ECE ILLINOIS

ECE 313/MATH 362

PROBABILITY WITH ENGINEERING APPLICATIONS

Spring 2018 - Sections B,C,D,F and G


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. Students taking ECE 313 might consider taking ECE 314, Probability Lab, at the same time.

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 on January 22).
In-person office hours
Online office hours (through SOS on MasterProbo. See Homework) SOS requests are answered throughout the day, but response will be almost real-time durring online office hours.
Hours Monday Tuesday Wednesday Thursday Friday
3-4pm 5034 ECEB 5034 ECEB 2036 ECEB
4-5pm
5-6pm 4036 ECEB
7-8pm Online Online
8-9pm


Section Meeting time and place Instructor
C 10 MWF
3017 ECE Building
Professor Olgica Milenkovic
e-mail: milenkov AT illinois dot edu
Office Hours: Wednesdays, 3-4pm, 5034 ECEB
G 11 MWF
3015 ECE Building
Professor Juan Alvarez
e-mail: alvarez AT illinois dot edu
Office Hours: Mondays, 3-4pm, 5034 ECEB
example figures and review notes
D 11 MWF
3017 ECE Building
Professor Alejandro Dominguez-Garcia
e-mail: aledan AT illinois dot edu
Office Hours: Thursdays, 3-4pm, 2036 ECEB
F 1 MWF
3017 ECE Building
Professor Idoia Ochoa
e-mail: idoia AT illinois dot edu
Office Hours: Wednesdays, 4-5pm, 5034 ECEB
B 2 MWF
3017 ECE Building
Professor Yi Lu
e-mail: yilu4 AT illinois dot edu
Office Hours: Online

Graduate Teaching Assistants
Cheng Chen
cchen130 AT illinois dot edu
Office Hours: Online
Ge Yu
geyu3 AT illinois dot edu
Office Hours: Online
Du Su
dusu3 AT illinois dot edu
Office Hours: Online
Vishesh Verma
vverma4 AT illinois dot edu
Office Hours: Thursdays 4-6pm, Fridays 5-6pm
Ali Yekkehkhany
yekkehk2 AT illinois dot edu
Office Hours: Online


Course schedule (subject to change)
Checkpoint #
Date
Lecture
dates
Concepts (Reading)[ Short videos]
1

Tue, 1/30
1/17-1/26 * 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]
2

Tue, 2/6
1/29-2/2 * 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]
* 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]
3

Tue, 2/13
2/5-2/9 * 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]
4

Tue, 2/20
2/12-2/16 * 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)
5

Tue, 2/27
2/19-2/23 * 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)
6

Tue, 3/6
2/26-3/2 * 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]
7

Tue, 3/13
No Lecture 3/9, EOH
3/5-3/7 * 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]
8

Tue, 3/20
3/12-3/16 * 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]
  3/19-3/23 Spring vacation
9

Tue, 4/3
3/26-3/30
* joint CDFs (Ch 4.1) [SAQ 4.1]
* joint pmfs (Ch 4.2) [SAQ 4.2]
* joint pdfs (Ch 4.3) [SAQ 4.3]
10

Tue, 4/17
(skip 4/10)
4/2-4/13 * 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 and 4.7.3 will not be tested in the exams)
11

Tue, 4/24
4/16-4/20 * 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]
12

Tue, 5/1
4/23-4/27 * 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]
- 4/30-5/2 wrap up and review  

Optional Reading:



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