INDICE: Chapter 1 – Sample Spaces and Random Variables 1.1 Discrete Sample Spaces 1.2 Events: Axioms of Probability 1.3 Probability Theorems 1.4 Conditional Probability and Independence 1.5 Some Examples 1.6 Reliability of Systems 1.7 Counting Techniques Chapter Review Problems for Review Supplementary Exercises for Chapter 1 Chapter 2 – Discrete Random Variables and Probability Distributions 2.1 Random Variables 2.2 Distribution Functions 2.3 Expected Values of Discrete Random Variables 2.4 Binomial Distribution 2.5 A Recursion 2.6 Some Statistical Considerations 2.7 Hypothesis Testing: Binomial Random Variables 2.8 Distribution of a Sample Proportion 2.9 Geometric and Negative Binomial Distributions 2.10 The Hypergeometric Random Variable; Acceptance Sampling 2.11 Acceptance Sampling (Continued) 2.12 The Hypergeometric Random Variable; Further Examples 2.13 The Poisson Random Variable 2.14 The Poisson Process Chapter Review Problems for Review Supplementary Exercises for Chapter 2 Chapter 3 – Continuous Random Variables and Probability Distributions 3.1 Introduction 3.2 Uniform Distribution 3.3 Exponential Distribution 3.4 Reliability 3.5 Normal Distribution 3.6 Normal Approximation to the Binomial Distribution 3.7 Gamma and Chi–Squared Distributions 3.8 Weibull Distribution Chapter Review Problems for Review Supplementary Exercises for Chapter 3 Chapter 4 – Functions of Random Variables, Generating Functions, and Statistical Applications 4.1 Introduction 4.2 Some Examples of Functions of Random Variables 4.3 Probability Distributions of Functions of Random Variables 4.4 Sums of Random Variables I 4.5 Generating Functions 4.6 Some Properties of Generating Functions 4.7 Probability Generating Functions for Some Specific Probability Distributions 4.8 Moment Generating Functions 4.9 Properties of Moment Generating Functions 4.10 Sums of Random Variables II 4.11 The Central Limit Theorem 4.12 Weak Law of Large Numbers 4.13 Sampling Distribution of the Sample Variance 4.14 Hypothesis Tests and Confidence Intervals for a Single Mean 4.15 Hypothesis Tests on Two Samples 4.16 Least Squares Linear Regression 4.17 Quality Control Chart for X Bar Chapter Review Problems for Review Supplementary Exercises for Chapter 4 Chapter 5 – Bivariate Probability Distributions 5.1 Introduction 5.2 Joint and Marginal Distributions 5.3 Conditional Distributions and Densities 5.4 Expected Values and the Correlation Coefficient 5.5 Conditional Expectations 5.6 Bivariate Normal Densities 5.7 Functions of Random Variables Chapter Review Problems for Review Supplementary Exercises for Chapter 5 Chapter 6 – Recursions and Markov Chains 6.1 Introduction 6.2 Some Recursions and Their Solutions 6.3 Random Walk and Ruin 6.4 Waiting Times for Patterns in Bernoulli Trials 6.5 Markov Chains Chapter Review Problems for Review Supplementary Exercises for Chapter 6 Chapter 7 – Some Challenging Problems 7.1 My Socks and √π 7.2 Coupon Collectors Problems 7.3 The Jackknife and the Bootstrap 7.4 On a Problem of Waldegrave 7.5 On a Problem of Huygens Bibliography Appendix 1 – Use of Mathematica in Probability and Statistics Appendix 2 – Answers to Odd–Numbered Problems Appendix 3 – Tables Index
- ISBN: 978-1-118-94708-1
- Editorial: Wiley–Blackwell
- Encuadernacion: Cartoné
- Páginas: 544
- Fecha Publicación: 28/11/2014
- Nº Volúmenes: 1
- Idioma: Inglés