Courses » Probability and Statistics

Probability and Statistics

About the course

The use of statistical reasoning and methodology is indispensable in modern world. It is applicable to every discipline, be it physical sciences, engineering and technology, economics or social sciences. Much of the advanced research in electronics, electrical, computer science, industrial engineering, biology, genetics, and information science relies increasingly on use of statistical tools. It is essential for the students to get acquainted with the subject of probability and statistics at an early stage. The present course has been designed to introduce the subject to undergraduate/postgraduate students in science and engineering. The course contains a good introduction to each topic and an advance treatment of theory at a fairly understandable level to the students at this stage. Each concept has been explained through examples and application oriented problems.



Must have good knowledge of Differential and Integral Calculus, sequences and series, Basic Linear/Matrix Algebra (usually students who have completed Mathematics-I and II at first year undergraduate

Industries that will recognize this course

Today all industries use statistical methods. So for students desirous to work in any type of industry, this course will be indispensable. In particular, companies dealing with Business Analytics, Banking and finance, Insurance machine learning, data mining etc. this course will be invaluable.


VuNet Systems( www.vunetsystems.com ) brings in a big data approach to manage the complex IT infrastructure of enterprises. With its powerful analytics and intuitive visualisations, it helps connect the 1000s of dots in an IT infrastructure to keep it always on and secure. VuNet has customers across verticals, from banks, manufacturing, consumer care to IT/ITES, with some leading retail payment companies as well.  VuNet has also been recognised among the NASSCOM Emerge50 innovative product startups and is also part of the Cisco Launchpad program - Cisco’s partnership program with top emerging startups.

We are always on the lookout for talented programmers and will interview the course toppers( top 5% ), who are interested in an internship/job opportunity. Upon completion of this course, the toppers can submit their resumes and programming code samples. VuNet will interview the candidates and offer internships or job opportunities based on the interview.

Course instructor

Somesh Kumar is a professor in the Department of Mathematics, IIT Kharagpur. He has over 28 years of experience of teaching courses on Probability Statistics, Statistical Inference, Sampling Theory, Stochastic Processes, Multivariate Analysis, Regression analysis, Time Series, Experimental Designs, Decision Theory to undergraduate, postgraduate and doctorate students. His NPTEL courses (under MHRD) on Probability and Statistics, Statistical Inference and Statistical Methods for Scientists and Engineers (each of 40 hours) are available online. He has also taught Mathematics-I in QEEE program of MHRD to 130 engineering college students in online mode during Autumn 2014-2015. He offered this course “Probability and Statistics” for certification program in Jan-April 2016.

His research interests are Statistical Decision Theory, Estimation Theory, Classification Problems, Directional Distributions, Limit Theorems. He has published more than 70 research papers in reputed international journals. He has supervised eight doctoral and more than a hundred and fifty Masters (M.Tech. and M.Sc.) dissertations.


Course layout

Week 1: Sets, Classes, Collections

Sequence of Sets

Ring, Field (Algebra)

Sigma-Ring, Sigma-Field, Monotone Class

Random Experiment, Events

Definitions of Probability

Properties of Probability Function-I

Properties of Probability Function-II


Week 2: Conditional Probability

Independence of Events

Problems in Probability-I

Problems in Probability-II

Random Variables

Probability Distribution of a Random Variable-I


Week 3: Probability Distribution of a Random Variable-II


Characteristics of Distributions-I

Characteristics of Distributions-II

Special Discrete Distributions-I

Special Discrete Distributions-II

Special Discrete Distributions-III


Week 4: Poisson Process-I

Poisson Process-II

Special Continuous Distributions-I

Special Continuous Distributions-II

Special Continuous Distributions-III

Special Continuous Distributions-IV

Special Continuous Distributions-V


Week 5: Normal Distribution

Problems on Normal Distribution

Problems on Special Distributions-I

Problems on Special Distributions-II

Function of a Random Variable-I

Function of a Random Variable-II


Week 6: Joint Distributions-I

Joint Distributions-II

Independence, Product Moments

Linearity Property of Correlation and Examples

Bivariate Normal Distribution-I

Bivariate Normal Distribution-II


Week 7: Additive Properties of Distributions-I

Additive Properties of Distributions-II

Transformation of Random Variables

Distribution of Order Statistics

Basic Concepts

Chi-Square Distribution


Week 8: Chi-Square Distribution
(Cont…), t-Distribution


Descriptive Statistics – I

Descriptive Statistics - II

Descriptive Statistics – III

Descriptive Statistics – IV


Week 9: Introduction to Estimation

Unbiased and Consistent Estimators


Examples on MME, MLE

Examples on MLE-I

Examples on MLE-II, MSE


Week 10: UMVUE, Sufficiency, Completeness

Rao-Blackwell Theorem and its Applications

Confidence Intervals-I

Confidence Intervals- II

Confidence Intervals- III

Confidence Intervals- IV


Week 11: Basic Definitions

Two Types of Errors

Neyman-Pearson Fundamental Lemma

Applications of N-P Lemma-I

Applications of N-P Lemma-II


Week 12: Testing for Normal Mean

Testing for Normal Variance

Large Sample Test for Variance and Two Sample Problem

Paired t-Test



Week 13: Testing Equality of Proportions

Chi-Square Test for Goodness Fit -I

Chi-Square Test for Goodness Fit –II

Testing for Independence in  Contingency Table –I

Testing for Independence in  Contingency Table-II



Certification exam:

• The exam is optional for a fee. Exams will be on 23 April 2017.

• Time: Shift 1: 9am-12 noons; Shift 2: 2pm-5pm

• Any one shift can be chosen to write the exam for a course.

• Registration url: Announcements will be made when the registration form is open for  registrations.

• The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published.


• Final score will be calculated as : 25% assignment score + 75% final exam score.

• 25% assignment score is calculated as 25% of average of 12 weeks course: Best 8 out of 12 assignments.

• E-Certificate will be given to those who register and write the exam and score greater than or equal to 40% final score. Certificate will have your name, photograph and the score in the final exam with the breakup. It will have the logos of NPTEL and IIT KHARAGPUR. It will be e-verifiable at nptel.ac.in/noc