دانلود کتاب Concepts of Probability Theory: Second Revised Edition

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Title Page......Page 2
Copyright Page......Page 3
PREFACE......Page 4
Contents......Page 8
Chapter 1. Introduction......Page 11
1-1. Basic Ideas and the Classical Definition......Page 12
1-2. Motivation for a More General Theory......Page 14
Selected References......Page 16
Chapter 2. A Mathematical Model for Probability......Page 17
2-1. In Search of a Model......Page 20
2-2. A Model for Events and Their Occurrence......Page 24
2-3. A Formal Definition of Probability......Page 38
2-4. An Auxiliary Model—Probability as Mass......Page 48
2-5. Conditional Probability......Page 52
2-6. Independence in Probability Theory......Page 66
2-7. Some Techniques for Handling Events......Page 80
2-8. Further Results on Independent Events......Page 96
2-9. Some Comments on Strategy......Page 112
Problems......Page 114
Selected References......Page 126
3-1. Random Variables and Events......Page 128
3-2. Random Variables and Mass Distributions......Page 140
3-3. Discrete Random Variables......Page 143
3-4. Probability Distribution Functions......Page 152
3-5. Families of Random Variables and Vector-valued Random Variables......Page 165
3-6. Joint Distribution Functions......Page 171
3-7. Independent Random Variables......Page 177
3-8. Functions of Random Variables......Page 184
3-9. Distributions for Functions of Random Variables......Page 190
3-10. Almost-sure Relationships......Page 206
Problems......Page 210
Selected References......Page 223
Chapter 4. Sums and Integrals......Page 224
4-1. Integrals of Riemann and Lebesgue......Page 225
4-2. Integral of a Simple Random Variable......Page 229
4-3. Some Basic Limit Theorems......Page 235
4-4. Integrable Random Variables......Page 236
4-5. The Lebesgue-Stieltjes Integral......Page 239
4-6. Transformation of Integrals......Page 243
Selected References......Page 246
5-1. Definition and Fundamental Formulas......Page 247
5-2. Some Properties of Mathematical Expectation......Page 253
5-3. The Mean Value of a Random Variable......Page 258
5-4. Variance and Standard Deviation......Page 263
5-5. Random Samples and Random Variables......Page 272
5-6. Probability and Information......Page 274
5-7. Moment-generating and Characteristic Functions......Page 288
Problems......Page 293
Selected References......Page 304
Chapter 6. Sequences and Sums of Random Variables......Page 306
6-1. Law of Large Numbers (Weak Form)......Page 307
6-2. Bounds on Sums of Independent Random Variables......Page 311
6-3. Types of Convergence......Page 316
6-4. The Strong Law of Large Numbers......Page 322
6-5. The Central Limit Theorem......Page 324
Problems......Page 326
Selected References......Page 329
Chapter 7. Random Processes......Page 331
7-1. The General Concept of a Random Process......Page 332
7-2. Constant Markov Chains......Page 335
7-3. Increments of Processes; The Poisson Process......Page 353
7-4. Distribution Functions for Random Processes......Page 357
7-5. Processes Consisting of Step Functions......Page 359
7-6. Expectations; Correlation and Covariance Functions......Page 364
7-7. Stationary Random Processes......Page 377
7-8. Expectations and Time Averages; Typical Functions......Page 381
7-9. Gaussian Random Processes......Page 389
Problems......Page 393
Selected References......Page 398
Appendix A. Some Elements of Combinatorial Analysis......Page 401
Appendix B. Some Topics in Set Theory......Page 405
Appendix C. Measurability of Functions......Page 416
Appendix D. Proofs of Some Theorems......Page 419
Appendix E. Integrals of Complex-valued Random Variables......Page 424
Appendix F. Summary of Properties and Key Theorems......Page 426
BIBLIOGRAPHY......Page 440
INDEX......Page 443
Back Cover......Page 456