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Probability and Statistical Inference, Books a la Carte Edition (8th Edition) [Loose Leaf]

Robert V. Hogg , Elliot Tanis
4.5 out of 5 stars  See all reviews (2 customer reviews)
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Book Description

July 24 2009 0321656717 978-0321656711 8


Written by two leading statisticians, this applied introduction to the mathematics of probability and statistics emphasizes the existence of variation in almost every process, and how the study of probability and statistics helps us understand this variation. Designed for students with a background in calculus, this book continues to reinforce basic mathematical concepts with numerous real-world examples and applications to illustrate the relevance of key concepts.



  • The included CD-ROM contains all of the data sets in a variety of formats for use with most statistical software packages. This disc also includes several applications of Minitab® and Maple.
  • Historical vignettes at the end of each chapter outline the origin of the greatest accomplishments in the field of statistics, adding enrichment to the course.

 Content updates

  • The first five chapters have been reorganized to cover a standard probability course with more real examples and exercises. These chapters are important for students wishing to pass the first actuarial exam, and cover the necessary material needed for students taking this course at the junior level.
  • Chapters 6 and 7 on estimation and tests of statistical hypotheses tie together confidence intervals and tests, including one-sided ones. There are separate chapters on nonparametric methods, Bayesian methods, and Quality Improvement.
  • Chapters 4 and 5 include a strong discussion on conditional distributions and functions of random variables, including Jacobians of transformations and the moment-generating technique. Approximations of distributions like the binomial and the Poisson with the normal can be found using the central limit theorem.
  • Chapter 8 (Nonparametric Methods) includes most of the standards tests such as those by Wilcoxon and also the use of order statistics in some distribution-free inferences.
  • Chapter 9 (Bayesian Methods) explains the use of the "Dutch book" to prove certain probability theorems.
  • Chapter 11 (Quality Improvement) stresses how important W. Edwards Deming's ideas are in understanding variation and how they apply to everyday life.





