Title Probability and Mathematical Statistics
Subtitle Theory, Applications, and Practice in R
Author Mary C. Meyer
ISBN 9781611975772
List price USD 109.00
Price outside India Available on Request
Original price
Binding Hardbound
No of pages 720
Book size 184 X 260 mm
Publishing year 2019
Original publisher SIAM - Society for Industrial and Applied Mathematics (Eurospan Group)
Published in India by .
Exclusive distributors Viva Books Private Limited
Sales territory India, Sri Lanka, Bangladesh, Pakistan, Nepal, .
Status New Arrival
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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.

 
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