This applied introduction to the mathematics of probability and statistics e mphasizes the existence of variation in almost every process, and how the study of probability and statistics helps us understand this variability. Designed for students with a background in calculus, it reinforces basic mathematical concepts with numerous real-world examples and applications to illustrate the relevance of key concepts.
FEATURES
Balanced coverage of probability and statistics - Includes five chapters which focus on probability and probability distributions, including discrete data, order statistics, multivariate distributions, and normal distribution. The texts second half emphasizes statistics and statistical inference, including estimation, Bayesian estimation, tests of statistical hypotheses, and methods for quality improvement.
Solid organization - Presents information in a logical, easy-to-grasp sequence, incorporating the latest trends and scholarship in the field of probability and statistical inference.
Student-friendly approach - Reinforces basic mathematical concepts, while not requiring extensive knowledge of math beyond calculus.
NEW TO THIS EDITION
New chapter on Bayesian estimation - Includes expanded coverage of Bayesian estimation in the texts section on statistical inference.
Integration of computer-based data and applications - Features increased use of data and the computer for calculating probabilities, analyzing data, solving problems, and conducting simulations.
Application-oriented content - Features more than 100 new real-world scenarios as exercises and examples, with applications in the areas of biology, economics, health, sociology, and sports.
Updated material throughout - Offers a brief history of probability in the chapter on normal distribution.
Accompanying CD-ROM - Contains data sets for all examples and exercises in multiple formats accessible to Minitab, Maple, and other program users.
Table of Contents
Chapter 1: Probability
Basic Concepts
Properties of Probability
Methods of Enumeration
Conditional Probability
Independent Events
Bayes' Theorem
Chapter 2: Discrete Distributions
Random Variables of the Discrete Type
Mathematical Expectation
Bernoulli Trials and the Binomial Distribution
The Moment-Generating Function
The Poisson Distribution
Chapter 3: Continuous Distributions
Continuous-Type Data and EDA
Random Variables of the Continuous Type
The Uniform and Exponential Distributions
The Gamma and Chi-Square Distributions
Distributions of Functions of a Random Variable
Additional Models
Chapter 4: Multivariate Distributions
Distributions of Two Random Variables
The Correlation Coefficient
Conditional Distributions
Transformations of Random Variables
Independent Random Variables
Distributions of Sums of Independent Random Variables
Chebyshev's Inequality and Convergence in Probability
Chapter 5: The Normal Distribution
A Brief History of Probability
The Normal Distribution
Random Functions Associated with Normal Distributions
The Central Limit Theorem
Approximations for Discrete Distributions
The Bivariate Normal Distribution
Limiting Moment-Generating Functions
Importance of Understanding Variability
Chapter 6: Estimation
Sample Characteristics
Point Estimation
Sufficient Statistics
Confidence Intervals for Means
Confidence Intervals for Difference of Two Means
Confidence Intervals for Variances
Confidence Intervals for Proportions
Sample Size
Order Statistics
Distribution-Free Confidence Intervals for Percentiles
A Simple Regression Problem
More Regression
Resampling Methods
Asymptotic Distributions of Maximum Likelihood Estimators
Chapter 7: Bayesian Methods
Subjective Probability
Bayesian Estimation
More Bayesian Concepts
Chapter 8: Tests of Statistical Hypotheses
Tests About Proportions
Tests About One Mean and One Variance
Tests of the Equality of Two Normal Distributions
The Wilcoxon Tests
Chi-Square Goodness of Fit Tests
Contingency Tables
One-Factor Analysis of Variance
Two-Factor Analysis of Variance
Tests Concerning Regression and Correlation
Kolmogorov-Smirnov Goodness of Fit Test
Run Test and Test for Randomness
Chapter 9: Theory of Statistical Inference
Power of a Statistical Test
Best Critical Regions
Likelihood Ratio Tests
Chapter 10: Quality Improvement Through Statistical Methods
Time Sequences
Statistical Quality Control
General Factorial and 2 k Factorial Designs
More on Design of Experiments
Epilogue
A Review of Selected Mathematical Techniques
Algebra of Sets
Mathematical Tools for the Hypergeometric Distribution
Limits
Infinite Series
Integration
Multivariate Calculus
Mathematical Statistics (Statistics)
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