ECE ILLINOIS

ECE 313/MATH 362

PROBABILITY WITH ENGINEERING APPLICATIONS

Summer 2018


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.
Daily review notes (Last update, Tuesday, June 19)


Summary of office hours times and locations, from June 12 to August 2.
  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
11am-12pm 3034 ECEB 3034 ECEB 3034 ECEB 3034 ECEB 3034 ECEB
except June 29
12-1pm   3034 ECEB  
1-2pm  


Section Meeting time and place Instructor
X 10 MTWRF
1013 ECE Building
Juan Alvarez
e-mail: alvarez AT illinois dot edu
Office Hours:
Mondays, 1.30-2.30pm, 3034 ECEB.
Wednesdays, 1.30-2.30pm, 3034 ECEB.
Thursdays, 1.30-2.30pm, 3034 ECEB.
figures and notes

Graduate Teaching Assistants
Usman Ahmed Syed (usyed3@ AT illinois dot edu) Office Hours: Tuesdays, 11am-2pm, 3034 ECEB.
Wednesdays 11am-12pm, 3034 ECEB.
Fridays 11am-2pm, 3034 ECEB.


Concept constellation
Concept matrix
Quiz # Quiz date
(tentative)
Concepts (Notes sections)[Short videos] Short Answer Questions (SAQ)
and Problems for Quizzes

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.
1 Tuesday,
June 19
* 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 Karnaugh maps for three sets (Ch 1.4)[Karnaughpuzzle, SAQ1.2]
* using principles of counting and over counting; binomial coefficients (Ch 1.3-1.4) [ILLINI, SAQ 1.3, SAQ 1.4, PokerIntro, PokerFH2P]
* conditional probability (Ch 2.3) [team selection][SAQ 2.3]
* SAQs for Sections 1.2, 1.3, 1.4, 2.3.
* Problems 1.2, 1.4, 1.6, 1.8, 1.10, 1.12, 2.12, 2.16 .

Optional: [SAQ 1.5]
2 Friday,
June 22
* independence of events (Ch 2.4.1)[SimdocIntro][Simdoc-Minhash1]???
* law of total probability (Ch 2.10) [deuce] [SAQ 2.10]
* Bayes formula (Ch. 2.10)
* random variables and probability mass functions (Ch 2.1) [pmfmean]
* SAQs for Section 2.10
* Problems 2.14, 2.32, 2.34, 2.2 (quiz won't ask for mean and variance), 2.4, 2.6 ((a) and (c)).
3 Tuesday,
June 26
*mean of a function of a random variable (LOTUS) (Ch 2.2) [pmfmean]
* scaling of expectation, variance, and standard deviation (Ch 2.2) [SAQ 2.2]
* independence of random variables and Bernoulli distribution (Ch 2.4.2-2.4.3)[SimdocIntro][Simdoc-Minhash1]
* SAQs for Section 2.2.
* Problems 2.2, 2.6 ((b), (d), (e) and (f)), 2.10.

Exam 1: Wednesday, June 27, during lecture.
4 Friday, June 29 * 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]
* SAQs for Sections 2.4-2.5.
* Problems 2.18, 2.20, 2.22, 2.24.
5 Tuesday,
July 3
* 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]
NO lecture on Wednesday, July 4.
* SAQs for Sections 2.6-2.7
6 Tuesday,
July 10
* Maximum likelihood parameter estimation (definition, how to calculate for continuous and discrete parameters) (Ch 2.8)[SAQ 2.8][hypergeometric]
- Skip Section 2.9.
* 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 Subsections 2.12.4 and 2.12.5.
* SAQs for Sections 2.8, 2.11-2.12
* Problems 2.26, 2.36, 2.38, 2.40, 2.42, 2.44, 2.46

Exam 2: Wednesday, July 11, during lecture.
7 Friday,
July 13
* 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 for Sections 3.1-3.4.
* Problems 3.2, 3.4, 3.6, 3.8, 3.10.
8 Tuesday,
July 17

* Poisson processes (Ch 3.5) [SAQ 3.5]
* scaling rule for pdfs (Ch. 3.6.1)[SAQ 3.6]
* SAQs for Sections 3.5 and 3.6.1
* Problems 3.12 and 3.14.
9 Friday,
July 20
* 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]
* the distribution of a function of a random variable (Ch 3.8.1)[SAQ 3.8]
* SAQs for Section 3.6.2-3.6.4, 3.7, 3.8.1 and 3.10.
* Problems 3.16, 3.18c, 3.20, 3.22, 3.24, 3.26, 3.28, 3.30, 3.32.
10 Tuesday,
July 24
* 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 for Sections 3.8.2, 4.1.

Exam 3: Wednesday, July 25, during lecture.
11 Friday,
July 27
* joint pdfs (Ch 4.3)[SAQ 4.3]
* joint pmfs (Ch 4.2)[SAQ 4.2]
* SAQs for Sections 4.2-4.3.
* Problems 4.2 (not part d), 4.6, 4.10 (not part a).
12 Thursday,
August 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.
* correlation and covariance (e.g. scaling properties) (Ch 4.8)[SAQ 4.8]
* minimum mean square error linear estimator (Ch 4.9.3)[SAQ 4.9]
* minimum mean square error unconstrained estimators (Ch 4.9.2)
* SAQs for Sections 4.4-4.6, 4.8-4.9
* Problems 4.2(d), 4.4, 4.8, 4.12, 4.14, 4.16, 4.18, 4.20, 4.22, 4.24, 4.26, 4.28.

Optional Reading:



More Detailed Information

The ECE 313 FAQ

About the Concept Matrix

Homework

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Quizzes and exams

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COMPASS (for grades)

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Powerpoint slides