概率论及其应用导论(第2卷第2版)(英文版)

这部畅销70年的概率论 经典著作，50多次重印发行 ，已经成为概率论及相关专 业的学者的不可或缺的读物 。这部著作的写作初衷是关 于概率论中的分析方法，分 析方法是纯数学的一个重要 分支，这样可以使得本书与 数学的格式更加一致，并且 从美学的观点更加令人满意 ，因而对纯粹的数学家更加 有吸引力。然而，本书最终 得到了广泛的支持，超出了 作者的预期，使得这本书雄 心勃勃，目标明确，不再费 力去满足各种各样的需求。 本书的目标是将概率论阐述 为一个自成体系的严谨 的数学科目，避免非数学的 观点。 本集为第2版第2卷。

CHAPTER I THE EXPONENTIAL AND THE UNIFORM DENSITES 1. Introduction 2. Densities. Convolutions 3. The Exponential Density 4. Waiting Time Paradoxes. The Poisson Process 5. The Persistence of Bad Luck 6. Waiting Times and Order Statistics 7. The Uniform Distribution 8. Random Splittings 9. Convolutions and Covering Theorems 10. Random Directions 11. The Use of Lebesgue Measure 12. Empirical Distributions 13. Problems for Solution CHAPTER II SPECIAL DENSITIES. RANDOMIZATION 1. Notations and Conventions 2. Gamma Distributions 3. Related Distributions of Statistics 4. Some Common Densities 5. Randomization and Mixtures 6. Discrete Distributions 7. Bessel Functions and Random Walks 8. Distributions on a Circle 9. Problems for Solution CHAFFER III DENSITIES IN HIGHER DIMENSIONS. NORMAL DENSTTES AND PROCESSES 1. Densities 2. Conditional Distributions 3. Return to the Exponential and the Uniform Distributions 4. A Characterization of the Normal Distribution 5. Matrix Notation. The Covariance Matrix 6. Normal Densities and Distributions 7. Stationary Normal Processes 8. Markovian Normal Densities 9. Problems for Solution CHAPTER IV PROBABILITY MEASURES AND SPACES □ 1. Baire Functions 2. Interval Functions and Integrals in 3. Algebras. Measurability 4. Probability Spaces. Random Variables 5. The Extension Theorem 6. Product Spaces. Sequences of Independent Variables. 7. Null Sets. Completion CHAPTER V PROBABILITY DISTRIBUTIONS IN □ 1. Distributions and Expectations