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Front Cover; Introduction to Applied Probability; Copyright Page; Table of Contents; Preface; Acknowledgments; Part I. INTRODUCTION; Chapter 1. An Approach to Probability; INTRODUCTION; 1-1. Classical Probability; 1-2. Toward a More General Theory; Chapter 2. Some Elementary Strategies of Counting; Introduction; 2-1. Basic Principles; 2-2. Arrangements; 2-3. Binomial Coefficients; 2-4. Verification of the Formulas for Arrangements; 2-5. A Formal Representation of the Arrangement Problem; 2-6. An Occupancy Problem Equivalent to the Arrangement Problem
2-7. Some Problems Utilizing Elementary Arrangements and Occupancy Situations as Component OperationsProblems; PART II . BASIC PROBABILITY MODEL; Chapter 3. Sets and Events; Introduction; 3-1. A Well-Defined Trial and Its Possible Outcomes; 3-2. Events and the Occurrence of Events; 3-3. Special Events and Compound Events; 3-4. Classes of Events; 3-5. Techniques for Handling Events; Problems; Chapter 4. A Probability System; Introduction; 4-1. Requirements for a Formal Probability System; 4-2. Basic Properties of a Probability System; 4-3. Derived Properties of the Probability System
4-4. A Physical Analogy: Probability as Mass4-5. Probability Mass Assignment on a Discrete Basic Space; 4-6. On the Determination of Probabilities; 4-7. Supplementary Examples; Problems; Chapter 5. Conditional Probability; Introduction; 5-1. Conditioning and the Assignment of Probabilities; 5-2. Some Properties of Conditional Probability; 5-3. Supplementary Examples; 5-4. Repeated Conditioning; 5-5. Some Patterns of Inference; Problems; Chapter 6. Independence in Probability Theory; Introduction; 6-1. The Defining Condition; 6-2. Some Elementary Properties; 6-3. Independent Classes of Events
6-4. Conditional Independence6-5. Supplementary Examples; Problems; Chapter 7. Composite Trials and Sequences of Events; Introduction; 7-1. Composite Trials; 7-2. Repeated Trials; 7-3. Bernoulli Trials; 7-4. Sequences of Events; Problems; PART III . RANDOM VARIABLES; Chapter 8. Random Variables; Introduction; 8-1. The Random Variable as a Function; 8-2. Functions as Mappings; 8-3. Events Determined by a Random Variable; 8-4. The Indicator Function; 8-5. Discrete Random Variables; 8-6. Mappings and Inverse Images for Simple Random Variables; 8-7. Mappings and Mass Transfer
8-8. Approximation by Simple Random VariablesProblems; Chapter 9. Distribution and Density Functions; Introduction; 9-1. Some Introductory Examples; 9-2. The Probability Distribution Function; 9-3. Probability Mass and Density Functions; 9-4. Additional Examples of Probability Mass Distributions; Problems; Chapter 10. Joint Probability Distributions; Introduction; 10-1. Joint Mappings; 10-2. Joint Distributions; 10-3. Marginal Distributions; 10-4. Properties of Joint Distribution Functions; 10-5. Mass and Density Functions; 10-6. Mixed Distributions; Problems
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Includes bibliographical references (pages 387-388).