●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 Rr
1.Distributions and Expectations
2.Preliminaries
3.Densities
4.Convolutions
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這部暢銷70年的概率論經典著作，50多次重印發行，已經成為概率論及相關專業的學者的不可或缺的讀物。這部著作的寫作初衷是關於概率論中的分析方法，分析方法是純數學的一個重要分支，這樣可以使得本書與數學的格式更加一致，並且從美學的觀點更加令人滿意，因而對純粹的數學家更加有吸引力。然而，本書最終得到了廣泛的支持，超出了作者的預期，使得這本書雄心勃勃，目標明確，不再費力去滿足各種各樣的需求。本書的目標是將概率論闡述為一個接近自成體繫的嚴謹的數學科目，避免非數學的觀點。本集為第2版第2卷。