**Description:**

This
book develops the theory of probability and mathematical statistics with the
goal of analyzing real-world data. Throughout the text, the R package is used
to compute probabilities, check analytically computed answers, simulate
probability distributions, illustrate answers with appropriate graphics, and
help students develop intuition surrounding probability and statistics.
Examples, demonstrations, and exercises in the R programming language serve to
reinforce ideas and facilitate understanding and confidence.

The
book’s Chapter Highlights provide a summary of key concepts, while the examples
utilizing R within the chapters are instructive and practical. Exercises that
focus on real-world applications without sacrificing mathematical rigor are
included, along with more than 200 figures that help clarify both concepts and
applications. In addition, the book features two helpful appendices: annotated
solutions to 700 exercises and a Review of Useful Math.

**Contents:**

**Preface**

**Chapter 1:** Probability Basics: Sample Spaces and
Probability Functions

**Chapter 2:** Using R to Simulate Events

**Chapter 3:** The Basic Principle of Counting,
Permutations, and Combinations

**Chapter 4:** Conditional Probability, Independence,
and Tree Diagrams

**Chapter 5:** Discrete Random Variables and Expected
Value

**Chapter 6:** Hypothesis Testing Terminology and
Examples

**Chapter 7:** Simulating Distributions for Hypothesis
Testing

**Chapter 8:** Bernoulli and Binomial Random Variables

**Chapter 9:** The Geometric Random Variable

**Chapter 10:** The Poisson Random Variable

**Chapter 11:** The Hypergeometric Random Variable

**Chapter 12:** The Negative Binomial Random Variable

**Chapter 13:** Continuous Random Variables and Density
Functions

**Chapter 14:** Moments and the Moment Generating
Function

**Chapter 15:** The Cumulative Distribution Function and
Quantiles of Random Variables

**Chapter 16:** The Exponential, Gamma, and Inverse Gamma
Random Variables

**Chapter 17:** The Beta Random Variable

**Chapter 18:** The Normal Random Variable

**Chapter 19:** CDF Tricks: Probability Plots and Random
Number Generation

**Chapter 20:** Chebyshev’s Inequality

**Chapter 21:** Transformation of Continuous Random
Variables, Using the CDF Method

**Chapter 22:** Log-Normal, Weibull, and Pareto Random
Variables

**Chapter 23:** Jointly Distributed Discrete Random
Variables

**Chapter 24:** Jointly Continuously Distributed Random
Variables

**Chapter 25:** Marginal Distributions for Jointly
Continuous Random Variables

**Chapter 26:** Conditional Distributions and Independent
Random Variables

**Chapter 27:** Covariance of Two Random Variables

**Chapter 28:** The Multinomial Distribution

**Chapter 29:** Conditional Expectation and Variance

**Chapter 30:** Transformations of Jointly Distributed
Random Variables

**Chapter 31:** Transformations Using Moment Generating
Functions

**Chapter 32:** The Multivariate Normal Distribution

**Chapter 33:** Order Statistics

**Chapter 34:** Some Distributions Related to Sampling
from a Normal Population

**Chapter 35:** Hypothesis Tests for a Normal Population
Parameter, Part I

**Chapter 36:** Hypothesis Tests for a Normal Population
Parameter, Part II

**Chapter 37:** Two-Independent-Samples Tests: Normal
Populations

**Chapter 38:** Paired-Samples Test: Normal Populations

**Chapter 39:** Distribution-Free Test for Percentiles

**Chapter 40:** Distribution-Free Two-Sample Tests

**Chapter 41:** The Central Limit Theorem

**Chapter 42:** Parameter Estimation

**Chapter 43:** Maximum Likelihood Estimation

**Chapter 44:** Estimation Using the Method of Moments

**Chapter 45:** Bayes Estimation

**Chapter 46:** Consistency of Point Estimators

**Chapter 47:** Modes of Convergence of Random Variables
and the Delta Method

**Chapter 48:** Quantifying Uncertainty: Standard Error
and Confidence Intervals

**Chapter 49:** Bayes Credible Intervals

**Chapter 50:** Evaluating Confidence Intervals: Length
and Coverage Probability

**Chapter 51:** Bootstrap Confidence Intervals

**Chapter 52:** Information and Maximum Likelihood
Estimation

**Chapter 53: **Sufficient Statistics

**Chapter 54:** Uniformly Minimum Variance Unbiased
Estimators

**Chapter 55:** Exponential Families

**Chapter 56:** Evaluating Hypothesis Tests: Test Size
and Power

**Chapter 57:** The Neyman—Pearson Lemma

**Chapter 58:** Likelihood Ratio Tests

**Chapter 59:** Chi-Squared Tests for Categorical Data

**Chapter 60:** One-Way Analysis of Variance

**A **Answers to Exercises** **

**B. **Useful Mathematics** **

B.1
Countable and Uncountable Infinity

B.2
Sums and Series

B.3
The Taylor Expansion

B.4
L’ Hopital’ s rule

B.5
The Gamma Function

B.6
The Laplace Method and Stirling Approximation

B.7
Multiple Integration

B.8
Matrix Notation and Arithmetic

B.9
Jacobian Matrix and Transformation of Variables

**Index**

**About the Author:**

**Mary
C. Meyer **is a
statistics professor at Colorado State University, where her main area of
research is estimation and inference in statistical models with inequality
constraints. This includes nonparametric function estimation using constrained
regression splines, density and hazard function estimation with shape
constraints, and models with order restrictions.

** **

**Target Audience:**

Written for use in applied
masters classes, *Probability and Mathematical Statistics: Theory,
Applications, and Practice in R* is also suitable for advanced
undergraduates and for self-study by applied mathematicians and statisticians
and qualitatively inclined engineers and scientists.