ECS315: Probability and Random Processes

Everything we do, everything that happens around us, obeys the laws of probability. We can no more escape them than we can escape gravity... "Probability," a philosopher (Bishop Butler) once said, "is the very guide of life." We are all gamblers who go through life making countless bets on the outcome of countless actions.

Every field of science is concerned with estimating probability. A physicist calculates the probable path of a particle. A geneticist calculates the chances that a couple will have blue-eyed children. Insurance companies, businessmen, stockbrokers, sociologists, politicians, military experts - all have to be skilled in calculating the probability of the events with which they are concerned.

[Gardner, 1986]

Synopsis

Probability theory is the branch of mathematics that tells us how to estimate degrees of probability. If an event is certain to happen, it is given a probability of 1. If it is certain not to happen, it has a probability of 0.

This course introduces the principles of probability and random processes to undergraduate students in electronics and communication. The topics to be covered include random experiments, events, probability, discrete and continuous random variables, probability density function, cumulative distribution function, functions of random variables, expectations, law of large numbers, central limit theorem, introduction to random processes, Gaussian random process, autocorrelation and power spectral density.

Announcements

• Information regarding the final exam [Updated @ 5PM on Dec 14]
  • Date: 22 Dec 2016
  • Time: 13:30 - 16:30
  • ROOM: BKD 3214 and 3207
  • Basic calculators, e.g. FX-991MS, are permitted.
  • Closed book. Closed notes.
  • 9 pages ( including the cover page)
  • To save time, read the cover page posted here before going into the exam room.
    
  • 11+1 = 12 questions. (20+18+6+4+9+8+2+3+2+20+7+1)
  • Closed book. Closed notes.
  • Two A4 sheets allowed.
    • The first sheet is your midterm study sheet.
      • May add more formulas on the remaining side or in the remaining space(s).
      • Q: Can I make a brand new study sheet?
        A: No.
        However, if you think the old one is in a bad shape (falling apart), you can use a photocopy of your own. (Reduction in size is not allowed though)
      • Q: What can I do if I lose my study sheet?
        A: Dr.Prapun can print out a scanned copy for you. (The writing won’t be as crisp as the original one but it’s better than nothing.)
      • Q: I think the midterm study sheet (and the thing I wrote on it) is cursed (making me get poor score); I don’t want to see or use anything on it anymore. What can I do?
        A: You may bring a brand new sheet for the final exam. However, you can only use one side of it.
    • The second sheet must contain the Phi/Q tables
      • Distributed in class on Dec 7.
      • May reprint if necessary but do not reduce the size.
      • May add more formulas on the remaining side.
• Basically, you have two whole pages to write down
• Same rules as the midterm:
  • Must be hand-written in your own handwriting (except for the Phi/Q tables).
  • No small pieces of paper notes glued/attached on top of it.
  • Indicate your name and ID on the upper-right corner of the sheet (in portrait orientation).
  • Do not modify (,e.g., add/underline/highlight) content on the sheet inside the exam room.
• Submit both of your A4 sheets with your exam.
• Cover all the materials that we discussed in class and practice in the HWs.
• Material Distribution (score-wise): 13(CH7&8) + 18 (CH9) + 43(CH10) + 21(CH11) + 5(CH12&13)
• For your studying pleasure....
• All post-midterm annotated notes combined in one pdf file.
• All post-midterm HWs and their solutions
  • Checked HWs can be picked up in front of the EC office on the 6th floor.
• All post-midterm exercises and their solutions
• Graded exercises are posted on the SIIT Lecture Note System
• If you have valid reason for missing class on the day that we have exercise, please indicate the date, exercise number, and the reason in the second self-evaluation form. Make sure that you also submit/email supporting document/evidence to me (if you haven't done so).
• All post-midterm slides
• 2010 Midterm Exam
  • Annotated version from 2015
  • Annotated version from 2014
  • Solution
• 2013 Midterm Exam
  • Annotated version from 2015
  • Annotated version from 2014
• 2013 Final Exam
  • You may skip the following parts because they are not covered this year: 6, 7, 8c
  • Annotated version from 2015
  • Annotated version from 2014
• 2011 Final Exam
  • We covered quite a different range of topics there because the curriculum was different. However, you can find some relevent problems in there as well.
  • Many of the relevant porblems have already been included as exercises in the current lecture notes.
• 2010 Final Exam
  • We covered quite a different range of topics there because the curriculum was different. However, you can find some relevent problems in there as well.
• Information regarding midterm exam
  • Result Announcement [Posted @ 5PM on Oct 20]
  • Check this course website regularly for breaking news about the midterm.
  • Date: 13 Oct 2016
    
