In this module, you will learn about counting principles, permutations, and combinations used to enumerate possible outcomes.

Sessions: 

• Session 02: Counting
• Session 03: Counting Exercises 

In this module, you will learn how to define sample spaces, events, and probability axioms for computing event probabilities.

Sessions: 

• Session 04: Probability of Events

In this module, you will learn about conditional probability, total probability, and Bayes’ theorem for updating probabilities.

Sessions: 

• Session 05: Conditional Probability
• Session 06: Conditional Probability Examples
• Session 07: Total Probability
• Session 08: Bayes’ Theorem

In this module, you will learn about random variables and their probability distributions, covering both discrete and continuous models commonly used in practice. The module explores expectation, variance, and functions of random variables, along with important distributions such as Bernoulli, Poisson, Normal, Exponential, and Log-normal, emphasizing real-world applications.

Sessions: 

• Session 09: Random Variables
• Session 10: Functions of Random Variables, Expectation, Variance, Chebyshev’s Theorem 
• Session 11: Uniform and Bernoulli Random Variables 
• Session 12: Negative Binomial, Geometric, Multinomial Random Variables
• Session 13: Hypergeometric Random Variable 
• Session 14: Poisson and Exponential Random Variables 
• Session 15: Normal Distribution 
• Session 16: Log Normal Random Variable
• Session 17: Maximum Likelihood Estimation 

In this module, you will learn about joint distributions and conditional distributions of multiple random variables.

Sessions: 

• Session 18: Joint Probability Mass Functions/Joint Probability Density Functions
• Session 19: Joint Distributions Continued
• Session 20: Conditional Probability Mass Functions 
• Session 21: Cumulative Conditional Mass Functions and Density Functions

In this module, you will learn about expectation, variance, covariance, correlation, moment generating functions, and probability inequalities.

Sessions: 

• Session 22: Expectation, Variance, Covariance, Correlation 
• Session 23: Moment Generating Functions 
• Session 24: Markov and Chebyshev Inequalities 

In this module, you will learn about fundamental results describing long-run behavior of random variables and averages.

Sessions: 

• Session 25: Law of Large Numbers
• Session 26: Central Limit Theorem 

In this module, you will learn about discrete-time Markov chains and stochastic processes with memoryless behavior.

Sessions: 

• Session 27: Discrete Time Markov Chains