ECE ILLINOIS

ECE 313/MATH 362

PROBABILITY WITH ENGINEERING APPLICATIONS

Summer 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, from June 15 to August 6.
  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
1-2pm   3034 ECEB 3034 ECEB  
2-3pm 3034 ECEB 3034 ECEB
3-4pm 3034 ECEB 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: Wednesdays and Thursdays, 1-2pm, 3034 ECEB.
figures and notes

Graduate Teaching Assistants
Chris Ryu (ryu1 AT illinois dot edu) Office Hours: Monday 2-4pm (3034 ECEB),
Tuesday 3-5pm (3034 ECEB),
Thursday 2-4pm (3034 ECEB),
Friday 3-5pm (3034 ECEB).


Concept constellation
Concept matrix
Quiz # Quiz date
(tentative)
Concepts (Notes sections)[Short videos] Short Answer Questions (SAQ)
and Problems for Quizzes
1 Monday,
June 22
* 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 Thursday,
June 25
* 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 Monday,
June 29
* 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 Thursday, July 2 * 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, 2.27.
5 Thursday,
July 9
* 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 9, 4-5.15pm, 1013 ECEB.
6 Tuesday,
July 14
* 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 Thursday,
July 16
* exponential distribution (Ch 3.4) [SAQ 3.4]
* Poisson processes (Ch 3.5) [SAQ 3.5]
* 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 144) for Sections 3.4-3.6. (except for part 4 of 3.6)
* Problems (pp. 150-153) 3.10, 3.12, 3.14, 3.16.
8 Monday,
July 20
* 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)
- Skip Sections 3.8.3 and 3.9
* SAQs (pp. 146-147) for Sections 3.6-3.8 (for 3.6, only part 4).
* Problems (pp. 154-156) 3.18c, 3.20, 3.22, 3.24, 3.26, 3.28, 3.30, 3.32.
9 Thursday,
July 23
* binary hypothesis testing for continuous type random variables (Ch 3.10) [SAQ 3.10]
* joint CDFs (Ch 4.1)[SAQ 4.1]
* joint pdfs (Ch 4.3)[SAQ 4.3]
* SAQs (p. 147) for Section 3.10.
* SAQs (p. 220-221) for Sections 4.1 and 4.3 (not 4.2).
* Problems (p. 156) 3.31.
* 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.

Exam 2: Thursday, July 23, 4-5.15pm, 1013 ECEB.
10 Monday,
July 27
* joint pmfs (Ch 4.2)[SAQ 4.2]
* 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.]
- Skip Section 4.7.
* SAQs (p. 221) for Sections 4.2 and 4.4-4.6.
* Problems (pp. 226-227) 4.2(d), 4.4, 4.8, 4.10(a), 4.12, 4.14, 4.16.
To shorten the problems on quizzes, Parts 4.4(c), 4.12(d) will not be included.
11 Thursday,
July 30
* 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.
12 Tuesday,
August 4, 10am
* 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.230-234) 4.30, 4.32, 4.34, 4.36, 4.38, 4.40, 4.42.
To compensate for afternoon exams, there will be NO lectures August 4-August 7.
Notice that there is a quiz on August 4, and it will be 10am.

Optional Reading:



More Detailed Information

The ECE 313 FAQ

About the Concept Matrix

Homework

Previous Web Pages

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Quizzes and exams

Piazza

COMPASS (for grades)

Grading Policies

Powerpoint slides