Stat 230 Waterloo

STAT 220/230/240 COURSE NOTES by Chris Springer

Revised by Jerry Lawless, Don McLeish and Cyntha Struthers Fall 2014 Edition

Contents

1. Introduction to Probability 1.1 1.2 Definitions of Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Problems on Chapter 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 4 5 5 12 15 15 31 35 39 39 44 49 54 56 61 66 66 73 76 78 82 84

2. Mathematical Probability Models 2.1 2.2 Sample Spaces and Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Problems on Chapter 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3. Probability – Counting Techniques 3.1 3.2 3.3 Counting Arguments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Review of Useful Series and Sums . . . . . . . . . . . . . . . . . . . . . . . . . . . . Problems on Chapter 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4. Probability Rules and Conditional Probability 4.1 4.2 4.3 4.4 4.5 4.6 General Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rules for Unions of Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Intersections of Events and Independence . . . . . . . . . . . . . . . . . . . . . . . . Conditional Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Product Rules, Law of Total Probablity and Bayes’ Theorem . . . . . . . . . . . . . . Problems on Chapter 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5. Discrete Random Variables and Probability Models 5.1 5.2 5.3 5.4 5.5 5.6 Random Variables and Probability Functions . . . . . . . . . . . . . . . . . . . . . . . Discrete Uniform Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hypergeometric Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Binomial Distribution . . . . . . . . . . . . . . . . . . . ....