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Concepts of Probability Theory: Second Revised Edition (Dover Books on Mathematics)by Paul E Pfeiffer
Synopses & ReviewsPublisher Comments:This approach to the basics of probability theory employs the simple conceptual framework of the Kolmogorov model, a method that comprises both the literature of applications and the literature on pure mathematics. The author also presents a substantial introduction to the idea of a random process. Intended for college juniors and seniors majoring in science, engineering, or mathematics, the book assumes a familiarity with basic calculus. After a brief historical introduction, the text examines a mathematical model for probability, random variables and probability distributions, sums and integrals, mathematical expectation, sequence and sums of random variables, and random processes. Problems with answers conclude each chapter, and six appendixes offer supplementary material. This text provides an excellent background for further study of statistical decision theory, reliability theory, dynamic programming, statistical game theory, coding and information theory, and classical sampling statistics. Synopsis:Using the Kolmogorov model, this intermediatelevel text discusses random variables, probability distributions, mathematical expectation, random processes, more. For advanced undergraduate students of science, engineering, or math. Includes problems with answers and six appendixes. 1965 edition. Synopsis:Mathematical model for probability, random variables, probability distributions, mathematical expectation, random processes, etc.
Synopsis:Using Kolmogorov model, book discusses random variables, probability distributions, mathematical expectation, random processes, etc. For college juniors, seniors in science, engineering or math. Problems with answers. 6 appendices. Intermediate level.
Synopsis:Using the Kolmogorov model, this intermediatelevel text discusses random variables, probability distributions, mathematical expectation, random processes, more. For advanced undergraduates students of science, engineering, or math. Includes problems with answers and six appendixes. 1965 edition. Table of ContentsPreface
Chapter 1. Introduction 11. Basic Ideas and the Classical Definition 12. Motivation for a More General Theory Selected References Chapter 2. A Mathematical Model for Probability 21. In Search of a Model 22. A Model for Events and Their Occurrence 23. A Formal Definition of Probability 24. An Auxiliary ModelProbability as Mass 25. Conditional Probability 26. Independence in Probabililty Theory 27. Some Techniques for Handling Events 28. Further Results on Independent Events 29. Some Comments on Strategy Problems Selected References Chapter 3. Random Variables and Probability Distributions 31. Random Variables and Events 32. Random Variables and Mass Distributions 33. Discrete Random Variables 34. Probability Distribution Functions 35. Families of Random Variables and Vectorvalued Random Variables 36. Joint Distribution Functions 37. Independent Random Variables 38. Functions of Random Variables 39. Distributions for Functions of Random Variables 310. Almostsure Relationships Problems Selected References Chapter 4. Sums and Integrals 41. Integrals of Riemann and Lebesque 42. Integral of a Simple Random Variable 43. Some Basic Limit Theorems 44. Integrable Random Variables 45. The LebesgueStieltjes Integral 46. Transformation of Integrals Selected References Chapter 5. Mathematical Expectation 51. Definition and Fundamental Formulas 52. Some Properties of Mathematical Expectation 53. The Mean Value of a Random Variable 54. Variance and Standard Deviation 55. Random Samples and Random Variables 56. Probability and Information 57. Momentgenerating and Characteristic Functions Problems Selected References Chapter 6. Sequences and Sums of Random Variables 61. Law of Large Numbers (Weak Form) 62. Bounds on Sums of Independent Random Variables 63. Types of Convergence 64. The Strong Law of Large Numbers 65. The Central Limit Theorem Problems Selected References Chapter 7. Random Processes 71. The General Concept of a Random Process 72. Constant Markov Chains 73. Increments of Processes; The Poisson Process 74. Distribution Functions for Random Processes 75. Processes Consisting of Step Functions 76. Expectations; Correlation and Covariance Functions 77. Stationary Random Processes 78. Expectations and Time Averages; Typical Functions 79. Gaussian Random Processes Problems Selected References Appendixes Appendix A. Some Elements of Combinatorial Analysis Appendix B. Some Topics in Set Theory Appendix C. Measurability of Functions Appendix D. Proofs of Some Theorems Appendix E. Integrals of Complexvalued Random Variables Appendix F. Summary of Properties and Key Theorems BIBLIOGRAPHY INDEX What Our Readers Are SayingBe the first to add a comment for a chance to win!Product Details
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