Introduction to Probability
Course Notes
Foundations, random variables, and distributions
Contents
1 Introduction To Probability
1.1 Introduction
1.2 Notation and Terminology
1.3 Definitions and Axioms of Probability
1.4 Independent Events, Conditional Probability and Bayes’ Theorem
1.5 Counting Techniques
2 Random Variables and Probability Distributions
2.1 Random Variables
2.2 Discrete Random Variables
2.3 Continuous Random Variables
2.4 Mathematical Expectations and Generating Functions of Random Variables
2.5 Some Important Discrete Probability Mass Function
2.6 Some Important Continuous Probability Density Functions
2.7 Cumulative Distribution Function (CDF)
2.8 Markov’s and Chebyshev’s Inequality
3 Jointly Distributed Random Variables
3.1 Introduction
3.2 Joint Distributions
3.3 Conditional Probability Functions and Independence of Random Variables
3.4 Joint Moment Generating Function
1 Introduction To Probability
1.1 Introduction
1.2 Notation and Terminology
1.3 Definitions and Axioms of Probability
1.4 Independent Events, Conditional Probability and Bayes’ Theorem
1.5 Counting Techniques
2 Random Variables and Probability Distributions
2.1 Random Variables
2.2 Discrete Random Variables
2.3 Continuous Random Variables
2.4 Mathematical Expectations and Generating Functions of Random Variables
2.5 Some Important Discrete Probability Mass Function
2.6 Some Important Continuous Probability Density Functions
2.7 Cumulative Distribution Function (CDF)
2.8 Markov’s and Chebyshev’s Inequality
3 Jointly Distributed Random Variables
3.1 Introduction
3.2 Joint Distributions
3.3 Conditional Probability Functions and Independence of Random Variables
3.4 Joint Moment Generating Function