Difference between revisions of "ACM/EE 116, Fall 2011"
(Created page with '{ width=100%   colspan=2 align=center  <font color='blue' size='+2'>Introduction to Probability and Random Processes with Applications</font>__NOTOC__  valign=top  width=…') 

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* Richard Murray (CDS/BE)  * Richard Murray (CDS/BE)  
* Lectures: Tu/Th, 910:30, 105 ANB  * Lectures: Tu/Th, 910:30, 105 ANB  
+  * Office hours: by request  
 width=50%    width=50%   
'''Teaching Assistants'''  '''Teaching Assistants'''  
−  *  +  * John Bruer (ACM), Yutong Chen (ACM), May Eaton (EE), Alex Gittens (ACM) 
−  * Office hours:  +  * Office hours: Fri, 34 pm, 213 ANB; Mon, 79 pm, 107 ANB. 
}  }  
Line 18:  Line 19:  
===Announcements ===  ===Announcements ===  
−  *  +  * 5 Dec 2011: Partial solutions for HW #9 are posted; will try to post additional solutions by Tue (6 Dec) evening. 
+  * 2 Dec 2011: The final exam is available for pickup outside 107 Steele. (Make sure to get the right exam! The ACM/EE 116 and CDS 110 exams look similar.)  
+  * 1 Dec 2011: HW #8 is graded. Scores: mean= 46/50, std dev = 6.1. Hours: mean=8.5, std dev = 2.9 (median=8)  
+  * 27 Nov 2011: Homework deadlines and office hours for this week:  
+  ** Office hours: Tue (29 Nov), 34 pm and Thu (1 Dec) 79 pm on first floor Annenberg  
+  ** Homework deadlines: HW #8 extensions are due by 29 Nov, 10:30 am. HW #9 is due 2 Dec (Fri) @ 5 pm (autoextension)  
+  ** Turn in homework in class or to the box outside 109 Steele  
+  * 21 Nov 2011: HW #7 is graded. Scores: mean=45/50, std dev = 6.7. Hours: mean = 11.8, std dev = 5.5 (median = 10)  
+  * 14 Nov 2011: HW #6 is graded. Scores: mean=43/50, std dev = 6.2. Hours: mean = 10.5, std dev = 4.5 (median = 9.5)  
+  * 7 Nov 2011: HW #5 is graded (except extensions). Scores: mean = 42/50, std dev = 5.6. Hours: mean = 10.7, std dev = 4.3  
+  * 31 Oct 2011: HW #4 is graded. Scores: mean = 46/50, std dev = 5.2. Hours: mean = 7.7, std dev = 3.5  
+  * 24 Oct 2011: HW #3 is graded. Scores: mean = 44/50, std dev = 5.1. Hours: mean = 6.2, std dev = 3.3  
=== Lecture Schedule ===  === Lecture Schedule ===  
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{ width=100% border=1 cellspacing=0 cellpadding=5  { width=100% border=1 cellspacing=0 cellpadding=5  
    
