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A Modern Approach to Probability Theory

  • Bert Fristedt
  • Lawrence Gray

Part of the Probability and its Applications book series (PA)

Table of contents

  1. Front Matter
    Pages i-xx
  2. Probability Spaces, Random Variables, and Expectations

    1. Front Matter
      Pages 1-2
    2. Bert Fristedt, Lawrence Gray
      Pages 3-10
    3. Bert Fristedt, Lawrence Gray
      Pages 11-24
    4. Bert Fristedt, Lawrence Gray
      Pages 25-40
    5. Bert Fristedt, Lawrence Gray
      Pages 41-58
    6. Bert Fristedt, Lawrence Gray
      Pages 59-74
    7. Bert Fristedt, Lawrence Gray
      Pages 75-84
    8. Bert Fristedt, Lawrence Gray
      Pages 85-100
    9. Bert Fristedt, Lawrence Gray
      Pages 101-118
  3. Independence and Sums

    1. Front Matter
      Pages 119-120
    2. Bert Fristedt, Lawrence Gray
      Pages 121-146
    3. Bert Fristedt, Lawrence Gray
      Pages 147-162
    4. Bert Fristedt, Lawrence Gray
      Pages 163-184
    5. Bert Fristedt, Lawrence Gray
      Pages 185-208
    6. Bert Fristedt, Lawrence Gray
      Pages 209-240
  4. Convergence in Distribution

    1. Front Matter
      Pages 241-242
    2. Bert Fristedt, Lawrence Gray
      Pages 243-270
    3. Bert Fristedt, Lawrence Gray
      Pages 271-288
    4. Bert Fristedt, Lawrence Gray
      Pages 289-322
    5. Bert Fristedt, Lawrence Gray
      Pages 323-346
    6. Bert Fristedt, Lawrence Gray
      Pages 347-366
    7. Bert Fristedt, Lawrence Gray
      Pages 367-392
  5. Conditioning

    1. Front Matter
      Pages 393-394
    2. Bert Fristedt, Lawrence Gray
      Pages 395-402
    3. Bert Fristedt, Lawrence Gray
      Pages 403-428
    4. Bert Fristedt, Lawrence Gray
      Pages 429-442
    5. Bert Fristedt, Lawrence Gray
      Pages 443-456
  6. Random Sequences

    1. Front Matter
      Pages 457-458
    2. Bert Fristedt, Lawrence Gray
      Pages 459-488
    3. Bert Fristedt, Lawrence Gray
      Pages 489-510
    4. Bert Fristedt, Lawrence Gray
      Pages 511-532
    5. Bert Fristedt, Lawrence Gray
      Pages 533-552
    6. Bert Fristedt, Lawrence Gray
      Pages 553-578
  7. Stochastic Processes

    1. Front Matter
      Pages 579-580
    2. Bert Fristedt, Lawrence Gray
      Pages 581-600
    3. Bert Fristedt, Lawrence Gray
      Pages 601-620
    4. Bert Fristedt, Lawrence Gray
      Pages 621-640
    5. Bert Fristedt, Lawrence Gray
      Pages 641-660
    6. Bert Fristedt, Lawrence Gray
      Pages 661-683
  8. Back Matter
    Pages 685-756

About this book

Introduction

Overview This book is intended as a textbook in probability for graduate students in math­ ematics and related areas such as statistics, economics, physics, and operations research. Probability theory is a 'difficult' but productive marriage of mathemat­ ical abstraction and everyday intuition, and we have attempted to exhibit this fact. Thus we may appear at times to be obsessively careful in our presentation of the material, but our experience has shown that many students find them­ selves quite handicapped because they have never properly come to grips with the subtleties of the definitions and mathematical structures that form the foun­ dation of the field. Also, students may find many of the examples and problems to be computationally challenging, but it is our belief that one of the fascinat­ ing aspects of prob ability theory is its ability to say something concrete about the world around us, and we have done our best to coax the student into doing explicit calculations, often in the context of apparently elementary models. The practical applications of probability theory to various scientific fields are far-reaching, and a specialized treatment would be required to do justice to the interrelations between prob ability and any one of these areas. However, to give the reader a taste of the possibilities, we have included some examples, particularly from the field of statistics, such as order statistics, Dirichlet distri­ butions, and minimum variance unbiased estimation.

Keywords

Algebra Finite Probability space Probability theory Random variable Sage Variable Variance bayesian statistics calculus function mathematics measure theory theorem

Authors and affiliations

  • Bert Fristedt
    • 1
  • Lawrence Gray
    • 1
  1. 1.School of MathematicsUniversity of MinnesotaMinneapolisUSA

Bibliographic information