Introduction to Applied Probability
- 1st Edition - January 1, 1973
- Imprint: Academic Press
- Authors: Paul E. Pfeiffer, David A. Schum
- Language: English
- Paperback ISBN:9 7 8 - 1 - 4 8 3 2 - 4 4 7 4 - 7
- eBook ISBN:9 7 8 - 1 - 4 8 3 2 - 7 7 2 0 - 2
Introduction to Applied Probability provides a basis for an intelligent application of probability ideas to a wide variety of phenomena for which it is suitable. It is intended as… Read more
Purchase options
Institutional subscription on ScienceDirect
Request a sales quoteIntroduction to Applied Probability provides a basis for an intelligent application of probability ideas to a wide variety of phenomena for which it is suitable. It is intended as a tool for learning and seeks to point out and emphasize significant facts and interpretations which are frequently overlooked or confused by the beginner. The book covers more than enough material for a one semester course, enhancing the value of the book as a reference for the student. Notable features of the book are: the systematic handling of combinations of events (Section 3-5); extensive use of the mass concept as an aid to visualization; an unusually careful treatment of conditional probability, independence, and conditional independence (Section 6-4); the resulting clarification facilitates the formulation of many applied problems; the emphasis on events determined by random variables, which gives unity and clarity to many topics important for interpretation; and the utilization of the indicator function, both as a tool for dealing with events and as a notational device in the handling of random variables. Students of mathematics, engineering, biological and physical sciences will find the text highly useful.
PrefaceAcknowledgmentsPart 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 Operations ProblemsPart 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 Mass 4-5. 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 Independence 6-5. 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 ProblemsPart 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 Variables Problems 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 Chapter 11 Independence of Random Variables Introduction 11-1. Definition and Examples 11-2. Independence and Probability Mass Distributions 11-3. A Simpler Condition for Independence 11-4. Independence Conditions for Distribution and Density Functions Problems Chapter 12. Functions of Random Variables Introduction 12-1. Examples and Definition 12-2. Distribution and Mapping for a Function of a Single Random Variable 12-3. Functions of Two Random Variables 12-4. Independence of Functions of Random Variables ProblemsPart IV. Mathematical Expectation Chapter 13. Mathematical Expectation and Mean Value Introduction 13-1. The Concept 13-2. Fundamental Formulas 13-3. A Mechanical Interpretation 13-4. The Mean Value 13-5. Some General Properties Problems Chapter 14. Variance and Other Movements Introduction 14-1. Definition and Interpretation of Variance 14-2. Some Properties of Variance 14-3. Variance for Some Common Distributions 14-4. Other Moments 14-5. Moment-Generating Function and Characteristic Function 14-6. Some Common Distributions Problems Chapter 15. Correlation and Covariance Introduction 15-1. Joint Distributions for Centered and Standardized Random Variables 15-2. Characterization of the Joint Distributions 15-3. Covariance and the Correlation Coefficient 15-4. Linear Regression 15-5. Additional Interpretations of p 15-6. Linear Transformations of Uncorrelated Random Variables Problems Chapter 16. Conditional Expectation Introduction 16-1. Averaging Over a Conditioning Event 16-2. A Conditioning Event Determined by a Second Random Variable 16-3. Averaging Over a Partition of an Event 16-4. Conditioning by a Discrete Random Variable 16-5. Conditioning by a Continuous Random Variable 16-6. Some Properties of Conditional Expectation 16-7. Regression Theory 16-8. Estimating a Probability ProblemsPart V. Sequences Of Random Variables Chapter 17. Sequences of Random Variables Introduction 17-1. Composite Trials 17-2. The Multinomial Distribution 17-3. The Law of Large Numbers 17-4. The Strong Law of Large Numbers 17-5. The Central Limit Theorem 17-6. Applications to Statistics Problems Chapter 18. Constant Markov Chains Introduction 18-1. Definitions and an Introductory Example 18-2. Some Examples of Markov Chains 18-3. Transition Diagrams and Accessibility of States 18-4. Recurrence and Periodicity 18-5. Some Results for Irreducible Chains Problems Appendix A. Numerical Tables A-1. Factorials and Their Logarithms A-2. The Exponential Function A-3. Binomial Coefficients A-4. The Summed Binomial Distribution A-5. Standardized Normal Distribution Function Appendix B. Some Mathematical Aids B-1. Binary Representation of Numbers B-2. Geometric Series B-3. Extended Binomial Coefficient B-4. Gamma Function B-5. Beta Function B-6. MatricesSelected ReferencesSelected Answers and HintsIndex of Symbols and AbbreviationsIndex
- Edition: 1
- Published: January 1, 1973
- No. of pages (eBook): 420
- Imprint: Academic Press
- Language: English
- Paperback ISBN: 9781483244747
- eBook ISBN: 9781483277202
Read Introduction to Applied Probability on ScienceDirect