Difference between revisions of "ACM/EE 116, Fall 2011"
Line 31:  Line 31:  
 27 Sep <br> 29 Sep   27 Sep <br> 29 Sep  
 Events, probabilities and random variables   Events, probabilities and random variables  
−  
* <math>\sigma</math> fields and probability spaces  * <math>\sigma</math> fields and probability spaces  
* Conditional probability and independence  * Conditional probability and independence  
+  * The law of large numbers  
* Random variables (discrete and continuous)  * Random variables (discrete and continuous)  
−  *  +   G&S, Chapters 1 and 2, Appendices 
+  * Read Appendices A & B (history; 4 pages)  
+  * Sections 1.11.5 (14 pages)  
+  * Sections 2.12.3 (10 pages)  
 <! Homework >   <! Homework >  
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Line 46:  Line 49:  
* Sums of random variables  * Sums of random variables  
 G&S, Chapter 3   G&S, Chapter 3  
+  * Sections 3.13.8 (26 pages)  
 <! Homework >   <! Homework >  
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Line 54:  Line 58:  
* Expectation and moments  * Expectation and moments  
* Conditional distributions and conditional expectation  * Conditional distributions and conditional expectation  
−  *  +  * Functions of random variables 
+  * Multivariate normal distribution  
 G&S, Chapter 4   G&S, Chapter 4  
+  * Sections 4.14.9 (30 pages)  
 <! Homework >   <! Homework >  
 valign=top   valign=top  
 18 Oct <br> 20 Oct   18 Oct <br> 20 Oct  
 Generating functions and their applications   Generating functions and their applications  
−  +  * Generating functions  
+  * Random walks, branching processes  
+  * Characteristic functions  
+  * Law of large numbers, central limit theorem  
+  * Sections 5.15.4, 5.6A, 5.75.10 (48 pages)  
 <! Homework >   <! Homework >  
 valign=top   valign=top  
 25 Oct <br> 27 Oct   25 Oct <br> 27 Oct  
 Convergence of random variables   Convergence of random variables  
−   G&S Chapter  +  * Modes of convergence 
+  * Laws of large numbers  
+  * The strong law  
+  * Martingales  
+   G&S Chapter 7.17.8 (38 pages)  
+  * Sections 7.1  
 <! Homework >   <! Homework >  
 valign=top   valign=top  
 1 Nov <br> 3 Nov   1 Nov <br> 3 Nov  
 Random and stationary processes   Random and stationary processes  
−   G&S Chapter  +  * Stationary processes 
+  * Examples: renewal processes, queues  
+  * Wiener process  
+  * Linear prediction  
+  * Autocovariances and spectra  
+  * Stochastic integration and the spectral representation  
+  * Gaussian processes  
+   G&S Chapter 8, 9  
+  * Sections 8.18.5 (11 pages)  
+  * Sections 9.19.4, 9.6 (28 pages)  
 <! Homework >   <! Homework >  
 valign=top   valign=top  
 8 Nov <br> 10 Nov*   8 Nov <br> 10 Nov*  
−   Markov  +   Markov Processes (introduction) 
−   G&S Chapter  +  * Markov processes 
+  * Classification of states and chains  
+  * Stationary distributions and the limit theorem  
+  * Examples  
+   G&S Chapter 6  
 <! Homework >   <! Homework >  
 valign=top   valign=top  
 15 Nov* <br> 17 Nov   15 Nov* <br> 17 Nov  
 Martingales   Martingales  
+  * Martingale differences and Hoeffding's inequality  
+  * Crossings and convergence  
+  * Stopping times  
 G&S Chapter 12   G&S Chapter 12  
 <! Homework >   <! Homework >  
Line 86:  Line 117:  
 Special Topics   Special Topics  
* Concentration of Measure inequalities  * Concentration of Measure inequalities  
−  *  +  * Estimation theory (Kalman filtering) 
 <! Reading >   <! Reading >  
 <! Homework >   <! Homework > 
Revision as of 21:02, 17 July 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
Date  Topic  Reading  Homework 
27 Sep 29 Sep 
Events, probabilities and random variables

G&S, Chapters 1 and 2, Appendices


4 Oct 6 Oct 
Discrete random variables

G&S, Chapter 3


11 Oct 13 Oct 
Continuous random variables

G&S, Chapter 4


18 Oct 20 Oct 
Generating functions and their applications


25 Oct 27 Oct 
Convergence of random variables

G&S Chapter 7.17.8 (38 pages)


1 Nov 3 Nov 
Random and stationary processes

G&S Chapter 8, 9


8 Nov 10 Nov* 
Markov Processes (introduction)

G&S Chapter 6  
15 Nov* 17 Nov 
Martingales

G&S Chapter 12  
22 Nov 29 Nov 
Special Topics


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 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.