Probability & Statistics Course | IIT Delhi Prof. Dharmaraja | 12-Week Guide
Course Details
| Exam Registration | 570 |
|---|---|
| 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 | 24 Apr 2026 IST |
| NCrF Level | 4.5 — 8.0 |
Introduction to Probability Theory and Statistics: A Foundational Course for the Modern World
In an era driven by data and uncertainty, a firm grasp of Probability Theory and Statistics is no longer a luxury—it's a necessity. These disciplines form the backbone of decision-making in fields ranging from artificial intelligence and finance to engineering and scientific research. Recognizing this critical need, the Indian Institute of Technology Delhi offers a comprehensive course, Introduction to Probability Theory and Statistics, designed and taught by the esteemed Prof. S. Dharmaraja.
About the Instructor: Prof. S. Dharmaraja
Learning from an expert with both deep academic roots and extensive practical experience is invaluable. Prof. Dharmaraja brings precisely that to this course. As the Head of the Department of Mathematics at IIT Delhi and an Institute Chair Professor, his credentials are impeccable.
He holds a Ph.D. from IIT Madras and has enriched his expertise through post-doctoral research at Duke University, USA. His prolific research in applied probability, queueing theory, and financial mathematics is reflected in over 45 international journal publications. Furthermore, he is the co-author of several key textbooks used in this very course, ensuring the curriculum is both authoritative and pedagogically sound. His global academic visits to institutions in the USA, Canada, Italy, and Korea bring a world-class perspective to the subject.
Course Overview and Objectives
This 12-week course is structured to take you from the fundamental axioms of probability to advanced statistical inference techniques. It is tailored for undergraduate and postgraduate students in mathematics, engineering, economics, and the sciences.
PREREQUISITES: A basic knowledge of Linear Algebra and Calculus is recommended to fully engage with the material.
The course aims to:
- Provide a rigorous, axiomatic foundation in probability.
- Explore key concepts like random variables, distributions, and moments.
- Delve into statistical methods for estimation, hypothesis testing, and modeling relationships via correlation and regression.
- Equip you with the tools to model and solve real-world problems involving uncertainty and data analysis.
Who Should Take This Course & Industry Relevance
This course is a cornerstone for anyone aspiring to a career in quantitative fields. The INDUSTRY SUPPORT listed speaks volumes: top-tier finance firms like Goldman Sachs, Morgan Stanley, and RBS, along with quantitative trading firms like Quant and Futures First, actively seek professionals with these skills.
Beyond finance, the curriculum is essential for:
- Data Scientists & Analysts: For building predictive models and drawing insights from data.
- Machine Learning Engineers: Probability is the language of machine learning algorithms.
- Researchers & Academics: Across physical, social, and biological sciences.
- Engineers: For reliability testing, signal processing, and systems design.
Detailed 12-Week Course Layout
| Week | Topic | Key Concepts |
|---|---|---|
| Week 1 | Basics of Probability | Axioms, conditional probability, independence |
| Week 2 | Random Variable | Definition, types (discrete/continuous), CDF, PDF/PMF |
| Week 3 | Moments and Inequalities | Expectation, variance, Chebyshev’s inequality |
| Week 4 | Standard Distributions | Binomial, Poisson, Normal, Exponential |
| Week 5 | Higher Dimensional Distributions | Joint distributions, marginal & conditional distributions |
| Week 6 | Functions of Several Random Variables | Transformations, sums of random variables |
| Week 7 | Cross Moments | Covariance, correlation, independence |
| Week 8 | Limiting Distributions | Convergence, Central Limit Theorem |
| Week 9 | Descriptive Statistics and Sampling Distributions | Mean, median, variance, t-distribution, chi-square |
| Week 10 | Point and Interval Estimations | MLE, confidence intervals |
| Week 11 | Testing of Hypothesis | Null/alternative hypothesis, p-values, t-tests |
| Week 12 | Analysis of Correlation and Regression | Linear regression, least squares, correlation coefficient |
Recommended Textbooks
The course is closely aligned with authoritative texts, including those co-authored by Prof. Dharmaraja himself:
- Introduction to Probability and Stochastic Processes with Applications by Liliana Blanco Castaneda, Viswanathan Arunachalam, and Selvamuthu Dharmaraja (Wiley).
- Introduction to Statistical Methods, Design of Experiments and Statistical Quality Control by Selvamuthu Dharmaraja and Dipayan Das (Springer).
- An Introduction to Probability and Statistics by Vijay K. Rohatgi and A.K. Md. Ehsanes Saleh (Wiley).
Conclusion: Building a Framework for the Future
The Introduction to Probability Theory and Statistics course from IIT Delhi is more than just an academic module; it's an investment in a fundamental skill set for the 21st century. Under the guidance of Prof. Dharmaraja, students gain not only theoretical knowledge but also an understanding of how to apply these principles to tangible, complex problems. Whether your goal is to innovate in fintech, advance AI research, or optimize engineering systems, this course provides the critical probabilistic and statistical framework to turn data into decisions and uncertainty into insight.
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