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 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 blueeyed 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
 All of your HWs are graded and put in the HW box. Please come and pick them up at your earliest convenience.
 Scores for HW6 to HW10
 Information about the Final Exam
 13 Oct 2010
 09:00  12:00
 BKD 3215
 8 Questions: 31 pt + 15 pt + 22 pt + 27 pt + 3 pt + 1 pt + 1 pt + 1 bonus pt.
 12 Pages: 10 pages + 1 cover sheet + 1 blank sheet
 Here is the first page of the exam.
 Closed book / Closed notes
 You will need a basic calculator e.g. FX991MS.
 It can cover all the materials that we discussed in class and practice in the HWs.
 In particular, I expect that you know a little bit about LLN and CLT in 4a because we have talk about them a little bit in class.
 In general, the topics that we spent a lot of time in class have high probability of showing up on the exam.
 I could ask something that I have never defined in class but, in such a case, I will give you the exact definition on the exam itself.
 One A4 sheet allowed.
 Must be handwritten.
 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
 Submit your formula sheet with your final exam. (You can get it back from me next semester.)
 More information may be posted.
 Scores for Quiz 5 and Quiz 6
 Scores for Quiz 4
 Scores for Quiz 3
 Midterm:
 9 Questions
 10 pages + 1 cover sheet + 1 formula sheet
 Closed book / Closed notes
 You will need a basic calculator e.g. FX991MS.
 Here is the formula sheet created by you during the last lecture before the midterm.
 Here is the first page of the exam.
 The exam covers every topics that we have studied.
 A pdf file combining (almost) all of the handwritten notes is posted.
 Scores
 Solution (draft)
 Scores for HW14 + Quiz 12. (The leftmost column contains the last three digits of your student IDs.)
 There will be NO class on Wednesday, July 21. The makeup class will be the first period (910:20AM) on Friday (July 23). [Posted @ 1PM on July 19]
 We will have the midterm on the ORIGINAL announced date. (6 Aug 2010 TIME 09:00  12:00 BUILDING IT & MT ROOM BKD 2605). Sorry for the confusion and for giving you some hope that the date might change. [Posted @ 1PM on July 19]
 A basic RSS feed is created to track and inform updates [Posted @ 5PM on Jun 25]
 This site can be access via prapun.com/ecs315 [Posted @ 5PM on Jun 25]
 Welcome to ECS315! Feel free to look around this site. [Posted @ 5PM on Apr 1]
General Information
 Instructor: Dr. Prapun Suksompong (prapun@siit.tu.ac.th)
 Course Syllabus
 Class
information
 Office Hours
 Room: BKD36017
 TBA
 Room: ETU (1st floor, Rangsit campus)
 Thursday 16:1517:00
 Please feel free to ask any question or express any concern after class.
 Textbook: 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: 9780471272144
 References
 Probability and stochastic processes : a friendly introduction for electrical and computer engineers / Roy D. Yates, David J. Goodman. Call No. QA273 Y384 2005
 Probability and probabilistic reasoning for electrical engineering / Terrence L. Fine. Call No. QA273 F477 2006
 Probability and random processes for electrical engineering / Alberto LeonGarcia. Call No. TK153 L425 1994
 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
 Random signals for engineers using MATLAB and Mathcad / Richard C. Jaffe. Call No. TK5102.9 J34 2000
 Introduction to Probability by Grinstead and Snell: online version
 Stochastic processes / Sheldon M. Ross. Call No. QA274 R65 1996
 Stochastic processes / Emanuel Parzen. Call No. QA273 P278 1962
 Probability theory and its applications, an introduction to / William Feller Call No. QA273 F37 1966
 Davenport, W.B., Probability and Random Processes, McGrawHill, 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.)
 Free textbooks
 Introduction to Probability by Charles M. Grinstead and J. Laurie Snell
Handouts and Course Material
 Notes covering 75% of topics that will be discussed in this course: SIIT version (pdf updated June 22, 2010), Cornell Version (old)
 Try not to print this out because it will be updated fequency.
 Probability Puzzles [Gardner, 1986] is available on the SIIT Lecture Note System
 Our course is listed as "ECS3151:Probability and Random Processes (Dr.Prapun Suksompong)"
 Slides from Lecture 1
 Chapter 1 of the textbook is available on the SIIT Lecture Note System
 Slides from Lecture 2 [Posted at 2 PM on June 18]
 Notes from Lecture 2 [Posted at 2 PM on June 21]
 Slides from Lecture 3 [Posted at 2 PM on June 23]
 Notes from Lecture 3 with updated notes from Lecture 2
 Slides from Lecture 4 + Notes from Lecture 4 [Posted at 5 PM on June 25]
 Updated Notes from Lecture 4. Now it includes more explanation about the "bars and stars" argument. [Posted at 9:30 AM on June 28]
 Slides from Lecture 5 + Notes from Lecture 5 [Posted at 2 PM on June 30]
 Slides from Lecture 6 + Notes from Lecture 6 [Posted at 4:30 PM on July 2]
 Slides from Lecture 7 + Notes from Lecture 7 [Posted at 5 PM on July 7]
 Notes from Lecture 8: Independence (updated July 14)
 For notes on random variables, use the one from Lecture 9.
 Compound Chance Experiment and Bernoulli Trials
 Notes from Lecture 9: Discrete random variables[Updated at 10 AM on July 19]
 This is an updated note from Lecture 8.
 Notes from Lecture 10: Commonly used discerete random variables[Posted at 10 AM on July 19]
 Notes from Lecture 1112: [Posted at 4:30M on July 23]
 Notes from Lecture 13[Posted at 2:30 PM on July 28]
 Notes from Lecture 14[Posted at 5:30 PM on July 30]
 Here is the original pdf file that I write comments on in Lectures 13 and 14. [Posted at 2:30M on Aug 3]
 Here is an updated version. [Posted at 12AM on Aug 5]
 Notes from Lecture 15 [Posted at 5PM on Aug 11]
 Summary of Lecture 15 [Posted at 2PM on Aug 18]
 Notes from lecture 16 [Posted at 2PM on Aug 18]
 Handwritten notes from lecture 16 [Posted at 10PM on Aug 19]
 Handwritten notes from lecture 17 [Posted at 10:30PM on Aug 23]
 Notes from lecture 17 [Posted at 10:30PM on Aug 23]
 Handwritten notes from lecture 18 [Posted at 6:30PM on Sep 1]
 Notes from lecture 18 [Posted at 6:30PM on Sep 1]
 Handwritten notes from lecture 19 [Posted at 5PM on Sep 3]
 Slides from lecture 20 + Handwritten notes from lecture 20 [Posted at 10PM on Sep 8]
 Notes from lecture 21 [Posted at 5:00PM on Sep 10, updated after Lecture 23 at 2PM on Sep 15, updated again after Lecture 24 at 12PM on Sep 20]
 MATLAB file for generating histogram from samples of Gaussian r.v. and then use it to approximate the pdf. (Also need this file for plotting to work.)
 OneNote Notes from Lecture 23 (Review + Quiz 7 Solution) [Posted at 2PM on Sep 15]
 Notes 3A [Posted at 11:30PM on Sep 14, updated after lecture 25 at at 12PM on Sep 20]
 MATLAB Code for the BillandLil Example
 MATLAB code to generate samples from bivariate Gaussian distribution and its joint pdf.
 Notes 3B [Posted at 5:30PM on Sep 21, updated at 5PM on Sep 24]
 Notes 3C [Posted at 11PM on Sep 24, updated at 4PM on Sep 29]
 Solution for Quiz 8.
 Note 4A [Posted at 11PM on Sep 28]
 Note 4B [Posted at 11PM on Sep 30]
Problem Set
 HW 1 (Due: June 29)
 Note: The correct version of the HW has just been uploaded @ 9PM on Thursday. A couple of questions are different.
 Solution for HW1
 HW2 (Due: July 9 @10:39 AM in class)
 Note: The version with updated due date of the HW is posted on July 4 @ 3:30 PM
 Solution for HW2
 Correction: The last conditional probability on page 27 is P(HU).
 HW3 (Due: July 15)
 Q7.b.ii: change "Show that" to "Check whether".
 Solution for HW3
 HW4 (Due: July 22)
 Q4: Change lambda to alpha. (Usually, Poisson r.v. uses lambda as its parameter. In class, I use alpha. There are reasons for not using lambda which we shall revisit later on in the lecture.)
 Q6: The mode may not be unique. If there are multiple x which attains the maximum pmf value, find all of them.
 Solution for HW4 (draft)
 Scores for HW14 + Quiz 12. (The leftmost column contains the last three digits of your student IDs.)
 HW5 with Solution (Not due) (Updated on Aug 3 @ 2:30 PM)
 HW6
(Due: Aug 27) [Fixed on August 24 @ 9PM]
 For Q7, here are the questions from [Yates & Goodman, 2005] [Fixed on August 21 @ 3PM]
 Solution for HW6
 MATLAB codes
 Solution for questions from [Y&G]
 HW7
(Due: Sep 9)
 For Q6, here are the questions from [Y&G]
 Table 3.1 & 3.2 from [Y&G]
 Solution for HW7
 MATLAB codes
 Solution
 Solution for questions from [Y&G]
 HW8 (Due: Sep 17) [Fixed on Sep 15 @ 2PM]
 HW9 (Due: Sep 27)
 This HW provides nice sample questions for final exam.
 Some questions from [Y&G]
 Solution+ MATLAB mfile + Q4.9.4 & Q4.9.7
 HW10 (Official Due Date: Oct 1; Extended Due Date: Oct 6)
 This HW provides nice sample questions for final exam.
 Selfevaluation form
 Solution
Calendar
Reading Assignment
 Probability Puzzles [Gardner, 1986] is available on the SIIT Lecture Note System
 Compound Chance Experiment and Bernoulli Trials
Course Outline

