Part A Probability and Random Variables
1 Axioms of Probability
1．i Introduction
1．2 Sample Space and Events
1．3 The Relative Frequency Definition of Probability
1．4 Axioms of Probability
1．5 Sample Spaces Having Equally Likely Outcomes
1．6 Conditional Probability
1．7 The Law of Total Probability （ Partition Theorem）
1．8 Bayes' Theorem
Exercises

2 Random Variables and Their Distributions
2．1 Random Variables
2．2 Discrete Random Variables
2．3 Some Important Discrete Probability Distributions
2．3．1 Uniform Distribution （Discrete Case）
2．3．2 Bernoulli Trial
2．3．3 Binomial Distribution
2．3．4 Poisson Distribution
2．3．5 Geometric Distribution
2．4 Cumulative Distribution Functions
2．5 Continuous Random Variables
2．6 Some Important Continuous Probability Distributions
2．6．1 Uniform Distribution （Continuous Case）
2．6．2 Normal Distribution
2．6．3 Exponential Distribution
2．7 Distributions of Functions of a Random Variable
Exercises

3 Multivariate Random Variables
3．1 Joint Distribution Function
3．1．1 Joint Distribution Function： Discrete Case
3．1．2 Joint Distribution Function： Continuous Case
3．2 Independent Random Variables
3．3 Conditional Distributions
3．3．1 Conditional Distributions： Discrete Case
3．3．2 Conditional Distributions： Continuous Case
3．4 Two Particular Multivariate Distribution
3．4．1 Uniform Distribution
3．4．2 Bivariate Normal Distribution
3．5 Distributions of Special Functions of Two Random Variables
3．5．1 Discrete Multivariate Random Variable
3．5．2 Continuous Multivariate Random Variable
Exercises

4 The Expectation and Variance
4．1 Expectations of Random Variables
4．2 The Variance of Random Variables
4．3 Some Important Expectations and Variance
4．3．1 Uniform Distribution （ Discrete Case）
4．3．2 Binomial Distribution
4．3．3 Poisson Distribution
……