Course Outline

UNIT 0. Preliminary

1. Introduction to the Course
2. The Basic Concept of Probability and its History
3. Review of Set Theory

UNIT 1. Probability

1. Building Blocks of the Probability Structure
2. Approaches of Assigning Probabilities
3. Probability Function (Axiomatic Definition of Probability)
4. Properties of a Probability Function and the Probability Space
5. The Event Composition Method
6. Finite Sample Spaces
7. Conditional Probability
8. Theorem of Total Probability
9. The Bayes’ Theorem/Bayes’ Rule
10. Multiplication Rule
11. Independence of Events

UNIT 2. Random Variables, Distribution Functions and Expectations

1. Random Variables
2. Cumulative Distribution Function (CDF)
3. Characteristics of Random Variables according to their Type
4. Expectations
5. Moments
6. Moment Generating Function
7. Factorial Moment Generating Function

UNIT 3. Some Special Parametric Families of Univariate Distributions

1. Parametric Families of Discrete Distributions
2. Parametric Families of Continuous Densities

UNIT 4. Joint and Conditional Distributions, Stochastic Independence, More Expectation

1. Joint Distribution Functions
2. Conditional Distributions and Stochastic Independence
3. Expectation

UNIT 5. Functions of Random Variables

1. Distribution of a Function of a Random Variable
2. Expectations of a Function of a Random Variable