Probability -I Course with R Examples | ISI Bangalore
Course Details
| Exam Registration | 70 |
|---|---|
| Course Status | Ongoing |
| Course Type | Elective |
| Language | English |
| Duration | 12 weeks |
| Categories | Mathematics, Foundations of Mathematics |
| Credit Points | 3 |
| Level | Undergraduate |
| 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 |
Master the Foundations of Probability with Computational Power
Welcome to an in-depth exploration of Probability -I with Examples Using R, a meticulously designed 12-week undergraduate course. This program, offered by the prestigious Indian Statistical Institute (ISI), Bangalore, bridges the gap between theoretical probability and practical application. Led by Prof. Siva Athreya, an expert in Probability Theory, this course is your gateway to understanding the mathematical framework that underpins statistics, data science, and countless scientific disciplines.
Course Overview: Blending Theory and Practice
This course is structured to build your understanding from the ground up. It begins with the fundamental building blocks—Sample Spaces, Events, and the axioms of Probability—before progressing to more advanced concepts like Random Variables, standard probability distributions, and culminating with powerful limit theorems like the Law of Large Numbers and the Central Limit Theorem.
A unique and defining feature of this course is the integration of the R programming language. Instead of treating theory in isolation, you will use R to simulate experiments, visualize distributions, and verify theoretical results. This hands-on approach ensures you not only learn the 'what' but also the 'how,' solidifying your understanding through practical computation.
Who Should Enroll?
This course is ideally suited for:
- Undergraduate students in Engineering, Physical Sciences, or Mathematics who have completed their first year.
- Anyone with a solid foundation in 12th-standard-level mathematics and basic calculus.
- Professionals or enthusiasts looking to build a rigorous, application-oriented understanding of probability.
Detailed 12-Week Course Layout
The course is systematically divided into weekly modules, each focusing on key concepts and their implementation in R.
| Week | Topics Covered |
|---|---|
| Week 1 | Sample Space, Events, Probability, Properties of Probability, Introduction to R |
| Week 2 | Equally Likely Outcomes, Conditional Probability, Bayes' Theorem |
| Week 3 | Independence, Sampling and Repeated Trials |
| Week 4 | Continued study of Sampling, Introduction to the Gambler's Ruin problem |
| Week 5 | Sampling with/without replacement, Hypergeometric Distribution, Discrete Random Variables |
| Week 6 | Deep dive into Discrete Random Variables and their properties |
| Week 7 | Conditional, Joint & Marginal Distributions; Memoryless property of Geometric Distribution |
| Week 8 | Expectation of Random Variables, Properties of Expectation, Variance |
| Week 9 | Expectation of functions, Markov & Chebyshev Inequalities, Conditional Expectation & Covariance |
| Week 10 | Functions of Random Variables, Sums of Independent Random Variables |
| Week 11 | Continuous Random Variables, Exponential & Normal Distributions, Binomial convergence to Normal |
| Week 12 | Normal Random Variable (cont'd), Distribution Functions, Course Conclusion |
Key Learning Outcomes
By the end of this course, you will be able to:
- Formally define and work with sample spaces, events, and probability measures.
- Understand and apply concepts of conditional probability, independence, and Bayes' Theorem.
- Define and manipulate both discrete and continuous random variables.
- Work fluently with standard probability distributions including:
- Discrete: Uniform, Binomial, Poisson, Geometric, Hypergeometric, Negative Binomial.
- Continuous: Normal, Exponential, Gamma, Beta, Chi-square, Cauchy.
- Compute and interpret expectation, variance, and covariance.
- Use R to simulate probabilistic experiments and visualize theoretical concepts.
- Comprehend the statements and implications of the Law of Large Numbers and the Central Limit Theorem.
Meet Your Instructor: Prof. Siva Athreya
The course is led by Prof. Siva Athreya, a distinguished professor at the Indian Statistical Institute, Bangalore. His research expertise lies in Probability Theory, and he brings this deep theoretical knowledge into the classroom. Prof. Athreya has extensive experience teaching in the B.Math (Hons.), M.Math, and Ph.D. programs at ISI, ensuring the course content is both rigorous and pedagogically sound.
Resources and Prerequisites
Prerequisites: A solid understanding of mathematics at the 12th-standard level (including set theory, combinatorics) and basic calculus (differentiation and integration) is essential to follow the course material.
Recommended Textbook: For further reading and deeper practice, students can refer to the material provided by the instructor at: https://www.isibang.ac.in/~athreya/psweur/.
Embark on this 12-week journey to build a strong, practical, and intuitive understanding of probability. With the combined power of mathematical theory and the R programming language, you will gain the skills necessary to analyze uncertainty and model random phenomena—a critical foundation for any future work in data analysis, machine learning, or scientific research.
Enroll Now →