Introduction to Probability with Statistical Applications

✍ Scribed by Geza Schay

• Publisher: Birkhäuser Boston
• Year: 2007
• Tongue: English
• Leaves: 316
• Edition: 1st ed
• Category: Library

✦ Synopsis

I am a PhD student in Computer Science at UMass Boston and I do research in data mining. I am particularly interested in probabilistic solutions to problems in data mining, which is why I wanted to know about probability and statistics. I had the privilege of learning the subject matter from the author (Prof. Schay) himself. I learned a lot, both from this excellent text, and from Prof. Schay's clear in-class explanations of the topics.

✦ Table of Contents

Introduction to Probability with Statistical Applications......Page 1
Preface......Page 5
Contents......Page 8
Introduction......Page 10
1.1 Sample Spaces, Statements, Events......Page 12
1.2 Operations with Sets......Page 16
1.3 Relationships between Compound Statements and Events......Page 20
2.1 The Addition Principle......Page 23
2.2 Tree Diagrams and the Multiplication Principle......Page 26
2.3 Permutations and Combinations......Page 31
2.4 Some Properties of Binomial Coefficients and the Binomial Theorem......Page 35
2.5 Permutations with Repetitions......Page 40
3.1 Relative Frequency and the Axioms of Probabilities......Page 44
3.2 Probability Assignments by Combinatorial Methods......Page 49
3.3 Independence......Page 55
3.4 Conditional Probabilities......Page 61
3.5 The Theorem of Total Probability and Theorem of Bayes......Page 67
4.1 Probability Functions and Distribution Functions......Page 78
4.2 Continuous Random Variables......Page 87
4.3 Functions of Random Variables......Page 94
4.4 Joint Distributions......Page 103
4.5 Independence of Random Variables......Page 113
4.6 Conditional Distributions......Page 124
5.1 Expected Value......Page 133
5.2 Variance and Standard Deviation......Page 146
5.3 Moments and Generating Functions......Page 155
5.4 Covariance and Correlation......Page 162
5.5 Conditional Expectation......Page 169
5.6 Median and Quantiles......Page 175
6.1 Poisson Random Variables......Page 182
6.2 Normal Random Variables......Page 190
6.3 The Central Limit Theorem......Page 198
6.4 Negative Binomial, Gamma and Beta Random Variables......Page 206
6.5 Multivariante Normal Random Variables......Page 216
7.1 Estimation......Page 226
7.2 Testing Hypotheses......Page 236
7.3 The Power Function of a Test......Page 244
7.4 Sampling from Normally Distributed Populations......Page 249
7.5 Chi-Square Tests......Page 258
7.6 Two-Sample Tests......Page 268
7.7 Kolmogorov-Smirnov Tests......Page 276
Appendix I: Tables......Page 281
Appendix II: Answers andHints for Selected Odd-Numbered Exercises......Page 287
References......Page 311
Index......Page 312