+   '''W'''  
 '''Date'''   '''Date'''  
 '''Topic'''   '''Topic'''  
Line 29:  Line 42:  
 '''Homework'''   '''Homework'''  
 valign=top   valign=top  
+    
+  ===== 1 =====  
 27 Sep <br> 29 Sep   27 Sep <br> 29 Sep  
−   <  +   Events, probabilities and random variables 
−   <  +  * <math>\sigma</math> fields and probability spaces 
−   <  +  * Conditional probability, independence, Bayes' formula 
+  * The law of averages  
+  * Random variables (discrete and continuous)  
+  
+  {{acm116 pdffa11L11_introduction.key.pdfLecture slides}}  
+   G&S, Chapters 1 and 2, Appendices  
+  * Optional: Read Appendices III and IV (history; 4 pages)  
+  * Sections 1.11.5 (14 pages)  
+  * Sections 2.12.3 (10 pages)  
+  Gubner, Chapters 1 and 2  
+    
+  {{acm116 pdffa11hw1.pdfHW 1}} <br>  
+  {{acm116 pdffa11bgsurvey.pdfSurvey}}<br>  
+  {{acm116 pdffa11/caltechsoln1.pdfSoln 1}}  
 valign=top   valign=top  
+    
+  
+  ===== 2 =====  
 4 Oct <br> 6 Oct   4 Oct <br> 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 3.13.8 (26 pages)  
+  Gubner, Chapter 23  
+    
+  {{acm116 pdffa11hw2.pdfHW 2}} <br>  
+  {{acm116 pdffa11/caltechsoln2.pdfSoln 2}}  
 valign=top   valign=top  
+    
+  ===== 3 =====  
 11 Oct <br> 13 Oct   11 Oct <br> 13 Oct  
−    +   Continuous random variables 
−   <  +  * Probability density functions 
−    +  * Independence 
+  * Expectation and moments  
+  * Conditional distributions and conditional expectation  
+  * Functions of random variables  
+   G&S, Chapter 4  
+  * Sections 4.14.9 (30 pages)  
+  Gubner, Chapters 4, 5  
+    
+  {{acm116 pdffa11hw3.pdfHW 3}} <br>  
+  {{acm116 pdffa11/caltechsoln3.pdfSoln 3}}  
 valign=top   valign=top  
+    
+  
+  ===== 4 =====  
 18 Oct <br> 20 Oct   18 Oct <br> 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 5.15.4, 5.6A, 5.75.10 (48 pages)  
+  Gubner, Chapters 4, 5  
+    
+  {{acm116 pdffa11hw4.pdfHW 4}}<br>  
+  {{acm116 pdffa11/caltechsoln4.pdfSoln 4}}  
 valign=top   valign=top  
+    
+  
+  ===== 5 =====  
 25 Oct <br> 27 Oct   25 Oct <br> 27 Oct  
−   <  +   Convergence of random variables/processes 
−   <  +  * Modes of convergence 
−  +  * BorelCantelli lemmas  
+  * Laws of large numbers  
+  * The strong law  
+  * Prediction and conditional expectation  
+  * <s>Monte Carlo simulation</s>  
+   G&S Chapter 7  
+  * Sections 7.17.5, 7.9 (35 pages)  
+  Gubner, Chapters 13, 14  
+    
+  {{acm116 pdffa11hw5.pdfHW 5}}<br>  
+  [http://www.surveymonkey.com/s/ZSD9TK6 Survey]<br>  
+  {{acm116 pdffa11/caltechsoln5.pdfSoln 5}}  
 valign=top   valign=top  
+    
+  
+  ===== 6 =====  
 1 Nov <br> 3 Nov   1 Nov <br> 3 Nov  
−    +   Introduction to random processes 
−    +  * Discrete and continuous time processes 
−   <  +  * Markov processes/chains (overview) 
+  * Poison processes, birthdeath processes  
+  * Properties of random processes (mean, covariance, time correlation...)  
+  {{acm116 pdffa11/caltechL61_randproc.key.pdfTue slides}}, {{acm116 pdffa11/caltechL61_randproc.pdfTue notes}}, {{acm116 pdffa11/caltechL62_randproc.pdfThu notes}}  
+   G&S Chapters 8  
+  * Sections 6.1, 6.8, 6.11  
+  * Sections 8.18.2  
+    
+  {{acm116 pdffa11hw6.pdfHW 6}}<br>  
+  {{acm116 pdffa11/caltechsoln6.pdfSoln 6}}  
 valign=top   valign=top  
−   8 Nov <br> 10 Nov*  +   
−    +  
−   <  +  ===== 7 ===== 
−    +   8 Nov <br> 10 Nov* 
+   Stationary processes and renewal processes  
+  * Stationary processes  
+  * Linear prediction  
+  * Spectral density  
+  * Renewal processes  
+  {{acm116 pdffa11/caltechL71_stationary.pdfTue notes}}, {{acm116 pdffa11/caltechL72_renewal.pdfThu notes}}  
+   G&S Chapter 9 and 10  
+  * Sections 9.19.3, 9.5  
+  * Sections 10.110.2, 10.4  
+    
+  {{acm116 pdffa11hw7.pdfHW 7}}<br>  
+  {{acm116 pdffa11/caltechsoln7.pdfSoln 7}} (partial)  
 valign=top   valign=top  
−   15 Nov* <br> 17 Nov  +   
−    +  
−    +  ===== 8 ===== 
−   <  +   15 Nov* <br> 17 Nov 
+   Stochastic systems  
+  * Multivariate normal distributions  
+  * Discretetime Gaussian processes  
+  * Continuoustime Gaussian processes  
+  * Linear stochastic systems with Gaussian noise  
+  * Random processes in the frequency domain  
+  * <s>Kalman filtering (if time)</s>  
+  {{acm116 pdffa11/caltechL81_disctime.pdfTue notes}}, {{acm116 pdffa11/caltechL82_stochsys.pdfThu notes}}  
+   G&S + Course notes  
+  * G&S, Section 4.9  
+  * {{acm116 pdffa11/caltechstochasticacm116.pdfStochastic Systems}}  
+  Gubner, Chapter 10  
+    
+  {{acm116 pdffa11hw8.pdfHW 8}}<br>  
+  {{acm116 pdffa11/caltechsoln8.pdfSoln 8}}  
 valign=top   valign=top  
+    
+  
+  ===== 9 =====  
 22 Nov <br> 29 Nov   22 Nov <br> 29 Nov  
−    +   Diffusion processes 
−   <  +  * Brownian motion, Wiener process 
−    +  * Diffusion properties, first passage times 
+  * Stochastic calculus  
+  * Ito integral, Ito formula (if time)  
+  {{acm116 pdffa11/caltechL91_diffusion.pdfTue notes}}, {{acm116 pdffa11/caltechL92_itocalc.pdf"Thu" notes}}  
+  
+   G&S Chapter 13  
+  * Sections 13.113.4 (27 pages)  
