Quick Facts

Medium Of Instructions	Mode Of Learning	Mode Of Delivery
English	Self Study	Video and Text Based

Course Overview

Advanced Probability Theory program is a core course in mathematics designed for undergraduate and postgraduate students who want to learn probability concepts from Kolmogorov’s Axioms. This financial industry-supported course will cover a variety of topics in 12 weeks.

Advanced Probability Theory certification will be conducted through a series of online lectures and regular assignments. Participants of the course can also appear for the final exam in person and gain a certificate upon passing all the criteria. The educator for this course is Professor Niladri Chatterjee from IIT Delhi.

Advanced Probability Theory will go through topics such as cumulative function distribution, probability density function and provide an introduction to the concept of a random variable. Participants will also learn about probability distributions, the function of one or two random variables, and the overview of order statistics. This is an AICTE approved program that also provides a list of books and references for the benefit of the participants.

The Highlights

Mathematics core course
Online course with in-person final exam
E-certificate available
AICTE approved undergraduate/postgraduate course
Course developed by IIT Delhi in association with Swayam
12-week program with regular assignments
List of references and books provided
Industry supported

Important dates

Certificate Exam Date

Start Date : 18 Apr, 2026

Programme Offerings

Mathematics core course
Course developed by IIT Delhi in association with Swayam
12-week programme with regular assignments
List of references and books provided
Online course with an in-person final exam
E-certificate available.

Courses and Certificate Fees

Certificate Availability	Certificate Providing Authority
yes	IIT Delhi

Advanced Probability Theory program fee structure -

Course Name	Fee
Exam fees	Rs. 1,000

Eligibility Criteria

Before joining the Advanced Probability Theory program, individuals must have a basic understanding of two variables, real analysis, and convergence of a function.

Certification qualification involves submitting assignments, passing the final exam, and scoring the minimum required marks in both. Additionally, they should achieve a final score of 40 marks and above to be awarded the e-certificate.

What you will learn

Statistical skills

Advanced Probability Theory program will throw light on the below-given topics:

Order statistics
Cumulative distribution function
Generating functions
Derived random variables
Probability density function
Derivation of distribution of a range
Functions of one or two random variables
Concept of a random variable
Derivation of distribution of the median
Theoretical probability distributions
Limit theorems

Who it is for

The Advanced Probability Theory course is best suited for undergraduate and postgraduate students learning about machine learning, mathematics, and statistics.

Admission Details

Step one: The admission process for the Advanced Probability Theory by Swayam begins with signing up or logging in on the Swayam website.
Step two: After signing in, visit https://onlinecourses.nptel.ac.in/noc25_ma04/preview preview and click on join.
Step three: Fill the online application form with all the necessary details. Pay the exam fee as per requirement. This completes the admission process.

Application Details

The online application form for the Advanced Probability Theory certification can be accessed by logging in or signing up on the Swayam website. Candidates have the choice of skipping the signup process by using their Google, Facebook, or Microsoft account. However, if you don’t already own Swayam credentials, you will have to fill an online application form while registering. The form requires you to fill in details such as contact information, personal information, educational qualifications, and occupational information.

The Syllabus

Introduction
Probability axioms
Sample space
Bertrand’s paradox
Theorems on Intersections and union of events in sample spaces
Bertrand’s Paradox.

Conditional Probability
Bayes Theorem
Probability on Finite Sample Spaces
Independence of Events.

Introduction to Random variables
Discrete & continuous Random variables Discrete random variables - Uniform, Bernoulli, Binomial, Geometric, Poisson Distributions, Hypergeometric, Negative Binomial.

Continuous Random variables
Uniform
Normal
Exponential
Gamma
Cauchy
Beta1 and Beta2

Moments of a distribution
Bivariate distribution
Covarience and Correlation

Generating Functions and their properties
Moment Generating Function Characteristic Functions and Probability Generating Function

Poisson Process
Conditional Expectations and Variance
Chebyshev's Inequality and Introduction to Bivariate Normal.

Functions of Random Variables
Introduction to t and F distribution.

Order statistics

Limit Theorems: Mode of convergence

Laws of large numbers

Central limit theorems

Evaluation process

Advanced Probability Theory training certification involves qualifying for the following conditions:

Payment of the exam fee will allow participants to sit for the in-person proctored exam. This exam will attribute to 75% of the final score. All 12 assignments need to be completed and submitted. The average score received from the best eight assignments will provide a balance of 25% of the final score.

Participants must score at least 40 marks out of 100 in the final score to pass. However, if they cannot score at least 10/25 and 30/75 in the assignments and exam respectively, they will not be given the e-certificate, regardless of their total final score.