1. Probability

1.1 Basic Concepts

1.2 Properties of Probability

1.3 Methods of Enumeration

1.4 Conditional Probability

1.5 Independent Events

1.6 Bayes's Theorem


2. Discrete Distributions

2.1 Random Variables of the Discrete Type

2.2 Mathematical Expectation

2.3 The Mean, Variance, and Standard Deviation

2.4 Bernoulli Trials and the Binomial Distribution

2.5 The Moment-Generating Function

2.6 The Poisson Distribution


3. Continuous Distributions

3.1 Continuous-Type Data

3.2 Exploratory Data Analysis

3.3 Random Variables of the Continuous Type

3.4 The Uniform and Exponential Distributions

3.5 The Gamma and Chi-Square Distributions

3.6 The Normal Distribution

3.7 Additional Models


4. Bivariate Distributions

4.1 Distributions of Two Random Variables

4.2 The Correlation Coefficient

4.3 Conditional Distributions

4.4 The Bivariate Normal Distribution


5. Distributions of Functions of Random Variables

5.1 Functions of One Random Variable

5.2 Transformations of Two Random Variables

5.3 Several Independent Random Variables

5.4 The Moment-Generating Function Technique

5.5 Random Functions Associated with Normal Distributions

5.6 The Central Limit Theorem

5.7 Approximations for Discrete Distributions


6. Estimation

6.1 Point Estimation

6.2 Confidence Intervals for Means

6.3 Confidence Intervals for Difference of Two Means

6.4 Confidence Intervals for Variances

6.5 Confidence Intervals for Proportions

6.6 Sample Size.

6.7 A Simple Regression Problem

6.8 More Regression


7. Tests of Statistical Hypotheses

7.1 Tests about Proportions

7.2 Tests about One Mean

7.3 Tests of the Equality of Two Means

7.4 Tests for Variances

7.5 One-Factor Analysis of Variance

7.6 Two-Factor Analysis of Variance

7.7 Tests Concerning Regression and Correlation


8. Nonparametric Methods

8.1 Chi-Square Goodness of Fit Tests

8.2 Contingency Tables

8.3 Order Statistics

8.4 Distribution-Free Confidence Intervals for Percentiles

8.5 The Wilcoxon Tests

8.6 Run Test and Test for Randomness

8.7 Kolmogorov-Smirnov Goodness of Fit Test

8.8 Resampling Methods


9. Bayesian Methods

9.1 Subjective Probability

9.2 Bayesian Estimation

9.3 More Bayesian Concepts


10. Some Theory

10.1 Sufficient Statistics

10.2 Power of a Statistical Test

10.3 Best Critical Regions

10.4 Likelihood Ratio Tests

10.5 Chebyshev's Inequality and Convergence in Probability

10.6 Limiting Moment-Generating Functions

10.7 Asymptotic Distributions of Maximum Likelihood Estimators


11. Quality Improvement Through Statistical Methods

11.1 Time Sequences

11.2 Statistical Quality Control

11.3 General Factorial and 2k Factorial Designs

11.4 Understanding Variation


A. Review of Selected Mathematical Techniques

      A.1 Algebra of Sets

      A.2 Mathematical Tools for the Hypergeometric Distribution

      A.3 Limits

      A.4 Infinite Series

      A.5 Integration

      A.6 Multivariate Calculus

B. References

C. Tables

D. Answers to Odd-Numbered Exercises

--This text refers to the Hardcover edition.

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Product Description

About the Author

Robert V. Hogg, Professor Emeritus of Statistics at the University of Iowa since 2001, received his B.A. in mathematics at the University of Illinois and his M.S. and Ph.D. degrees in mathematics, specializing in actuarial sciences and statistics, from the University of Iowa. Known for his gift of humor and his passion for teaching, Hogg has had far-reaching influence in the field of statistics. Throughout his career, Hogg has played a major role in defining statistics as a unique academic field, and he almost literally "wrote the book" on the subject. He has written more than 70 research articles and co-authored four books including  Introduction of Mathematical Statistics, 6th edition, with J. W. McKean and  A.T. Craig, Applied Statistics for Engineers and Physical Scientists 3rd edtion with J. Ledolter and A Brief Course in Mathematical 1st edition with E.A. Tanis. His texts have become classroom standards used by hundreds of thousands of students


Among the many awards he has received for distinction in teaching, Hogg has been honored at the national level (the Mathematical Association of America Award for Distinguished Teaching), the state level (the Governor's Science Medal for Teaching), and the university level (Collegiate Teaching Award). His important contributions to statistical research have been acknowledged by his election to fellowship standing in the ASA and the Institute of Mathematical Statistics.


Elliot Tanis, Professor Emeritus of mathematics at Hope College, In addition to this text, received his M.S. and Ph.D. degrees from the University of Iowa. Tanis is the co-author of A Brief Course in Mathematical Statistics with R. Hogg and Probability and Statistics: Explorations with MAPLE 2nd edition with Z. Karian. He has authored over 30 publications on statistics and is a past chairman and governor of the Michigan MAA, which presented him with both its Distinguished Teaching and Distinguished Service Awards.  He taught at Hope for 35 years and in 1989 received the HOPE Award (Hope's Outstanding Professor Educator) for his excellence in teaching.  In addition to his academic interests, Dr. Tanis is also an avid tennis player and devoted Hope sports fan. --This text refers to the Hardcover edition.

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Customer Reviews

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Most helpful customer reviews
5.0 out of 5 stars amazing Sept. 16 2013
Format:Loose Leaf|Verified Purchase
Great price n so much easy to just take the req pages than the whole book.
In general good Txt has a lot of examples and questions
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4.0 out of 5 stars Why all the hate? Dec 14 2011
By Kevin C
This book is getting lots of bad reviews. I used this book during a second-year course in Probability, and I found it to be a useful reference. On the rare occasion that I missed a lecture, the book was quite readable, and easily allowed me to catch up. Also, most theorems are proven in adequate detail, so it is easy to get an understanding of why a result works. There are also plenty of examples. Open the book to a random set of two pages - chances are there's an example being started somewhere on it.

