ECE 313/MATH 362

PROBABILITY WITH ENGINEERING APPLICATIONS

Spring 2017 - Sections B, D, and F

The webpage for section G can be found here.

#### 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.
Optional Reading: D. V. Sarwate, Probability with Engineering Applications, Powerpoint Slides for ECE 313, Fall 2000

Instructors:

• Section D, MWF, 11-11:50 AM, ECEB 3017, Prof. Juliy Baryshnikov (office hours: F 1-2)
• Section F, MWF, 1-1:50 PM, ECEB 3017, Prof. Idoia Ochoa (office hours: Th 3-4)
• Section B, MWF, 2-2:50 PM, ECEB 3017, Prof. Yi Lu (office hours: F 3-4)

Teaching Assistants:

Summary of office hours times and locations (starting January 23).

• priority to concept matrix certification
• Monday: 2-6 pm ECEB 2015
• Tuesday: 1-4 pm ECEB 3036, 3:30-7 pm ECEB 3020
• priority for Q&A about lectures, SAQs, problems, exams
• Wednesday: 1-3 pm, ECEB 5034
• Thursday: 1-4 pm, ECEB 5034
• Friday: 1-5 pm, ECEB 5034

### Concept matrix

Checkpoint # Lecture Concepts (Reading)[ Short videos] Date dates Course schedule (subject to change) 1 Sun, 1/29 1/18-1/27 * 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 Sun, 2/5 1/30-2/3 * 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 Sun, 2/12 2/6-2/10 * 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 Sun, 2/19 2/13-2/17 * 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 Sun, 2/26 2/20-2/24 * 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 Sun, 3/5 2/27-3/3 * 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 Sun, 3/12 No Lecture 3/10, EOH 3/6-3/8 * 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 Sun, 3/26 3/13-3/17 * 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] 3/20-3/24 Spring vacation 9 Sun, 4/2 3/27-3/31 * 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 Sun, 4/16 (skip 4/9) 4/3-4/14 * 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 for concept certification nor in the exams) 11 Sun, 4/23 4/17-4/21 * 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 Sun, 4/30 4/24-4/28 * 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] - 5/1-5/3 wrap up and review