  • TIME: 13:30-16:30
  • Room: BKD 2506 and 2501-2
  • 9 pages + cover page
  • To save time, read the cover page posted here before going into the exam room.
    
  • 13+1 = 14 questions. (12+5+4+12+8+10+10+5+12+2+9+6+4+1)
  • Closed book. Closed notes.
  • (1 pt) One A4 page allowed.
    • Must be hand-written in your own handwriting.
    • No small pieces of paper notes glued/attached on top of it.
    • Indicate your name and ID on the upper right corner of the sheet (in portrait orientation).
    • Do not modify (,e.g., add/underline/highlight) content on the sheet inside the exam room.
    • Make sure that another side is blank. This will be used for the final exam.
    • Submit your A4 sheet with your exam. (You can get it back from me after the midterm is graded.)
    • Q: I don't need any formulas. What should I do?
      A: Bring in and submit a blank sheet of paper with your name and ID. Note that you can still only use one side on the final exam.
      
    • Violating the above instructions will cost you 10 pt.
  • Basic SIIT-approved calculators, e.g,. FX-991MS, are permitted, but borrowing is not allowed.
• Cover all the materials that we discussed in class and practice in the HWs.
• Material Distribution (score-wise): 12 (CH2)+6 (CH3)+20(CH4)+14.5(CH5) +18.5(Sec6.1)+ 11(Sec6.2)+ 12(Sec6.3)+ (CH7)5
• For your studying pleasure....
• All pre-midterm annotated notes combined in one pdf file.
• All pre-midterm HWs and their solutions
  • Checked HWs can be picked up in front of the EC office on the 6th floor.
• All pre-midterm exercises and their solutions
• Graded exercises are posted on the SIIT Lecture Note System
• All pre-midterm slides
• Sample Exams:
  • 2010 Midterm Exam
    • You may skip the following parts because we haven't studied the corresponding topics yet in class: 5-9
    • Annotated version from 2015
    • Annotated version from 2014
    • Solution
  • 2013 Midterm Exam
    • You may skip the following parts because we haven't studied the corresponding topics yet in class: 6bii, 6c, 7
    • Annotated version from 2015
    • Annotated version from 2014
• For those who have already obtained the textbook [Y&G], this table gives the corresponding positions (if any) in the textbook that correspond to the material dfiscussed in class.
• During Sep 7 - Sep 15, we will have only the afternoon lectures.
• This site can be accessed via ecs315.prapun.com.

• Welcome to ECS315! Feel free to look around this site.

