包邮Probability and Stochastic Processes

Chapter 1 Events and Their Probabilities
1．1 The History of Probability
1．2 Experiment， Sample Space and Random Event
1．2．1 Basic Definitions
1．2．2 Events as Sets
1．3 Probabilities Defined on Events
1．3．1 Classical Probability
1．3．2 Geometric Probability
1．3．3 The Frequency Interpretation of Probability
1．4 Probability Space
1．4．1 Axiomatic Definition of Probability
1．4．2 Properties of Probability
1．5 Conditional Probabilities
1．5．1 The Definition of Conditional Probability
1．5．2 The Multiplication Rule
1．5．3 Total Probability Formula
1．5．4 Bayes' Theorem
1．6 Independence of Events
1．6．1 Independence of Two Events
1．6．2 Independence of Several Events
1．6．3 Bernoulli Trials
1．7 Review
1．8 Exercises

Chapter 2 Random Variable
2．1 The Definition of a Random Variable
2．2 The Distribution Function of a Random Variable
2．2．1 The Definition and Properties of Distribution Function ． ． ．
2．2．2 The Distribution Function of Function of a Random Variable
2．3 Mathematical Expectation and Variance
2．3．1 Expectation of a Random Variable
2．3．2 Expectation of Functions of a Random Variable
2．3．3 Variance of a Random Variable
2．3．4 The Application cf Expectation and Variation
2．4 Discrete Random Variables
2．4．1 Binomial Distribution with Parameters n and p
2．4．2 Geometric Distribution
2．4．3 Poisscn Distribution with Parameters
2．5 Continuous Rsndom Variables
2．5．1 Uniform Distribution
2．5．2 Exponential Distribution
2．5．3 Normal Distribution
2．6 Review
2．7 Exerciscs

Chapter 3 Random Vectors
3．1 Random Vectors and Joint Distributions
3．1．1 Random Vectors and Joint Distributions
3．1．2 Discrete Random Vectors
3．1．3 Continuous Random Vectors
3．2 Independence cf Random Variables
3．3 Conditional Distributions
3．3．1 Discrete Case
3．3．2 Continuous Case
3．4 One Function of Two Random Variables
3．4．1 Discrete Case
3．4．2 Continuous case
3．5 Transformation of Two Random Variables
3．6 Numerical Charscteristics of Random Vectors
3．6．1 Expectation cf Sums and PIoducts
3．6．2 Covariance and Correlation
3．7 Multivariate Distributions
3．7．1 Distribution Functions of Multiple Random Vectors
3．7．2 Numerical Characteristics of Random Vectors
3．7．3 Multiple Normal Distribution
3．8 Review
3．9 Exercises

Chapter 4 Sequences of Random Variables
4．1 Family of Distribution Functions and Numerical Characteristics
4．2 Modes of Convergence
4．3 The Law of Large Numbers
4．4 The Central Limit Theorem
4．5 Review
4．6 Exercises

Chapter 5 Introduction to Stochastic Processes
5．1 Definition and Classification
5．2 The Distribution Family and the Moment Functions
5．3 The Moments of the Stochastic Processes
5．3．1 Mean， Autocorrelation and Autocovariance
5．3．2 Cross-correlation and Cross-covariance
5．4 Stochastic Analysis
5．5 Review
5．6 Exercises

Chapter 6 Stationary Processes
6．1 Stationary Processes
6．1．1 Strict Stationary Processes
6．1．2 Wide Stationary Processes
6．1．3 Joint Stationary Processes
6．2 Ergodicity of Stationary Processes
6．3 Power Spectral Density of Stationary Processes
6．3．1 Average Power and Power Spectral Density
6．3．2 Power Spectral Density and Autocorrelation Function
6．3．3 Cross-Power Spectral Density
6．4 Stationary Processes and Linear Systems
6．5 Review
6．6 Exercises

Chapter 7 Finite Markov Chains
7．1 Basic Concepts
7．2 Markov Chains Having Two States
7．3 Higher Order Transition Probabilities and Distributions
7．4 Invariant Distributions and Ergodic Markov Chain
7．5 How Does Google Work?
7．6 Review
7．7 Exercises

Chapter 8 Independent-Increment Processes
8．1 Independent-Increment Processes
8．2 Poisson Process
8．3 Gaussian Processes
8．4 Brownian Motion and Wiener Processes
8．5 Review
8．6 Exercises

Bibliography
Appendix
Table of Binomial Cofficients
Table of Binomial Probabilities
Table of Poisson Probabilities
Table of Normal Probabilities