# ECE 313/MATH 362 PROBABILITY WITH ENGINEERING APPLICATIONS Summer 2017

#### 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, Friday, July 28, 2017)
figures, videos, handouts, etc.

Summary of office hours times and locations, from June 12 to August 3.
 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 1.30-2pm 3036 ECEB* 3034 ECEB* 3036 ECEB* 2-2.30pm 3034 ECEB 2.30-3pm 3034 ECEB 3034 ECEB 3.00-3:30pm 3:30-4pm 4-5pm
* Except June 15, June 26, July 4, and August 1-3.

## Concept constellation Concept matrix Quiz # Quiz date(tentative) Concepts (Notes sections)[Short videos] Short Answer Questions (SAQ) and Problems for Quizzes 1 Tuesday,June 20 * 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 23 * 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 27 * 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, June 30 * 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 7 * 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. NO lecture on Tuesday, July 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 6, 5.15-6.30pm, 3015 ECEB 6 Tuesday,July 11 * 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 14 * 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 18 * 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 21 * 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 (p. 147) for Section 3.8. * Problems (pp. 154-156) 3.26, 3.28, 3.30, 3.32. Exam 2: Thursday, July 20, 5.15-6.30pm, 3015 ECEB 10 Tuesday,July 25 * joint CDFs (Ch 4.1)[SAQ 4.1] * joint pmfs (Ch 4.2)[SAQ 4.2] * joint pdfs (Ch 4.3)[SAQ 4.3] * SAQs (pp. 220-221) for Sections 4.1-4.3. * Problems (pp. 223-226) 4.2 (not part d), 4.6, 4.10 (not part a). 11 Friday,July 28 * 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. 12 Tuesday, August 1 (beginning of lecture) - 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. -- * law of large numbers (Ch 4.10.1) * central limit theorem (Ch 4.10.2)[SAQ 4.10] * SAQs (p.222) for Section 4.10(part 2 only) * Problems (pp.230-234) 4.30, 4.32, 4.34 To compensate for evening exams, there will be NO lectures August 1-August 3 BUT there is a quiz on August 1, at the beginning of the lecture.

Optional Reading: