Computer Applications For Engineers

Computer Applications for EngineersET 601Asst. Prof. Dr. Prapun Suksompongprapun@siit.tu.ac.thIntroductionOffice Hours:BKD 3601-7Thursday14:40-16:00Wednesday 9:30-11:301

Eye Examination Are you sitting too far away? You should be able to read this line, and this line, and this line.2

iCourse Organization Course Website:http://www2.siit.tu.ac.th/prapun/ET601/ Lectures: Wednesday 13:00-16:00 BKD 3206 Textbook: “Simulation” By Sheldon M. Ross 5th Edition Academic Press 2012 ISBN-10: 0124158250 ISBN-13: 978-01241582523

iCourse Web Site Please check the course website regularly. Announcements References Handouts (Posted before correspondinglectures) Slides (Posted after corresponding lectures) Calendar Lectures Exercises and projects due dates Presentation Slots4www2.siit.tu.ac.th/prapun/ET601/

Course Web Siteprapun.com5

iCourse Website: Notes & Slides I frequently use Microsoft OneNote on my tablet instead ofthe whiteboard. The files will be exported as pdf and postedafter the corresponding lectures. PDF notes (if any) will be posted before the correspondinglectures. In lectures PDF notes and slides will be annotated. The slides and updated notes will be posted on the coursewebsite after the corresponding lectures. Remind me the day after the lecture if the notes/slidesfrom the day before are still not posted on the web.6

iMe? Ph.D. from Cornell University, USA In Electrical and Computer Engineering Minor: Mathematics (Probability Theory) Ph.D. Research: Neuro-Information Theory Modeling and analyzing neurons in human brainfrom communication engineering perspective. Current Research: Wireless Communication Mobile Communications,WiFi (802.11) 2009 SIIT Best Teaching Award 2011 SIIT Research Awardprapun.com7

Synopsis Main Focus: Model random phenomenon and usesimulation study to analyze it.8

Motivation Formulation of model to describe and study a real phenomenon Traditional choices: choosing a model that is a realistic replica of the actual situation choosing one whose mathematical analysis is tractable. Traditional tradeoff: Can’t choose a model that is faithfully conformed to the phenomenonunder study if it were not possible to mathematically analyze thatmodel. Concentration on asymptotic or steady-state results as opposed to themore useful ones on transient time. New Approach: Relatively recent advent of fast and inexpensivecomputational power has opened up another approach-namely, totry to model the phenomenon as faithfully as possible and then torely on a simulation study to analyze it.9

Goals Main Focus: Model random phenomenon and usesimulation study to analyze it.To do this Use a computer to generate random (more precisely,pseudorandom) numbers. Use these random numbers to generate the values of randomvariables from arbitrary distributions. Use random variables to generate the behavior of a stochasticmodel over time.10

Computer Applications for EngineersET 601Asst. Prof. Dr. Prapun Suksompongprapun@siit.tu.ac.th1 Review of Basic ProbabilityOffice Hours:BKD 3601-7Thursday14:40-16:00Wednesday 9:30-11:3011

References Chapter 14 (Review of Basic Probability) In “Operations Research: An Introduction”By Hamdy A. Taha2011, 9th EditionPrentice Hall Chapter 2 (Elements of Probability) In “Simulation”By Sheldon M. Ross2012, 5th EditionAcademic Press My undergraduate course on probability http://www2.siit.tu.ac.th/prapun/ecs315/12

Recommended Reading Understanding Probability: Chance Rules in 13Everyday LifeBy Henk TijmsCall No. QA273 T48 2012Cambridge University Press“Part One” provides many motivatingexamples and problems from everyday life“Part Two” teaches clearly and simply themathematics of probability theory.Sample materials are available at the author’swebsite: ge.org/aus/catalogue/catalogue.asp?isbn 9781107658561&ss exc2nd Edition (2007)3rd Edition (2012)

Randomness14

Life is random15

In 2005, this statement (which is true)Life is random16showed up all over the world

Life is random17

“Random”-ness Most people have preconceived notions of randomnessthat often differ substantially from true randomness. Truly random data sets often have unexpected propertiesthat go against intuitive thinking. These properties can be used to test whether data sets havebeen tampered with when suspicion arises.18

Success Runs (1/4) Suppose that two people are separately asked to toss a faircoin 120 times and take note of the results. Heads is notedas a “one” and tails as a “zero”. Results: Two lists of compiled zeros and ones:19[Tijms, 2007, p 192]

Success Runs (2/4) Which list is more likely?20[Tijms, 2007, p 192]

Success Runs (3/4) Fact: Suppose we know that one of the two individuals hascheated and has fabricated a list of numbers without havingtossed the coin. Which list is more likely be the fabricated list?21[Tijms, 2007, p 192]

Success Runs (4/4) Fact: In 120 tosses of a fair coin, there is a very large probabilitythat at some point during the tossing process, a sequence of fiveor more heads or five or more tails will naturally occur. The probability of this is approximately 0.9865. In contrast to the second list, the first list shows no such sequenceof five heads in a row or five tails in a row. In the first list, thelongest sequence of either heads or tails consists of three in a row. In 120 tosses of a fair coin, the probability of the longestsequence consisting of three or less in a row is equal to0.000053 which is extremely small . Thus, the first list is almost certainly a fake. Most people tend to avoid noting long sequences of consecutiveheads or tails. Truly random sequences do not share this humantendency!22[Tijms, 2007, p 192]