+  * Sections 13.713.9 (10 pages)  
+  Gubner, Chapter 11  
+  * Section 11.3  
+    
+  {{acm116 pdffa11hw9.pdfHW 9}}<br>  
+  {{acm116 pdffa11/caltechsoln9.pdfSoln 9}}  
+  
 valign=top   valign=top  
+    
+  
+  ===== 10 =====  
 1 Dec   1 Dec  
−    +   Course review 
+  {{acm116 pdffa11/caltechL101_review.pdfReview for final}} (watch out for typos!)  
 <! Reading >   <! Reading >  
−    +   
+  Final  
}  }  
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{  {  
 valign=top   valign=top  
−   align=right  [G & S]  +   align=right  [G&S] 
 G. R. Grimmett and D. R. Stirzaker, ''Probability and Random processes'', third edition. Oxford University Press, 2001.   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):  The following additional texts may be useful for some students (on reserve in SFL):  
{  {  
 valign=top   valign=top  
−   align=right  [J&S]  +   align=right  [Gubner] 
−    +   J. A. Gubner, ''Probability and Random Processes for Electrical and Computer Engineers''. Cambridge University Press, 2006. 
+   valign=top  
+   align=right  [S&W]  
+   H. Stark and J. W. Woods, ''Probability and Random Processes with Applications to Signal Processing'', third edition. Prentice Hall, 2002.  
}  }  
−  
=== Grading ===  === Grading ===  
The ﬁnal grade will be based on homework and a ﬁnal exam:  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.  +  * Homework (75%)  There will be 9 oneweek problem sets, due in class (or the mailbox outside 109 Steele) 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)  * 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.  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.  
+  
+  In addition, all students in the class must sign in at office hours at least once in the first three weeks of the course, or sign up for [http://piazza.com Piazza] and post at least one question or response.  
=== Collaboration Policy ===  === 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.  +  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 (eg, Course Hero, instructors manuals, other course web sites) is not allowed. All solutions that are handed should reﬂect your understanding of the subject matter at the time of writing. 
+  * [http://piazza.com/caltech/fall2011/acmee116 ACM/EE 116 Piazza page]  an online collaboration site for the course has been established using [http://piazza.com Piazza]. This site can be used to post questions and give responses (from students or instructors). Postings can be anonymous if desired.  
No collaboration is allowed on the ﬁnal exam.  No collaboration is allowed on the ﬁnal exam.  
== Old Announcements ==  == Old Announcements ==  
+  * 17 Jul 2011: web page creation  
+  * 22 Sep 2011: added TAs and office hours. Established a [http://piazza.com/class#fall2011/acmee116 Piazza] account for the class.  
+  * 26 Sep 2011: Background survey and lecture 1 slides are posted  
+  * 4 Oct 2011: HW #2 is now posted; due 11 Oct 2011 in class  
+  * 5 Oct 2011: Office hour locations have moved (to rooms with more board space and seats)  
+  * 7 Oct 2011: HW #1 is graded. Scores: mean = 64/70, std dev = 5.4. Hours: mean = 5.9, std dev = 3.0  
+  * 12 Oct 2011: HW #3 is now posted  
+  * 18 Oct 2011: HW #4 is now posted  
+  * 18 Oct 2011: HW #2 is graded. Scores: mean = 63/70, std dev = 5.3. Hours: mean = 8.2, std dev = 4.3  
+  * 25 Oct 2011: HW #5 is posted as well as the midterm [http://www.surveymonkey.com/s/ZSD9TK6 course survey]  
+  * 1 Nov 2011: HW #6 is now posted  
+  * 8 Nov 2011: HW #7 is posted.  
+  
+  [[Category:Courses]] 
Latest revision as of 04:55, 27 June 2021
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
 5 Dec 2011: Partial solutions for HW #9 are posted; will try to post additional solutions by Tue (6 Dec) evening.
 2 Dec 2011: The final exam is available for pickup outside 107 Steele. (Make sure to get the right exam! The ACM/EE 116 and CDS 110 exams look similar.)
 1 Dec 2011: HW #8 is graded. Scores: mean= 46/50, std dev = 6.1. Hours: mean=8.5, std dev = 2.9 (median=8)
 27 Nov 2011: Homework deadlines and office hours for this week:
 Office hours: Tue (29 Nov), 34 pm and Thu (1 Dec) 79 pm on first floor Annenberg
 Homework deadlines: HW #8 extensions are due by 29 Nov, 10:30 am. HW #9 is due 2 Dec (Fri) @ 5 pm (autoextension)
 Turn in homework in class or to the box outside 109 Steele
 21 Nov 2011: HW #7 is graded. Scores: mean=45/50, std dev = 6.7. Hours: mean = 11.8, std dev = 5.5 (median = 10)
 14 Nov 2011: HW #6 is graded. Scores: mean=43/50, std dev = 6.2. Hours: mean = 10.5, std dev = 4.5 (median = 9.5)
 7 Nov 2011: HW #5 is graded (except extensions). Scores: mean = 42/50, std dev = 5.6. Hours: mean = 10.7, std dev = 4.3
 31 Oct 2011: HW #4 is graded. Scores: mean = 46/50, std dev = 5.2. Hours: mean = 7.7, std dev = 3.5
 24 Oct 2011: HW #3 is graded. Scores: mean = 44/50, std dev = 5.1. Hours: mean = 6.2, std dev = 3.3
Lecture Schedule
W  Date  Topic  Reading  Homework 
1 
27 Sep 29 Sep 
Events, probabilities and random variables