General Information

• Instructor: Asst. Prof. Dr.Prapun Suksompong (prapun@siit.tu.ac.th)
  • Office: BKD, 6th floor of Sirindhralai building
  • Office Hours: T 9-10, W 14:20-15:20, R 9-10
    • Also shown in the Google calendar below.
• Course Syllabus [Posted @ 11:30AM on Aug 13]
• Textbook: [Y&G] R. D. Yates and D. J. Goodman, Probability and Stochastic Processes: A Friendly Introduction for Electrical and Computer Engineers, 2nd ed., Wiley, 2004.
  • Call No. QA273 Y384 2005. ISBN: 978-0-471-27214-4
  • Student Companion Site
• References
• Probability and probabilistic reasoning for electrical engineering / Terrence L. Fine. Call No. QA273 F477 2006
• Probability and random processes for electrical engineering / Alberto Leon-Garcia. Call No. TK153 L425 1994
• Free textbook: Introduction to Probability by Charles M. Grinstead and J. Laurie Snell
• Henk Tijms. Understanding Probability: Chance Rules in Everyday Life. Cambridge University Press, 3rd edition, 2012. Call No. QA273 T48 2012
• Probability, random variables, and stochastic processes / Athanasios Papoulis, S. Unnikrishna Pillai. Call No. QA273 P2 2002
  • Probability, random variables, and stochastic processes / Athanasios Papoulis. Call No. QA273 P2 1991
• A first course in probability / Sheldon Ross. Call No. QA273 R83 2002
  • A first course in probability / Sheldon Ross. Call No. QA273 R83 1976
• Probability models, introduction to / Sheldon M. Ross. Call No. QA273 R84 1997

Handouts and Course Material

• Slides: Course Introduction [Posted @ 1AM on Aug 14]
  • Full version [Posted @ 4PM on Aug 17]
• Part I: Introduction, Set Theory, Classical Probability theory, and Combinatorics [Posted @ 1AM on Aug 14]
  • Section 1: Probability and You
  • Annotated notes [Posted @ 4:30PM on Aug 18]
  • Slides [Posted @ 3:30PM on Aug 24]
  • Section 2: Review of Set Theory
  • Annotated notes [Posted @ 4:30PM on Aug 19]
  • Slides [Posted @ 3:30PM on Aug 24]
  • Section 3: Classical Probability
  • Annotated notes [Posted @ 4:30PM on Aug 19; Updated @ 3:30PM on Aug 24]
  • Slides [Posted @ 3:30PM on Aug 24]
  • Section 4: Enumeration / Combinatorics / Counting
  • Annotated notes [Posted @ 3:30PM on Aug 24; Updated @5PM on Aug 25, @5PM on Aug 31, and @ 5:30PM on Sep 1]
  • Slides [Posted @ 3:30PM on Aug 24; Updated @5PM on Aug 31and @ 5:30PM on Sep 1]
  • Exercise 1 Solution [Posted @ 5:30PM on Sep 1]
  • Exercise 2 Solution [Posted @ 10PM on Sep 28]
• Part II: Kolmogorov's Formal Probability Theory and Event-Based Probability Theory
• Section 5: Probability Foundations [Posted @ 9AM on Aug 30]
• Annotated notes [Posted @ 5:30PM on Sep 2; Updated @ 11:30PM on Sep 2 and @11PM on Sep 9]
• Slides [Posted @ 11PM on Sep 9]
• Section 6.1: Conditional Probability [Posted @ 9AM on Aug 30]
  • Annotated notes [Posted @11PM on Sep 9; Updated @ 9:30PM on Sep 15, @3PM on Sep 21, and @ 5PM on Sep 22]
  • Slides [Posted @ 11PM on Sep 9; Updated @ 3PM on Sep 21 and @ 5PM on Sep 22]
  • "The Theory That Would Not Die, How Bayes' Rule Cracked the Enigma Code, Hunted Down Russian Submarines & Emerged Triumphant from Two Centuries of Controversy" (Yale University Press, 2011)
  • A book review (The New York Times)
  • An article (Scientific American)
  • An interview (BBC Radio Wales' Sunday Supplement)
    
