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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£º Discrete Case
3£®1£®2 Joint Distribution Function£º Continuous Case
3£®2 Independent Random Variables
3£®3 Conditional Distributions
3£®3£®1 Conditional Distributions£º Discrete Case
3£®3£®2 Conditional Distributions£º 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
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