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Probability with Statistical Applications

  • Textbook
  • © 2001

Overview

Authors:
  1. Rinaldo B. Schinazi

    1. Department of Mathematics, University of Colorado, Colorado Springs, USA

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Probability Space

    • Rinaldo B. Schinazi
    Pages 1-21

  3. Random Variables

    • Rinaldo B. Schinazi
    Pages 23-58

  4. Binomial and Poisson Random Variables

    • Rinaldo B. Schinazi
    Pages 59-86

  5. Limit Theorems

    • Rinaldo B. Schinazi
    Pages 87-101

  6. Estimation and Hypothesis Testing

    • Rinaldo B. Schinazi
    Pages 103-141

  7. Linear Regression

    • Rinaldo B. Schinazi
    Pages 143-159

  8. Moment Generating Functions and Sums of Independent Random Variables

    • Rinaldo B. Schinazi
    Pages 161-175

  9. Transformations of Random Variables and Random Vectors

    • Rinaldo B. Schinazi
    Pages 177-212

  10. Back Matter

    Pages 213-219
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Keywords

About this book

This book is intended as a one-semester first course in probability and statistics, requiring only a knowledge of calculus. It will be useful for students majoring in a number of disciplines:for example,biology, computer science, electrical engineer­ ing, mathematics, and physics. Many good texts in probability and statistics are intended for a one-year course and consist of a large number of topics. In this book, the number of topics is dras­ tically reduced. We concentrate instead on several important concepts that every student should understand and be able to apply in an interesting and useful way. Thus statistics is introduced at an early stage. The presentation focuses on topics in probability and statistics and tries to min­ imize the difficulties students often have with calculus. Theory therefore is kept to a minimum and interesting examples are provided throughout. Chapter I contains the basic rules of probability and conditional probability with some interesting ap­ plications such asBayes' rule and the birthday problem. In Chapter 2 discrete and continuous random variables, expectation and variance are introduced. This chapter is mostly computational with a few probability concepts and many applications of calculus. In Chapters 3 and 4 we get to the heart of the subject: binomial distribu­ tion, normal approximation of the binomial, Poisson distribution, the Law of Large Numbers and the Central Limit Theorem. Wealso cover the Poisson approximation of the binomial (in a nonstandard way) and the Poisson scattering theorem.

Reviews

"This book is well-written and the presentation is clear and concise. The textbook is an introduction to probability theory and statistics. The text is intended for a one-semester course for undergraduates, but it can also serve as a basis for a high-school course. The level of the book is very elementary and in most of the chapters of the book only basic calculus is required. As promised by the author ``theory is kept to a minimum'' and it is successfully tried to ``minimize the difficulties students often have with calculus''. No measure theory is required. In the huge variety of examples rather explicit calculations are presented: moments of several distributions, confidence intervals, testing some parameters or proportions, linear regression and more. Every subsection is rounded off by numerous exercises. Only the last part of the book relies on advanced calculus: Taylor's formula, Fubini's theorem, and calculus of severable variables. In the appendix some tables of quantiles are provided."

—Zentralblatt Math

Authors and Affiliations

  • Department of Mathematics, University of Colorado, Colorado Springs, USA

    Rinaldo B. Schinazi

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