Some people think that building up to probability and statistics, and not calculus (how our mathematics education is currently structured), 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.

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

**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

- 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

**Grading: **(grades will be posted on Blackboard)

- 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).

**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

.

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.

Topic revision: r8 - 2011-12-12 - 04:17:58 - Main.devroye

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