So I really don't see what the problem with this textbook is. It definitely isn't worth it to buy it new, but if you can land a used copy, then it should suit any early-mid undergraduate student just fine. Maybe it isn't as useful for a course in Statistics, and this is what people don't like about it?
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Most Helpful Customer Reviews on Amazon.com (beta)
Amazon.com: 2.9 out of 5 stars  35 reviews
12 of 12 people found the following review helpful
5.0 out of 5 stars This is an excellent text Aug. 5 2012
By Finance Prof - Published on Amazon.com
Format:Hardcover|Verified Purchase
This book is a kinder, friendlier version of Hogg, McKean, and Craig "Introduction to Mathematical Statistics," which is also an excellent text. Hogg and Tanis is less dense than its older brother, having more examples of applications and more verbal development and discussion surrounding equations and results. The book is premised on a background of three semesters of calculus, although two semesters (differential and integral) is probably enough as multiple integrals can be readily grasped without a whole semester's treatment. If you lack the mathematical foundation, you will struggle with this material regardless of the textbook used. This is an excellent textbook for an introduction to this material. As the authors note, the first five chapters are good preparation for the first actuarial exam.
7 of 7 people found the following review helpful
5.0 out of 5 stars I don't understand why so many people are rating this book low Aug. 13 2012
By Knowledge Seeker - Published on Amazon.com
Format:Hardcover|Verified Purchase
I just finished 2 semeseter-long courses (Probability, and Mathematical Statistics) based on first half and second half of this book respectively. This was in an online learning setting. Just to give you a sense for my background, I already have a Masters degree in Mech Engg, plus an MBA in Finance, and am currently pursuing a Masters in Applied Statistics.

I rate the book a 4.5 stars. The 0.5 stars held back for lack of clear separation throughout the book between where examples end, and where the next topic starts. Plus Chapter 9 (Bayesian Statistics) was a bit wordy/difficult (could just be me).

Other than that, it's been a great book to follow for an Applied Statistics focus. It is not 100% suited for self study (I'd say more like 70% suited), because a Solutions Manual is not readily available. However, with the Home work problems from this book that my instructor assigned every week, and the worked out solutions he provided subsequently, this book was just "fantastic" in getting a good intuition about the subject matter. Especially if you give an honest effort to solving the problems yourself prior to looking at solutions. The homework problems cover many areas of interest, and you can clearly tell are not just made up - at the same time, serve to explain/drill concepts well, without overemphasis on the nonstatitical background of the problem.

Like another reviewer pointed out, this book's "elder sibling", the Hogg/Craig book (which I bought too), is more theoretical/dense/concise in explanations, and is the one probably better suited for a pure Statistics focus.

There might be other books that might be even better if your focus is only on certain areas: for example I really liked Jim Pitman's Probability book (which also I own), and this book could have been used as the text for the Probability portion of the syllabus (i.e., first sem of two semesters). However, there is something to be said about having the same book for 2 courses in 2 semesters, especially when you have to refer back to the earlier course for some concepts.

Another book that is similar to current book and merits a look I believe is Larsen's Introduction to Mathematical Statistics and Its Applications, though I am not a professor who can give you a more educated comparison of the two books based on a ton of experience.
10 of 13 people found the following review helpful
1.0 out of 5 stars Not a worthwhile purchase July 27 2010
By orderinchaos - Published on Amazon.com
My review is for the International Edition, but I presume it is textually almost identical to the US version.

I got this book for a course I was doing externally through university - it claims to be suitable for "students at the junior level who have taken a good standard course in calculus", but I was decidedly unimpressed by the book's lack of logical progression. The authors would often state something and jump to the conclusion without explaining how they got there. It also failed to build a holistic picture so that one developed a problem-by-problem ability in the subject, not a conceptual framework. I ended up falling back on two books, Larsen/Marx (1986) and Mendenhall (1990), both of which were more suited to the intended level and explained carefully where they were going. There is also some evidence of a lack of proof-reading at times with grammatical and spelling issues (including on the first line of the preface!)
3 of 3 people found the following review helpful
5.0 out of 5 stars I'm confused as to why so many people dislike this book Dec 10 2012
By SKC - Published on Amazon.com
I used this book for my elementary probability and statistics class, and I still reference it now in graduate school. This book gives very good explanation for why probability works the way it does, and the important proofs of why we view statistics the way we do. This is a book that will provide a solid foundation in probability and statistics through quick proofs and less examples. It teaches you to acquire good intuition about probability and statistics, and I constantly recommend my peers to use this book as reference.
2 of 2 people found the following review helpful
1.0 out of 5 stars awful textbook Jan. 29 2014
By Adam - Published on Amazon.com
Format:Hardcover|Verified Purchase
This book has unclear discussions of the topics and does a poor job of explaining concepts. It does the bare minimum when it comes to explaining things. Just providing the answers to the odd questions is lazy and deceitful, because it forces you to buy/find the answers to the even questions. It is lazy because the problems are not worked out, and only the answers are given, which is practically useless to a student. Even in the instructor's manual with the even solutions worked out, the authors did a bare minimum when working out the solutions to explain to a student. Poorly written textbook by lazy authors. Complain to your teachers and let's get this book off the shelves!!!
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