Advanced Probability Theory Course | IIT Delhi | Prof. Niladri Chatterjee
Course Details
| Exam Registration | 163 |
|---|---|
| Course Status | Ongoing |
| Course Type | Core |
| Language | English |
| Duration | 12 weeks |
| Categories | Mathematics |
| Credit Points | 3 |
| Level | Undergraduate/Postgraduate |
| Start Date | 19 Jan 2026 |
| End Date | 10 Apr 2026 |
| Enrollment Ends | 02 Feb 2026 |
| Exam Registration Ends | 20 Feb 2026 |
| Exam Date | 18 Apr 2026 IST |
| NCrF Level | 4.5 — 8.0 |
Unlock the Mathematical Foundations of Data Science with Advanced Probability Theory
Probability theory forms the bedrock of modern data science, artificial intelligence, and quantitative finance. For students and professionals aiming to build a rigorous understanding of these fields, a deep grasp of advanced probability is non-negotiable. We are proud to present a comprehensive 12-week course on Advanced Probability Theory, meticulously designed and delivered by Prof. Niladri Chatterjee from the prestigious Indian Institute of Technology (IIT) Delhi.
Meet Your Instructor: Prof. Niladri Chatterjee
Learning from an expert with both depth and breadth of experience is crucial. Prof. Chatterjee brings over 30 years of research and teaching experience to this course. His distinguished academic journey includes:
- B.Stat and M.Stat from the Indian Statistical Institute, Kolkata.
- M.Tech in Computer Science and a PhD in Computer Science from University College London.
- His major research interests span Artificial Intelligence, Machine Learning, Natural Language Processing, and Statistical Modeling.
- He serves as a member of several Government of India committees related to AI and Machine Learning policy.
This unique blend of statistical rigor and computer science application makes him the perfect guide to bridge theoretical probability with its real-world implementations in AI and finance.
Who is This Course For?
- Intended Audience: Undergraduate and Postgraduate students in Statistics, Mathematics, Computer Science, and Machine Learning.
- Prerequisites: A solid foundation in Basics of Real Analysis, Functions of Two Variables, and Convergence of a Sequence/Series is required to fully benefit from this advanced material.
- Industry Support: This knowledge is highly valued in most Financial companies, quantitative trading firms, and cutting-edge AI research labs.
Course Overview: A 12-Week Journey into Probability
This course builds probability theory from its axiomatic foundations, progressing to advanced concepts crucial for statistical inference and machine learning. Here’s a detailed week-by-week breakdown:
| Week | Topics Covered |
|---|---|
| Week 1 | Introduction, Sample Space, Kolmogorov’s Probability Axioms, Theorems on Union/Intersection, Bertrand’s Paradox. |
| Week 2 | Conditional Probability, Bayes Theorem, Probability on Finite Sample Spaces, Independence of Events. |
| Week 3 | Discrete Random Variables: Uniform, Bernoulli, Binomial, Geometric, Poisson, Hypergeometric, Negative Binomial. |
| Week 4 | Continuous Random Variables: Uniform, Normal, Exponential, Gamma, Cauchy, Beta distributions. |
| Week 5 | Moments of a Distribution, Bivariate Distributions, Covariance and Correlation. |
| Week 6 | Generating Functions & Properties: Moment Generating Function (MGF), Characteristic Function, Probability Generating Function (PGF). |
| Week 7 | Poisson Process, Conditional Expectation & Variance, Chebyshev's Inequality, Introduction to Bivariate Normal Distribution. |
| Week 8 | Functions of Random Variables, Introduction to t-distribution and F-distribution. |
| Week 9 | Order Statistics: Derivation of distributions for range, median, etc. |
| Week 10 | Limit Theorems: Modes of Convergence (in probability, almost surely, in distribution). |
| Week 11 | Laws of Large Numbers (Weak and Strong). |
| Week 12 | Central Limit Theorems – The cornerstone of statistical inference. |
Key Learning Outcomes
By the end of this course, you will have mastered:
- The axiomatic approach to probability via Kolmogorov’s framework.
- Properties and applications of key discrete and continuous probability distributions.
- The power of generating functions (MGF, PGF, Characteristic) for analyzing distributions.
- Techniques to handle functions of random variables and understand derived distributions like t, chi-square, and F.
- The fundamentals of Order Statistics, essential for non-parametric statistics.
- The critical Limit Theorems that justify most statistical sampling and machine learning methods.
Recommended Textbooks
To supplement the lectures, the following authoritative texts are recommended:
- An Introduction to Probability and Statistics by Vijay K. Rohatgi and A.K. Md. Ehsanes Saleh (Wiley).
- Mathematical Statistics by Suddhendu Biswas and G.L. Sriwastav (Narosa).
Why Enroll in This Advanced Probability Theory Course?
This is more than just a mathematics course. It is training in a fundamental mode of thinking required to model uncertainty, make inferences from data, and build robust AI systems. Whether you aim for a career in quantitative finance, data science, AI research, or academic statistics, the rigorous understanding provided by this course, under the guidance of an IIT Delhi professor, will be an invaluable asset. Move beyond applied tutorials and build the theoretical mastery that will set you apart.
Enroll Now →