G&S, Chapters 1 and 2, Appendices
Gubner, Chapters 1 and 2 

2 
4 Oct 6 Oct 
Discrete random variables

G&S, Chapter 3
Gubner, Chapter 23 

3 
11 Oct 13 Oct 
Continuous random variables

G&S, Chapter 4
Gubner, Chapters 4, 5 

4 
18 Oct 20 Oct 
Generating functions and their applications

G&S, Chapter 5
Gubner, Chapters 4, 5 

5 
25 Oct 27 Oct 
Convergence of random variables/processes

G&S Chapter 7
Gubner, Chapters 13, 14 

6 
1 Nov 3 Nov 
Introduction to random processes

G&S Chapters 8


7 
8 Nov 10 Nov* 
Stationary processes and renewal processes

G&S Chapter 9 and 10


8 
15 Nov* 17 Nov 
Stochastic systems

G&S + Course notes
Gubner, Chapter 10 

9 
22 Nov 29 Nov 
Diffusion processes

G&S Chapter 13
Gubner, Chapter 11


10 
1 Dec  Course review
Review for final (watch out for typos!) 
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 (or the mailbox outside 109 Steele) 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.
In addition, all students in the class must sign in at office hours at least once in the first three weeks of the course, or sign up for Piazza and post at least one question or response.
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 (eg, Course Hero, instructors manuals, other course web sites) is not allowed. All solutions that are handed should reﬂect your understanding of the subject matter at the time of writing.
 ACM/EE 116 Piazza page  an online collaboration site for the course has been established using Piazza. This site can be used to post questions and give responses (from students or instructors). Postings can be anonymous if desired.
No collaboration is allowed on the ﬁnal exam.
Old Announcements
 17 Jul 2011: web page creation
 22 Sep 2011: added TAs and office hours. Established a Piazza account for the class.
 26 Sep 2011: Background survey and lecture 1 slides are posted
 4 Oct 2011: HW #2 is now posted; due 11 Oct 2011 in class
 5 Oct 2011: Office hour locations have moved (to rooms with more board space and seats)
 7 Oct 2011: HW #1 is graded. Scores: mean = 64/70, std dev = 5.4. Hours: mean = 5.9, std dev = 3.0
 12 Oct 2011: HW #3 is now posted
 18 Oct 2011: HW #4 is now posted
 18 Oct 2011: HW #2 is graded. Scores: mean = 63/70, std dev = 5.3. Hours: mean = 8.2, std dev = 4.3
 25 Oct 2011: HW #5 is posted as well as the midterm course survey
 1 Nov 2011: HW #6 is now posted
 8 Nov 2011: HW #7 is posted.