# Applied Probability

• Kenneth Lange
Textbook

Part of the Springer Texts in Statistics book series (STS)

1. Front Matter
Pages i-xvii
2. Pages 1-20
3. Pages 21-38
4. Pages 39-58
5. Pages 59-79
6. Pages 81-96
7. Pages 97-114
8. Pages 115-139
9. Pages 141-168
10. Pages 169-201
11. Pages 203-229
12. Pages 231-255
13. Pages 257-280
14. Pages 281-297
15. Pages 299-316
16. Pages 317-339
17. Back Matter
Pages 341-367

### Introduction

Despite the fears of university mathematics departments, mathematics educat,ion is growing rather than declining. But the truth of the matter is that the increases are occurring outside departments of mathematics. Engineers, computer scientists, physicists, chemists, economists, statis- cians, biologists, and even philosophers teach and learn a great deal of mathematics. The teaching is not always terribly rigorous, but it tends to be better motivated and better adapted to the needs of students. In my own experience teaching students of biostatistics and mathematical bi- ogy, I attempt to convey both the beauty and utility of probability. This is a tall order, partially because probability theory has its own vocabulary and habits of thought. The axiomatic presentation of advanced probability typically proceeds via measure theory. This approach has the advantage of rigor, but it inwitably misses most of the interesting applications, and many applied scientists rebel against the onslaught of technicalities. In the current book, I endeavor to achieve a balance between theory and app- cations in a rather short compass. While the combination of brevity apd balance sacrifices many of the proofs of a rigorous course, it is still cons- tent with supplying students with many of the relevant theoretical tools. In my opinion, it better to present the mathematical facts without proof rather than omit them altogether.

### Keywords

Analysis Markov Measure Probability theory algorithm biostatistics combinatorial optimization combinatorics expectation–maximization algorithm linear algebra mathematical modeling model modeling numerical analysis optimization

#### Authors and affiliations

• Kenneth Lange
• 1
1. 1.Department of BiomathematicsUCLA School of MedicineLos AngelesUSA

### Bibliographic information

• DOI https://doi.org/10.1007/b98849
• Copyright Information Springer-Verlag New York, Inc. 2003
• Publisher Name Springer, New York, NY
• eBook Packages
• Print ISBN 978-0-387-00425-9
• Online ISBN 978-0-387-22711-5
• Series Print ISSN 1431-875X
• Buy this book on publisher's site