STAT 121 - Probability Theory I
Course Description
This course covers elements of probability; random variables; discrete and continuous random variables; probability
distributions; special distributions; mathematical expectations.
Course Learning Outcomes
At the end of this course, students will:
- Explain the notion of probability and derive its properties;
- Compute and interpret the probability of events including conditional and independent events;
- Evaluate random variables through their distribution and density functions, expectations, and
moments;
- Explain different parametric univariate distributions, derive its properties and use it to model
typical phenomena;
- Develop distribution of a function of a random variable.
Course Outline
UNIT 1. Preliminaries
- Introduction to the Course
- The Basic Concept of Probability and its History
- Review of Set Theory
UNIT 2. Probability
- Building Blocks of the Probability Structure
- Probability Functions
- Methods of Assigning Probabilities
- Properties of a Probability Function
- The Even Composition Model
- Probability Space
- Finite Sample Space
- Conditional Probability
- Theorem of Total Probability
- The Baye's Theorem
- Multiplication Rule
- Independence of Events
UNIT 3. Random Variables, Distribution Functions and Expectations
- Random Variables
- Distribution Functions
- Density and Mass Functions
- Expectations
- Moments and Moment Generating Functions
UNIT 4. Some Special Parametric Families of Univariate Distributions
- Discrete Uniform Distribution
- Bernoulli Distribution
- Binomial Distribution
- Hypergeometric Distribution
- Poisson Distribution
- Geometric Distribution
- Negative Binomial Distribution
- Uniform Distribution
- Normal Distribution
- Exponential Distribution
- Gamma Distribution
- Beta Distribution
UNIT 5. Functions of Random Variable
- Distribution of a Function of a Random Variable
- Expectation of a Function of a Random Variable