Introduction to Probability

Some Handouts are Listed Below:

• Introduction

• Sets and Probabilistic Models

• Conditional Probability, Total Probability Theorem, Bayes Rule

• Independence and Counting

• Discrete Random Variables: Basics

• Discrete Random Variables: Expectation, Mean and Variance

• Discrete Random Variables: Joint PMFs, Conditioning and Independence

• Continuous Random Variables: Basics

• Continuous Random Variables: Conditioning, Expectation and Independence

• Further Topics on Random Variables: Derived Distributions

• Further Topics on Random Variables: Covariance and Correlation

• Further Topics on Random Variables: Conditional Expectation and Variance Revisited

• Further Topics on Random Variables: Transforms (Moment Generating Functions)

• Limit Theorems

References:

• D. P. Bertsekas, J. N. Tsitsiklis, “Introduction to Probability,” Athena Scientific, 2008.