MITx: Probability – The Science of Uncertainty and Data course Syllabus
Full curriculum breakdown — modules, lessons, estimated time, and outcomes.
This course provides a comprehensive and mathematically rigorous introduction to probability theory, designed to build a strong foundation for data science, machine learning, and AI applications. Organized into five core modules and a final project, the course spans approximately 14–22 weeks of study with a recommended commitment of 8–10 hours per week. Learners will progress from foundational concepts to advanced theorems, applying theoretical knowledge to real-world data contexts through problem sets and a capstone project.
Module 1: Foundations of Probability
Estimated time: 32 hours
- Axioms of probability
- Events and sample spaces
- Counting techniques
- Combinatorics
Module 2: Conditional Probability and Bayes’ Rule
Estimated time: 24 hours
- Dependence and independence
- Conditional probability
- Bayes’ theorem
- Real-world applications of conditional events
Module 3: Random Variables and Distributions
Estimated time: 36 hours
- Discrete random variables
- Continuous random variables
- Binomial, geometric, and normal distributions
- Expectation and variance
Module 4: Limit Theorems and Applications
Estimated time: 28 hours
- Law of Large Numbers
- Central Limit Theorem
- Applications in data analysis
Module 5: Advanced Probability Applications
Estimated time: 20 hours
- Statistical independence
- Joint distributions
- Problem solving with probability models
Module 6: Final Project
Estimated time: 20 hours
- Analysis of a real-world dataset using probability theory
- Application of Bayes’ theorem and conditional probability
- Interpretation of results using expectation, variance, and distribution models
Prerequisites
- Strong background in calculus
- Familiarity with basic mathematical reasoning
- Some exposure to probability concepts recommended
What You'll Be Able to Do After
- Understand and apply foundational probability theory
- Analyze random variables and probability distributions
- Apply conditional probability and Bayes’ theorem in practical scenarios
- Work confidently with discrete and continuous probability distributions
- Build a strong mathematical foundation for data science and machine learning