• Section 6.2: Event-based Independence [Posted @ 9AM on Aug 30]
• Annotated notes [Posted @ 5PM on Sep 22; Updated @ 3:30PM on Sep 28]
• Slides [Posted @ 8PM on Sep 29]
• Section 6.3: Bernoulli Trials[Posted @ 9AM on Aug 30]
• Annotated notes [Posted @ 3:30PM on Sep 28; Updated @ 8PM on Sep 29]
• Slides [Posted @ 8PM on Sep 29]
• Part III: Discrete Random Variables
• Section 7: Random Variables [Posted @9PM on Sep 26]
• Annotated notes [Posted @ 8PM on Sep 29 and @ 9PM on Oct 19]
• Sections 8.1-8.2: Discrete RV: PMF and CDF [Posted @ 9PM on Sep 26]
• Annotated notes [Posted @ 9PM on Oct 19; Updated 4PM on Oct 26]
• Slides [Posted @ 5PM on Oct 20]
• Exercise 3 Solution [Posted @ 10PM on Nov 12]
• Sections 8.3-8.4: Families of Discrete Random Variables [Posted @ 9PM on Oct 17]
• Annotated notes [Posted @ 4PM on Oct 26; Updated @ 5:30PM on Oct 27]
• Slides [Posted @ 4PM on Oct 2]
• Exercise 4 Solution [Posted @ 10PM on Nov 12]
• Section 9: Expectation and Variance [Posted @ 9PM on Oct 17]
• Annotated notes [Posted @ 5:30PM on Oct 27; Updated @ 9PM on Nov 2, @ 5PM on Nov 3, and @ 4PM on Nov 9]
• Slides [Posted @ 5PM on Nov 3]
• Exercise 5 Solution [Posted @ 10PM on Nov 12]
• References: [Y&G] Chapter 2
• Part IV: Continuous Random Variables
  • Sections 10.1-10.3: pdf [Posted @ 2PM on Nov 1]
  • Annotated notes [Posted @ 4PM on Nov 9; Updated @ 8:30PM on Nov 10, @ 4PM on Nov 16, and @4PM on Nov 18]
  • Exercise 6 Solution [Posted @ 10PM on Nov 12]
  • Sections 10.4-10.5: More on continuous RVs [Posted @ 9AM on Nov 9]
  • Annotated notes [Posted @4PM on Nov 18; Updated@ 4:30PM on Nov 23, @5PM on Nov 24, and @ 5PM on Dec 1]
  • Slides [Posted @ 5PM on Dec 1]
  • References
    • From Discrete to Continuous Random Variables: [Y&G] Sections 3.0 to 3.1
    • PDF and CDF: [Y&G] Sections 3.1 to 3.2
    • Expectation and Variance: [Y&G] Section 3.3
    • Families of Continuous Random Variables: [Y&G] Sections 3.4 to 3.5
    • SISO: [Y&G] Section 3.7; [Z&T] Section 5.2.5
• Part V: Multiple Random Variables
  • Sections 11.1-11.2 [Posted @ 9:30PM on Nov 22]
    • Annotated notes [Posted @ 5PM on Dec 1; Updated 4PM on Dec 7]
  • Sections 11.3-11.6 [Posted @ 9:30PM on Nov 22]
  • Annotated notes [Updated 4PM on Dec 7 and @ 5PM on Dec 8]
  • Slides [Posted @ 5PM on Dec 1; Updated @ 5PM on Dec 8]
  • References:
    • A Pair of Random Variables: [Y&G] Sections 4.1 to 4.3 and Section 4.10
    • Extending the Definitions to Multiple RVs: [Y&G] Sections 5.1 to 5.4
    • Function of Discrete Random Variables: [Y&G] Section 4.6 (Theorem 4.9)
    • Expectation of function of discrete random variables: [Y&G] Sections 4.7 and 6.1
    • Linear Dependence: [Y&G] Section 4.7
• Part VI: Limiting Theorems
  • Sections 12.1-12.2 (LLN and CLT) [Posted @ 9PM on Dec 5]
    • Annotated notes [Posted @ 5PM on Dec 8]
    • Slides [Posted @ 5PM on Dec 8]
• Part VII: Additional Topics
  • Section 13  [Posted @ 9PM on Dec 5]
    • Annotated notes [Posted @ 5PM on Dec 8]

