ)
and Problems for Quizzes
1 Tuesday,
June 21
* 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 (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 Friday,
June 24
* 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]
* 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)) , 2.10 (quiz skips part (c)), 2.12.
3 Tuesday,
June 28
* 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 (p. 75) for Section 2.4.
* Problems (pp. 83-84 ) 2.14, 2.16, 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 Friday, July 1 * 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][hypergeometric]
- Skip Section 2.9.
* SAQs (p. 75) for Sections 2.5-2.8.
* Problems (pp. 85-86) 2.22, 2.24, 2.26.
5 Friday,
July 8
* 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)
* union bound (Ch 2.12.1) [SAQ 2.12]
* network outage probability and distribution of capacity (Ch 2.12.2-2.12.3)
- Skip Subsection 2.12.4.
* SAQs (p. 76) for Sections 2.10-2.12
* Problems (pp. 87-93) 2.32, 2.34, 2.36, 2.40, 2.42, 2.44, 2.46

Exam 1: Thursday, July 7, 8.45-10pm, 1013 ECEB.
6 Tuesday,
July 12
* 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]
* SAQs (p. 145-146) for Sections 3.1-3.3.
* Problems (pp.148-150) 3.2, 3.4, 3.6, 3.8.
7 Friday,
July 15
* exponential distribution (Ch 3.4) [SAQ 3.4]
* Poisson processes (Ch 3.5) [SAQ 3.5]
* SAQs (p 144) for Sections 3.4-3.5
* Problems (pp. 150-153) 3.10, 3.12, 3.14.
8 Tuesday,
July 19
* 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]
* ML parameter estimation for continuous type random variables (Ch. 3.7)[SAQ 3.7]
- Skip Sections 3.8 temporarliy and section 3.9 completely.
* binary hypothesis testing for continuous type random variables (Ch 3.10) [SAQ 3.10]
* SAQs (pp. 146-147) for Sections 3.6, 3.7 and 3.10
* Problems (pp. 154-156) 3.16, 3.18c, 3.20, 3.22, 3.24.
9 Friday,
July 22
* 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)
- Skip Sections 3.8.3 and 3.9
* joint CDFs (Ch 4.1)[SAQ 4.1]
* SAQs (p. 147) for Section 3.8.
* SAQs (p. 220-221) for Section 4.1.

* Problems (pp. 154-156) 3.26, 3.28, 3.30, 3.32.

Exam 2: Thursday, July 21, 8.45-10pm, 1013 ECEB.
10 Tuesday,
July 26
* joint pmfs (Ch 4.2)[SAQ 4.2]
* joint pdfs (Ch 4.3)[SAQ 4.3]
* SAQs (p. 221) for Sections 4.2-4.3.
* Problems (p. 223-226) 4.2 (not part d), 4.6, 4.10 (not part a).
To shorten the problems on quizzes, Parts 4.2(c), 4.6(c), 4.10(e) will not be included.
11 Friday,
July 29
* 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.]
* SAQs (p. 222) for Sections 4.4-4.6.
* Problems (pp. 226-230) 4.2(d), 4.4, 4.8, 4.10, 4.12, 4.14, 4.16.
To shorten the problems on quizzes, Parts 4.4(c), 4.12(d) will not be included.
12 Tuesday,
August 2

- Skip Section 4.7.
* 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 (pp.230-234) 4.18, 4.20, 4.22, 4.24, 4.26, 4.28.
--
NOTE: the material in section 4.10 will not be discussed during lectures nor will it be tested. All students will automatically get concept matrix credit for them.

* law of large numbers (Ch 4.10.1)
* central limit theorem (Ch 4.10.2)[SAQ 4.10]

NOTE: the material in section 4.11 will be discussed during lecture on Monday, August 1 and Tuesday, August 2 BUT will not be tested in the quizzes nor in the concept matrix. All students will automatically get concept matrix credit for them. However, it will be tested in the final exam.

* joint Gaussian distribution (Ch 4.11) (e.g. five dimensional characterizations)[SAQ 4.11]
To compensate for afternoon exams, there will be NO lectures August 3-August 4 BUT I will be in room 3017 during regular lecture time to answer questions.

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