MODULE 1 THE WHOLE MODULE - 1. Probability Basics Dave...

Info iconThis preview shows pages 1–11. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 1. Probability Basics Dave Goldsman Georgia Institute of Technology, Atlanta, GA, USA 10/19/10 Goldsman 10/19/10 1 / 98 Outline 1 Intro / Examples 2 Set Theory 3 Experiments 4 Probability 5 Finite Sample Spaces 6 Counting Techniques 7 Counting Applications 8 Conditional Probability and Independence 9 Bayes Theorem Goldsman 10/19/10 2 / 98 Intro / Examples Mathematical Models for describing observable phenomena: Deterministic Probabilistic Deterministic Models Ohms Law ( I = E/R ) Drop an object from height h . After t sec, height is h ( t ) = h- 16 t 2 . Deposit $1000 in a continuously compounding checking 3% account. At time t , its worth $1000 e . 03 t . Goldsman 10/19/10 3 / 98 Intro / Examples Probabilistic Models Involve uncertainty How much snow will fall tomorrow? Will IBM make a profit this year? Should I buy a call or put option? Can I win in blackjack if I use a certain strategy? What is the cost-effectiveness of a new drug? Which horse will win the Kentucky Derby? Goldsman 10/19/10 4 / 98 Intro / Examples Some Cool Examples 1. Birthday Problem Assume all 365 days have equal probability of being a persons birthday (ignore Feb 29). Then. . . If there are 23 people in the room, the odds are better than 5050 that there will be a match. If there are 50 people, the probability is about 97%! 2. Monopoly In the long run, the property having the highest probability of being landed on is Illinois Ave. Goldsman 10/19/10 5 / 98 Intro / Examples 3. Poker Pick 5 cards from a standard deck. Then P ( exactly 2 pairs ) . 0475 P ( full house ) . 00144 P ( flush ) . 00198 4. Stock Market Monkeys randomly selecting stocks could have outperformed most market analysts during the past year. Goldsman 10/19/10 6 / 98 Intro / Examples 5. A couple has two kids and at least one is a boy. Whats the probability that BOTH are boys? Possibilities: GG, BG, GB, BB. Eliminate GG since we know that theres at least one boy. Then P ( BB ) = 1 / 3 . 6. Vietnam Lottery 7. Ask Marilyn. You are a contestant at a game show. Behind one of three doors is a car; behind the other two are goats. You pick door A. Monty Hall opens door B and reveals a goat. Monty offers you a chance to switch to door C. What should you do? Goldsman 10/19/10 7 / 98 Intro / Examples Working Definitions Probability Methodology that describes the random variation in systems. (Well spend about 40% of our time on this.) Statistics Uses sample data to draw general conclusions about the population from which the sample was taken. (60% of our time.) Goldsman 10/19/10 8 / 98 Set Theory Outline 1 Intro / Examples 2 Set Theory 3 Experiments 4 Probability 5 Finite Sample Spaces 6 Counting Techniques 7 Counting Applications 8 Conditional Probability and Independence 9 Bayes Theorem Goldsman 10/19/10 9 / 98 Set Theory The Joy of Sets Definition: A set is a collection of objects. Members of a set are called elements ....
View Full Document

This note was uploaded on 08/27/2011 for the course ISYE 3770 taught by Professor Goldsman during the Spring '07 term at Georgia Institute of Technology.

Page1 / 98

MODULE 1 THE WHOLE MODULE - 1. Probability Basics Dave...

This preview shows document pages 1 - 11. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online