Problem Set

1. HW 1 (Due: Aug 30)
   • Please read the instruction carefully!
   • Solution [Posted @ 11PM on Sep 5]
2. HW2 (Due: Sep 6)
   • Solution [Posted @ 3PM on Sep 7]
3. HW3 (Due: Sep 13)
   • Solution [Posted @ 9AM on Sep 20]
4. HW4 (Due: Sep 20
   • Solution [Posted @ 9PM on Sep 26]
5. HW5 (Due: Sep 27)
   • Some commments added in the tutorial on Sep 30
   • Solution [Posted @ 10PM on Sep 28]
6. HW6 (Not Due )
   • Solution [Posted @ 9PM on Sep 29]
7. Self-Evaluation Form (Due: Oct 13)
8. HW7 (Due: Oct 25)
   • Solution [Posted @ 4PM on Oct 26]
9. HW8 (Due: Nov 1)
   • Solution [Posted @ 9PM on Nov 3]
10. HW9 (Due: Nov 8)
    • Solution [Posted @ 10:30PM on Nov 12]
11. HW10 (Due: Nov 15)
    • Solution [Posted @ 4:30PM on Dec 28]
12. HW11 (Due: Nov 22)
    • Solution [Posted @ 4:30PM on Dec 28]
13. HW12 (Due: Nov 29)
    • Solution [Posted @ 4:30PM on Dec 28]
14. HW13 (Due: Dec 6)
    • Solution [Posted @ 4:30PM on Dec 28]
15. HW14 (Not Due)
    • Solution [Posted @ 4:30PM on Dec 28]
    • P_XY_EVarCov.m
    • P_XY_marginal_2
16. Self-Evaluation Form (2) (Due: Dec 22)

• HW Score

Calendar

Reading Assignment

1. Section 1.2 in the lecture notes
2. 2.5 in the lecture notes

More References

• Older version of the textbook: Probability and stochastic processes : a friendly introduction for electrical and computer engineers / Roy D. Yates, David J. Goodman. Call No. QA273 Y384 1999
• Encyclopædia Britannica Online: Probability Theory
• Random signals for engineers using MATLAB and Mathcad / Richard C. Jaffe. Call No. TK5102.9 J34 2000
• Davenport, W.B., Probability and Random Processes, McGraw-Hill, New York, 1970. (Excellent introductory text.)
• Feller, W., An Introduction to Probability Theory and its Applications, Vols. 1, 2, John Wiley, New York, 1950. (Definitive work on probability—requires mature mathematical knowledge.)
  • Call No. QA273 F37 1966
• Peter Olofsson, Probabilities The Little Numbers That Rule Our Lives, Wiley, 2006
  
• Stochastic processes / Sheldon M. Ross. Call No. QA274 R65 1996
• Stochastic processes / Emanuel Parzen. Call No. QA273 P278 1962
• MATLAB Primer, 8th edition T. A. Davis. CRC Press, 2010.
  • Seventh Edition by T. A. Davis and K. Sigmon: Call No. QA297 D38 2005
  • Third Edition by K. Sigmon (Free)
  • Second Edition by K. Sigmon (Free)

