INDICE: Part I: THE BASIC MODEL. Introduction to Part I. Sec. 1 Dealing with 'Real World' Problems. Sec. 2 The Probabilistic Experiment. Sec. 3 Outcomes.Sec. 4 Events. Sec. 5 The Connection to the Mathematical World. Sec. 6 Elements and Sets. Sec. 7 Classes of Sets. Sec. 8 Elementary Set Operations. Sec. 9 Additional Set Operations. Sec. 10 Functions. Sec. 11 The Size of a Set. Sec. 12 Multiple and Infinite Set Operations. Sec. 13 More About Additive Classes. Sec. 14 Additive Set Functions. Sec. 15 More about Probabilistic Experiments. Sec. 16 The Probability Function. Sec. 17 Probability Space. Sec. 18 Simple Probability Arithmetic. Summary of Part I. Part II: THE APPROACH TO ELEMENTARY PROBABILITY PROBLEMS. Introduction to Part II. Sec. 19 About Probability Problems. Sec. 20 Equally Likely Possible Outcomes. Sec. 21 Conditional Probability.Sec. 22 Conditional Probability Distributions. Sec. 23 Independent Events. Sec. 24 Classes of Independent Events. Sec. 25 Possible Outcomes Represented as Ordered k-tuples. Sec. 26 Product Experiments and Product Spaces. Sec. 27 Product Probability Spaces. Sec. 28 Dependence Between the Components in an Ordered k-tuple. Sec. 29 Multiple Observations Without Regard to Order. Sec. 30 Unordered Sampling with Replacement. Sec. 31 More Complicated Discrete ProbabilityProblems. Sec. 32 Uncertainty and Randomness. Sec. 33 Fuzziness. Summary of Part II. Part III: INTRODUCTION TO RANDOM VARIABLES. Introduction to Part III. Sec. 34 Numerical-Valued Outcomes. Sec. 35 The Binomial Distribution. Sec. 36 The Real Numbers. Sec. 37 General Definition of a Random Variable. Sec. 38 TheCumulative Distribution Function. Sec. 39 The Probability Density Function. Sec. 40 The Gaussian Distribution. Sec. 41 Two Discrete Random Variables. Sec. 42 Two Arbitrary Random Variables. Sec. 43 Two-Dimensional Distribution Functions. Sec. 44 Two-Dimensional Density Functions Sec. 45 Two Statistically Independent Random Variables. Sec. 46 Two Statistically Independent R.V.'s Absolutely Continuous Case. Summary of Part III. Part IV: TRANSFORMATIONS AND MULTIPLERANDOM VARIABLES. Introduction to Part IV. Sec. 47 Transformation of a RandomVariable. Sec. 48 Transformation of a Two-Dimensional Random Variable. Sec. 49 The Sum of Two Discrete Random Variables. Sec. 50 The Sum of Two Arbitrary Random Variables. Sec. 51 n-Dimensional Random Variables. Sec. 52 Absolutely Continuous n-Dimensional Random Variables. Sec. 53 Coordinate Transformations. Sec. 54 Rotations and the Bivariate Gaussian Distribution. Sec. 55 Several Statistically Independent RandomVariables. Sec. 56 Singular Distributions in One Dimension. Sec. 57 Conditional Induced Distribution, Given an Event. Sec. 58 Resolving a Distribution into Components of Pure Type. Sec. 59 Conditional Distribution Given the Value of a Random Variable. Sec. 60 Random Occurrences in Time. Summary of Part IV. Part V: PARAMETERS FOR DESCRIBING R.V.S AND INDUCED DISTRIBUTIONS. Introduction to Part V. Sec. 61 Some Properties of a Random Variable. Sec. 62 Higher Moments. Sec. 63 Expectation of a Function of a Random Variable. Sec. 64 The Variance of a Function of a Random Variable. Sec. 65 Boundson the Induced Distribution. Sec. 66 Test Sampling. Sec. 67 Conditional Expectation With Respect to an Event. Sec. 68 Covariance and Correlation Coefficient. Sec. 69 The Correlation Coefficient as Parameter in a Joint Distribution. Sec. 70 More General Kinds of Dependence Between Random Variables. Sec. 71 The Covariance Matrix. Sec. 72 Random Variables as the Elements of a Vector Space.Sec. 73 Estimation. Sec. 74 The Stieltjes Integral. Summary of Part V. Part VI: FURTHER TOPICS IN RANDOM VARIABLES. Introduction to Part VI. Sec. 75 Complex Random Variables. Sec. 76 The Characteristic Function. Sec. 77 Characteristic Function of a Transformed Random Variable. Sec. 78 Characteristic Function of a Multi-Dimensional R.V. Sec. 79 The Generating Function . Sec. 80 Several Jointly Gaussian Random Variables. Sec. 81 Spherically Symmetric Vector R.V.'s.Sec. 82 Entropy Associated with Random Variables. Sec. 83 Copulas. Sec. 84 Sequences of Random Variables. Sec. 85 Convergence of Sequences. Sec. 86 Convergence of Probability Distributions and the Central Limit Theorem. Summary of Part VI. APPENDIX. Table of Query Solutions. Table of Gaussian Integral. Problems for PART I. Problems for PART II. Problems for PART III. Problems for PART IV. Problems for PART V. Problems for PART VI. Notation and Abbreviations. References. Index.
- ISBN: 978-0-470-74855-8
- Editorial: John Wiley & Sons
- Encuadernacion: Cartoné
- Páginas: 616
- Fecha Publicación: 26/11/2010
- Nº Volúmenes: 1
- Idioma: Inglés