“The Perfect Thing”What is this?23

“The Perfect Thing”24

What about the shuffle lectronics.howstuffworks.com/ipod-shuffle2.htm

Shuffle function on iPod Apple ran into an issue with the random shuffle method itinitially employed in its iPod music players: true randomness sometimes produces repetition When users heard the same song or songs by the same artistplayed back-to-back, they believed the shuffling wasn’trandom. So the company made the feature “less random to make itfeel more random,” said Apple founder Steve Jobs.26

Monty Hall Problem (MHP): Origin Problem, paradox, illusion Loosely based on the American television game showLet’s Make a Deal. (Thai CH7 version: ประตูดวง.) The name comes from the show’s original host, MontyHall. One of the most interesting mathematical brain teasers ofrecent times.27

Monty Hall Problem: Math Version Originally posed in a letter by Steve Selvin to the AmericanStatistician in 1975. A well-known statement of the problem was published inMarilyn vos Savant’s “Ask Marilyn” column in Parademagazine in 1990:“Suppose you're on a game show, and28you're given the choice of three doors:Behind one door is a car; behind the others,goats.You pick a door, say No. 1, and thehost, who knows what's behind the doors,opens another door, say No. 3, which has agoat. He then says to you, "Do you want topick door No. 2?" Is it to your advantage toswitch your choice?”

Marilyn vos Savant Vos Savant was listed in each edition of the Guinness Bookof World Records from 1986 to 1989 as having the “HighestIQ.” Since 1986 she has written “Ask Marilyn” Sunday column in Parade magazine Solve puzzles and answer questions from readers29[ http://www.marilynvossavant.com ]

MHP: Step 0 There are three closed doors. They look identical.30

MHP: Step 0 Behind one of the doors is the star prize - a car. The car is initially equally likely to be behind each door. Behind each of the other two doors is just a goat.31

MHP: Step 1 Obviously we want to win the car, but do notknow which door conceals the car. We are asked to choose a door. That door remains closed for the time being.32“Pick one ofthese doors”

MHP: Step 2 The host of the show (Monty Hall), who knows what is behindthe doors, now opens a door different from our initial choice. He carefully picks the door that conceals a goat. 33We stipulate that if Monty has a choice of doors to open, then he chooses randomly from among his options.

MHP: Step 3“Do you wantto switchdoors?” Monty now gives us the options of either1.2.sticking with our original choice orswitching to the one other unopened door. After making our decision, we win whatever is behind our door.34

Monty Hall ProblemAssuming that our goal is to maximizeour chances of winning the car, whatdecision should we make? Will you do better bysticking with your first choice, orby switching to the other remaining door? Make no difference?35

Let’s play!36

Interactive Monty Hall 8http://www.math.ucsd.edu/ crypto/Monty/monty.html

Interactive Monty HallThe New York Times’s 8monty.html38

Back to the boringadministrative stuff!39

cture

iClass Participation If you come only to receive, you will fall asleep. Do not simply sit quietly in the class. Need interaction between the lecturer and students. Ask question when there is something that you don’tunderstand. Don’t be shy! It is very likely that your peers don’t understand it as well. If you already understand what I’m presenting, SHOW ME! Point out the errors/typos. I will raise many issues/questions in class. Try to comment onthem.41

iPolicy We will start the class on time and will finish on time. Time reference: Not the clock in classroom. Use time server. Please come to class on time. Raise your hand and tell me immediately if I go over the timelimit. Does NOT mean that I will leave the room immediately afterlecture. I will stay and answer questions. Mobile phones must be turned off or set in silent mode. We may have some pop quizzes (without prior warning orannouncement) and in-class exercises. Pop quizzes will be taken/given irregularly and randomly.42 Feel free to stop me when I talk too fast or too slow.

Tips Almost everything including what I have written on my tabletwill be saved and posted on web soon after class. No need to take detailed lecture notes (if you don’t want to). Put all of your energy into understanding thematerial. Of course, there is always someone (in the class) who will takegood notes anyway and you can (potentially) borrow or make acopy of the notes from them. Have fun with the materials presented in class.43

Remarks Get as much legitimate help as you can Participate actively in class and outside of class If you feel that the class is very easy, you might overlooksomething. If you feel that the class is very difficult, you are probably notthe only one who feel that way. Don’t give up. Chat with me. It takes me a long time to feel comfortable with these materials;yet, I still make mistakes. My notation can be different from the textbook. Every notation has some advantages and disadvantages.44

iPolicy: Summary Please stop me if I go over the time limit. Please stop me if I talk too fast. Please stop me if you have any question.45

Monty Hall Problem: a short revisitAssuming that our goal is to maximizeour chances of winning the car, whatdecision should we make? Will you do better bysticking with your first choice, orby switching to the other remaining door? Make no difference?46

Monty Hall Problem: vos Savant’sAnswer“You double your chances ofwinning by switching doors.”47

Monty Hall Problem: Controversy Approximately 10,000 readers, including nearly 1,000 with PhDs (many of them mathprofessors), wrote to the magazine claiming the published solution was wrong. “You blew it,” wrote a mathematician from George MasonUniversity. From Dickinson State University came this: “I am in shockthat after being corrected by at least three mathematicians,you still do not see your mistake.”48[Mlodinow, 2008, p 42-45]