Misc. Links

• Video: Probability 101
• More information about theMonty Hall Problem
  • Video: The Monty Hall Problem Explained
• Video: The Monty Hall Problem
• Video: Monty Hall Problem: Numb3rs and 21
• Paper: Monty Hall, Monty Fall, Monty Crawl
• Articles: How Random is the iPod Shuffle? [HowStuffWorks]; Is iTunes’ Shuffle Mode Truly Random?[About.com]; iTunes: Just how random is random?[CNET.com.au, 2007]; My IPod for a Random Playlist [wired.com, 2005];
• Video: It *could* just be coincidence
• MV: Bill Nye the Science Guy - "50 Fifty"
• Video: Chevalier de Mere's Scandal of Arithmetic
• Free educational software: Orstat2000
  • Originally developed to promote probability and operations research in the senior forms of Dutch high schools (and early college).
  • Contain modules for coin-tossing, central limit theorem, etc.
• Probability review from MATH REVIEW for Practicing to Take the GRE General Test
• Video: Mlodinow’s talk @ Google
• Video: How many ways can you arrange a deck of cards? (There Are More Ways To Arrange a Deck of Cards Than Atoms on Earth)
  • Provide nice animation explaining permutation and factorial.
  • "Any time you pick up a well shuffled deck, you are almost certainly holding an arrangement of cards that has never before existed and might not exist again."
• Video: The Binomial Distribution / Binomial Probability Function
• Article: Greenlighting Movies: A High-Risk Game
• Video: The Poisson Distribution
• If you want to experience probability theory at a more advance level, one standard textbook that you can refer to is "Probability: Theory and Examples" by Prof. Durrett. Currently, the 4th edition of the textbook is available online.
• Video: Peter Donnelly shows how stats fool juries (same clip on youtube)
• Video: Lies, damned lies and statistics (about TEDTalks): Sebastian Wernicke on TED.com
• Article about clinical/medical decision making: Jill G. Klein, "5 pitfalls in diagnosis and prescribing: psychological biases that can lead to poor judgement," 2005.
  • Related topics: Pitfall #1 (representatiove heuristic), Pitfall #2(availability heuristic), and Pitfall #5 (illusory correlation).
    
• The Median Isn't the Message by Stephen Jay Gould
• Video: Daniel Kahneman: The riddle of experience vs. memory
  • Happiness Can Be Bought For About $60,000 Per Year
• Articles on risk intelligence
  • Dylan Evans, How to Beat the Odds at Judging Risk, The Wall Street Journal, May, 2012
  • Alison George, What Gamblers and Weather Forecasters Can Teach Us About Risk: An interview with the creator of the "risk quotient" intelligence scale., pp 30-31, New Scientist, May 19, 2012
• Generation of random numbers
  • Article: Park, S.K., and K.W. Miller. "Random Number Generators: Good Ones Are Hard to Find." Communications of the ACM, 31(10):1192–1201. 1998.
  • Article: Tom McNichol, "Totally Random: How two math geeks with a lava lamp and a webcam are about to unleash chaos on the Internet"
  • Article: C. Moler, Random thoughts, "10^435 years is a very long time", MATLAB News and Notes, Fall, 1995
  • Article: Ziggurat algorithm generates normally distributed random numbersdescribing the ziggurat algorithm introduced in MATLAB version 5.
• Games of chance
  • Poker
    • Paper: Cheung, Y. L. "Why Poker is Played with Five Cards." Math. Gaz. 73, 313-315, 1989.
    • Tim Farajian's Texas Hold'Em Poker Analyzer in MATLAB
      • Allow a user to simulate different scenarios in a Texas Hold'Em game.
      • Automatically simulate as many hands as you would like, and display winning probabilities or expected returns.
  • Blackjack
    • Cleve Moler's Blackjack in MATLAB + article
      • Paper: Simulating Blackjack with MATLAB
    • Michael Iori's Blackjack in MATLAB
• Quotations about Statistics
• Video: Statistics - Dream Job of the next decade
• Virtual Laboratories in Probability and Statistics
• Google Calculator (Cheat Sheet)
• Sometimes the easiest way to get information on a counting problem is to compute a few small values of a function, then look for a match at the sequence server; if you find a hit, you can sometimes get citations to the literature.
• Prapun's Notes on Probability Theory (Cornell Version)
• MATLAB
  • MIT OpenCourseWare > Electrical Engineering and Computer Science > 6.094 Introduction to MATLAB (January (IAP) 2009)
  • Fundamentals: Academic Tutorial
  • Video: Controlling Random Number Generation
  • Free online book: Cleve Moler, Experiments with MATLAB, 2008
  • Free textbook: Cleve Moler,Numerical Computing with MATLAB, 2004
• Learn the Greek Alphabet in less than 10 minutes
• The Greek Alphabet Song