Probability and Statistical Inference

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  • Edition: 8th
  • Format: Hardcover
  • Copyright: 2008-12-28
  • Publisher: Pearson
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Normal 0 false false false 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. Probability; Discrete Distributions; Continuous Distributions; Bivariate Distributions; Distributions of Functions of Random Variables; Estimation; Tests of Statistical Hypotheses; Nonparametric Methods; Bayesian Methods; Some Theory; Quality Improvement Through Statistical Methods For all readers interested in mathematical statistics.

Author Biography

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.

Table of Contents

Basic Concepts
Properties of Probability
Methods of Enumeration
Conditional Probability
Independent Events
Bayes's Theorem
Discrete Distributions
Random Variables of the Discrete Type
Mathematical Expectation
The Mean, Variance, and Standard Deviation
Bernoulli Trials and the Binomial Distribution
The Moment-Generating Function
The Poisson Distribution
Continuous Distributions
Continuous-Type Data
Exploratory Data Analysis
Random Variables of the Continuous Type
The Uniform and Exponential Distributions
The Gamma and Chi-Square Distributions
The Normal Distribution
Additional Models
Bivariate Distributions
Distributions of Two Random Variables
The Correlation Coefficient
Conditional Distributions
The Bivariate Normal Distribution
Distributions of Functions of Random Variables
Functions of One Random Variable
Transformations of Two Random Variables
Several Independent Random Variables
The Moment-Generating Function Technique
Random Functions Associated with Normal Distributions
The Central Limit Theorem
Approximations for Discrete Distributions
Point Estimation
Confidence Intervals for Means
Confidence Intervals for Difference of Two Means
Confidence Intervals for Variances
Confidence Intervals for Proportions
Sample Size
A Simple Regression Problem
More Regression
Tests of Statistical Hypotheses
Tests about Proportions
Tests about One Mean
Tests of the Equality of Two Means
Tests for Variances
One-Factor Analysis of Variance
Two-Factor Analysis of Variance
Tests Concerning Regression and Correlation
Nonparametric Methods
Chi-Square Goodness of Fit Tests
Contingency Tables
Order Statistics
Distribution-Free Confidence Intervals for Percentiles
The Wilcoxon Tests
Run Test and Test for Randomness
Kolmogorov-Smirnov Goodness of Fit Testp. 8
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