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Revision as of 12:29, 12 September 2011
Introduction to Probability and Random Processes with Applications  
Instructors

Teaching Assistants

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 WienerKhinchine 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
W  Date  Topic  Reading  Homework 
1 
27 Sep 29 Sep 
Events, probabilities and random variables

G&S, Chapters 1 and 2, Appendices

HW 1 
2 
4 Oct 6 Oct 
Discrete random variables

G&S, Chapter 3

HW 2 
3 
11 Oct 13 Oct 
Continuous random variables

G&S, Chapter 4

HW 3 
4 
18 Oct 20 Oct 
Generating functions and their applications

G&S, Chapter 5

HW 4 
5 
25 Oct 27 Oct 
Convergence of random variables/processes

G&S Chapter 7

HW 5 
6 
1 Nov 3 Nov 
Introduction to random processes

G&S Chapters 8

HW 6 
7 
8 Nov 10 Nov* 
Discrete time stochastic processes

G&S Chapter 9

HW 7 
8 
15 Nov* 17 Nov 
Continuous time stochastic processes

G&S Chapter 9

HW 8 
9 
22 Nov 29 Nov 
Diffusion processes

G&S Chapter 13

HW 9 
10 
1 Dec  Course review 
Final 
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. 
The following additional texts may be useful for some students (on reserve in SFL):
[Gubner]  J. A. Gubner, Probability and Random Processes for Electrical and Computer Engineers. Cambridge University Press, 2006. 
[S&W]  H. Stark and J. W. Woods, Probability and Random Processes with Applications to Signal Processing, third edition. Prentice Hall, 2002. 
Grading
The ﬁnal grade will be based on homework and a ﬁnal exam:
 Homework (75%)  There will be 9 oneweek 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.