Introduction to Continuous Probability Theory

Table of Contents

Chapter 1. One Random Variable

• Introduction
• Single Random Variable
• Indicator Functions
• Density Functions and Probability of Events
• Distribution Functions
• New Notation for Px ([a, b[)
• Exercises

Chapter 2. Two Random Variables

• Joint Density Functions and Joint Probability
• Marginal and Conditional Density Functions
• Transformations of Random Variables
• Exercises

Chapter 3. Expected Value and Moments

• Expected Value
• Conditional Expectation Random Variable
• Variance, Covariance and Correlation
• Moments and Generating Functions
• Exercises

Chapter 4. Discrete Probability Distributions

• Introduction
• Bernoulli Trials
• The Geometric Distribution
• The Binomial Distribution
• The Poisson Distribution
• The Typergeometric Distribution
• The Multinomial Distribution
• Exercises

Chapter 5. Continuous Probability Distributions

• The Normal Distribution
• Bivariate Normal Distribution
• The Gamma Function and Distribution
• The Chi-Square Distribution
• "Student's" t Distribution
• F Distribution
• Exercises

Chapter 6. Limit Theorems

• Introduction
• Law of Large Numbers
• Convergence in Probability
• Characteristic Functions
• Some Simple Central Limit Theorems
• Exercises

References

Appendix

Index