ACM/EE 116, Fall 2011

Introduction to Probability and Random Processes with Applications
Instructors Richard Murray (CDS/BE) Lectures: Tu/Th, 9-10:30, 105 ANB	Teaching Assistants TBD Office hours: TBD

Course Description

Introduction to fundamental ideas and techniques of stochastic analysis and modeling. Random variables, expectation and conditional expectation, joint distributions, covariance, moment generating function, central limit theorem, weak and strong laws of large numbers, discrete time stochastic processes, stationarity, power spectral densities and the Wiener-Khinchine theorem, Gaussian processes, Poisson processes, Brownian motion. The course develops applications in selected areas such as signal processing (Wiener filter), information theory, genetics, queuing and waiting line theory, and finance.

Announcements

• 17 Jul 2011: web page creation

Lecture Schedule

Date	Topic	Reading	Homework
27 Sep 29 Sep	Events, probabilities and random variables	G&S, Chapters 1 and 2 $\sigma$ fields and probability spaces Conditional probability and independence Random variables (discrete and continuous) The law of large numbers
4 Oct 6 Oct	Discrete random variables Probability mass functions Independence Expectation and moments Conditional distributions and conditional expectation Sums of random variables	G&S, Chapter 3
11 Oct 13 Oct	Continuous random variables Probability density functions Independence Expectation and moments Conditional distributions and conditional expectation Sums of random variables	G&S, Chapter 4
18 Oct 20 Oct	Generating functions and their applications	G&S Chapter 5
25 Oct 27 Oct	Convergence of random variables	G&S Chapter 6
1 Nov 3 Nov	Random and stationary processes	G&S Chapter 7, 8
8 Nov 10 Nov*	Markov Chains (introduction)	G&S Chapter 9
15 Nov* 17 Nov	Martingales	G&S Chapter 12
22 Nov 29 Nov	Special Topics Concentration of Measure inequalities
1 Dec	Course review

Textbook

The primary text for the course (available via the online bookstore) is

[G&S]

G. R. Grimmett and D. R. Stirzaker, Probability and Random processes, third edition. Oxford University Press, 2001.

Grading

The final grade will be based on homework and a final exam:

• Homework (75%) - There will be 9 one-week problem sets, due in class one week after they are assigned. Students are allowed three grace periods of two days each that can be used at any time (but no more than 1 grace period per homework set). Late homework beyond the grace period will not be accepted without a note from the health center or the Dean.
• Final exam (25%) - The final will be handed out the last day of class and is due back at the end of finals week. Open book, time limit to be decided (likely 3 hours in one sitting)

The lowest homework score you receive will be dropped in computing your homework average. In addition, if your score on the final is higher than the weighted average of your homework and final, your final will be used to determine your course grade.

Collaboration Policy

Collaboration on homework assignments is encouraged. You may consult outside reference materials, other students, the TA, or the instructor. Use of solutions from previous years in the course or from other external sources is not allowed. All solutions that are handed should reflect your understanding of the subject matter at the time of writing.

No collaboration is allowed on the final exam.