Introduction, Classical probability, Mathematical background

Counting Methods (Combinatorics)

Probability Foundation

Random variable (realvalued)

Realvalued functions of a random variable

Expectation, moment, variance, standard deviation, central moment

Independence

MIDTERM: 6 Aug 2010 TIME 09:00  12:00

Function of random variables

Random vectors

Realvalued jointly Gaussian random vectors

Summation of i.i.d. random variable and laws of large numbers

Transform method: Characteristic function

Central limit theorem

Random processes, Crosscorrelation and Power spectral density

FINAL: 13 Oct 2010 TIME 09:00  12:00
Misc. Links
 More information about Monty Hall Problem
 Bill Nye the Science Guy  "50 Fifty" (MV)
 Probability review from MATH REVIEW for Practicing to Take the GRE General Test
 If you want to feel 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.
 Cheung, Y. L. "Why Poker is Played with Five Cards." Math. Gaz. 73, 313315, 1989.
 Peter Donnelly shows how stats fool juries (same clip on youtube)
 Lies, damned lies and statistics (about TEDTalks): Sebastian Wernicke on TED.com
 The Median Isn't the Message by Stephen Jay Gould
 Daniel Kahneman: The riddle of experience vs. memory
 Quotations about 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)
 Learn the Greek Alphabet in less than 10 minutes
 The Greek Alphabet Song