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## ECE 341 - Probability and Random Processes for Engineers

Some people think that building up to probability and statistics, and not calculus (the current regime), should be the end-goal of high-school mathematics. Understanding risk, probabilities, expectations, standard deviations is not only relevant in our daily lives, but also in designing, understanding and analyzing engineering systems. This course is an introduction to the fascinating field of probability theory aimed at engineers; we will related the theoretical concepts to real world problems.

Quoting Arthur Benjamin, if calculus = analog (which is of course beautiful), then probability = discrete; welcome to the digital era.

### Announcements

Topics for the final:

Textbook: Ch. 1 (all), Ch. 2 (all), Ch.3 (all), Ch. 4 (all), Ch.5 (all), Ch. 6 (all EXCEPT for 6.8 and 6.9), Ch. 10 (10.1, 10.2, 10.3, 10.4, 10.8, 10.9, 10.10, 10.11), Ch. 11 (11.1, 11.5, 11.7 + 11.8 only the continuous time versions, no discrete time random sequences).

Non-textbook: Quantization and minimum mean squared quantization error; linear MMSE (see also book Ch. 9.2); signals in additive white Gaussian noise; entropy and Huffman coding

Change the grading scheme (to the students' benefit).

Midterm 1 = max(Midterm 1, Midterm 2, Exam)
Midterm 2 = max(Midterm 2, Exam)
Exam = Exam

Quiz 2 solution is posted in "Additional Material".

Midterm 1 is on Monday, Feb.6, 2012 during class. You may bring one 8.5x11in double-sided cheat sheet with whatever you like on it. No calculators or other electronic devices are permitted. Cheating will be taken seriously.

I posted a practice Midterm 1 that I will solve in class on Feb. 3, 2012 in "Additional Material".

Quiz 1 solutions are up, in "Additional Material".

Homeworks will be assigned every Wednesday, due in class the next Wednesday. -- NatashaDevroye - 2011-12-06

### Syllabus

Course description: This course covers probability, random variables, discrete and continuous distributions, transformation of random variables, expectation, generating functions, statistical inference, hypothesis testing, estimation, random processes, stationarity, and applications.

Prerequisite: Credit or concurrent registration in ECE 310.

Instructor: Natasha Devroye devroye@uic.edu Science and Engineering Offices (SEO) room 1039 Website Office hours: Tuesday 8:30-10am, Wednesday after class 1:50-3pm

Teaching Assistant: Diana Maamari dmaama2@uic.edu Office hours: Monday 2-3:30, Thursday 2-3:30, SEO 900

Lecture: MWF 1-1:50pm, Douglas Hall 210

Topics:

• Probability
• Random Variables
• Discrete and Continuous Distributions
• Joint and Conditional Densities
• Transformation of Random Variables
• Expected Values and Moment Generating Functions
• Hypothesis Testing
• Estimation in Communications
• Gaussian Random Variables
• Random Processes, Gaussian and Poisson Arrival Process
• Autocorrelation and Stationarity
• Applications
ECE-related application areas that may be covered:

• Amplitude limiting (mixed discrete and continuous random variables)
• Amplitude quantization, signal-to-noise power ratio
• Basic information theory, entropy of a discrete random variable
• Huffman coding, efficiency of a binary code
• Sample mean, biased and unbiased estimators
• Bit-rate-error analysis of a noisy communication channel
• Correlation coefficient, linear estimation
• Estimating PDF: histogram method, moment generating function method
• Estimating PSD: autocorrelation method
• Linear filtering stationary random processes
Simulations: We will use the MATLABŪ programming language throughout the course to confirm predictions from probability theory. This will be done by performing experiments using simulated random variables and by plotting various statistical waveforms. MATLABŪ is available for students use on both ACCC and ECE computer networks; a personal student version may also be purchased from Mathworks, Inc. (see www.mathworks.com)

• Class participation 3%
• Homework and Matlab (weekly) 17%
• Random in-class quizzes (will give 5 over the semester, will drop the 1 lowest score) 10%
• Midterm 1 20% = max(Midterm 1, Midterm 2, Final) (may bring one 8.5x11 inch double-sided cheat sheet) 02.06.2012
• Midterm 2 20% = max(Midterm 2, Final) (may bring two 8.5x11 inch double-sided cheat sheets) 03.16.2012
• Final 30% (may bring three 8.5x11 inch double-sided cheat sheets).
Policy: Late homeworks will under no circumstances be accepted. There will be no make-up midterms or finals. Solution manuals are known to be available for this course; it is strongly encouraged that you solve problems and learn think independently, NOT by looking at the solutions. This will decrease your understanding and ultimately haunt you in the midterms and finals.

Textbook chapters (subject to change): Chapters 1-5
Chapter 6 (§6.1-6.7)
Chapter 7
Chapter 9 (§9.1-9.2)
Chapter 10 (§10.1-10.3,10.8-10.11)
Chapter 11 (§11.1, 11.5, 11.7, 11.8)

Textbook: “Probability and Stochastic Processes: A Friendly Introduction for Electrical and Computer Engineers” by Roy D. Yates and David J. Goodman. John Wiley & Sons; 2nd edition, 2004

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ISBN-10: 0471272140, ISBN-13: 9780471272144

WARNING: It is urgent that you read the "A Message to Students from the Authors" on pages xi-xii of the textbook.

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Topic revision: r7 - 2011-12-06 - 01:58:22 - Main.devroye

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