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 electrical engineering. 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
- Welcome to EES315! Feel free to look around this site.
- Main materials are posted in Google Classroom.
- Log in with your "@g.siit.tu.ac.th" email account to access the site.
- Your account should have been added automatically by the computer center.
- This site serves as an accompanying web site.
General Information
- Instructor: Asst. Prof. Dr.Prapun Suksompong (prapun@siit.tu.ac.th)
- Office Hours: See Google calendar below.
- Lectures: See Google calendar below.
- References
- [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.
- 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. 6E Call No. QA273 R83 2002
- A first course in probability / Sheldon Ross. Call No. QA273 R83 1976
- A first course in probability / Sheldon Ross. 9E
- Probability models, introduction to / Sheldon M. Ross. 10E Call No. QA273 R84 2010
- Probability models, introduction to / Sheldon M. Ross. 6E Call No. QA273 R84 1997
- Probability models, introduction to / Sheldon M. Ross. 11E
Handouts and Course Material
- Lecture notes are posted in Google Classroom
- Part I: Introduction, Set Theory, Classical Probability theory, and Combinatorics
- Chapter 1: Probability and You
- Chapter 2: Set Theory
- Chapter 3: Classical Probability
- Chapter 4: Enumeration / Combinatorics / Counting
- Part II: Kolmogorov's Formal Probability Theory and Event-Based Probability Theory
- Chapter 5: Probability Foundations
- Chapter 6: Event-based Independence and Conditional Probability
- Section 6.1: Conditional Probability
- 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)
- 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)
- Section 6.2: Event-based Independence
- Section 6.3: Bernoulli Trials
- Section 6.1: Conditional Probability
- Part III: Discrete Random Variables
- Chapter 7: Random Variables [Posted @ 11AM on Oct 12]
- Chapter 8: Discrete Random Variables [Posted @ 11AM on Oct 12]
- Sections 8.1-8.2: PMF and CDF
- Section 8.3-8.4: Families of Discrete Random Variables
- Chapter 9: Expectation and Variance [Posted @ 2PM on Nov 3]
- References: [Y&G] Chapter 2
- Part IV: Continuous Random Variables
- Chapter 10: Continuous Random Variables [Posted @ 2PM on Nov 3]
- 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
- Part V: Advanced Topics
- Chapter 11: Multiple Random Variables
- 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
- Chapter 12: Limiting Theorems (LLN and CLT)
- Chapter 13: Three Types of Random Variables
- Appendix
Calendar
More References
- 10-page probability cheatsheet compiled from Harvard's Introduction to Probability course
- Allen B. Downey, Think Stats: Exploratory Data Analysis, O'Reilly Media, 2014 (free book)
- Allen B. Downey, Think Bayes: Bayesian Statistics in Python, O'Reilly Media, 2013 (free book)
- 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
- Henk Tijms, Probability: A Lively Introduction, Cambridge University Press, 2017, Call No. QA273 P278 1962
- 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
- 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).
- 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
- 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
- Michael Iori's Blackjack in MATLAB
- Poker
- 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