ACM/EE 116, Fall 2011

From Murray Wiki
Jump to navigationJump to search

Introduction to Probability and Random Processes with Applications


  • 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.


  • 17 Jul 2011: web page creation

Lecture Schedule

Date Topic Reading Homework
27 Sep
29 Sep
Events, probabilities and random variables
  • fields and probability spaces
  • Conditional probability and independence
  • The law of large numbers
  • Random variables (discrete and continuous)
G&S, Chapters 1 and 2, Appendices
  • Read Appendices A & B (history; 4 pages)
  • Sections 1.1-1.5 (14 pages)
  • Sections 2.1-2.3 (10 pages)

HW 1

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
  • Sections 3.1-3.8 (26 pages)

HW 2

11 Oct
13 Oct
Continuous random variables
  • Probability density functions
  • Independence
  • Expectation and moments
  • Conditional distributions and conditional expectation
  • Functions of random variables
  • Multivariate normal distribution
G&S, Chapter 4
  • Sections 4.1-4.9 (30 pages)

HW 3

18 Oct
20 Oct
Generating functions and their applications
  • Generating functions
  • Random walks, branching processes
  • Characteristic functions
  • Law of large numbers, central limit theorem
G&S, Chapter 5
  • Sections 5.1-5.4, 5.6A, 5.7-5.10 (48 pages)

HW 4

25 Oct
27 Oct
Introduction to random processes
  • Discrete and continuous time processes
  • Markov processes/chains (overview)
  • Properties of random processes (mean, covariance, time correlation...)
  • Examples and applications
G&S Chapters 6, 8
  • Sections 6.1 (Markov processes, recurrent states; 11 pages)
  • Sections 8.1-8.6 (14 pages)

HW 5

1 Nov
3 Nov
Convergence of random variables/processes
  • Modes of convergence
  • Laws of large numbers
  • The strong law
  • Martingales
G&S Chapter 7
  • Sections 7.1-7.5 (27 pages)

HW 6

8 Nov
10 Nov*
Stochastic processes
  • Stationary processes
  • Examples: renewal processes, queues
  • Wiener process
  • Linear prediction
  • Autocovariances and spectra
  • Stochastic integration and the spectral representation
  • Gaussian processes
G&S Chapter 9
  • Sections 9.1-9.4, 9.6 (28 pages)
  • Supplementary notes (OBC, Ch 4)

HW 7

15 Nov*
17 Nov
Special Topics (instructor dependent)

HW 8

22 Nov
29 Nov
Special Topics (instructor dependent)

HW 9

1 Dec Course review



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.


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.

Old Announcements