# Introduction to Probability Theory and Statistics

By Prof. S Dharmaraja   |   IIT Delhi
Learners enrolled: 3548
ABOUT THE COURSE:
This course provides axiomatic definition of probability, random variable, distributions, moments, modes of convergences, descriptive statistics, sampling distribution, point and interval estimations, hypothesis testing and analysis of correlation and regression. It explains the concepts of probability theory and statistics which are needed for handling various real-world problems.

PREREQUISITES: A basic course on Linear Algebra and Calculus

INDUSTRY SUPPORT: Goldman Sachs, Morgan Stanley, RBS, Quant, Futures First, Towers and other finance companies
Summary
 Course Status : Completed Course Type : Core Duration : 12 weeks Category : Mathematics Credit Points : 3 Level : Undergraduate/Postgraduate Start Date : 25 Jul 2022 End Date : 14 Oct 2022 Enrollment Ends : 08 Aug 2022 Exam Date : 30 Oct 2022 IST

Note: This exam date is subject to change based on seat availability. You can check final exam date on your hall ticket.

### Course layout

Week 1: Basics of Probability
Week 2: Random Variable
Week 3: Moments and Inequalities
Week 4: Standard Distributions
Week 5: Higher Dimensional Distributions
Week 6: Functions of Several Random Variables
Week 7: Cross Moments
Week 8: Limiting Distributions
Week 9: Descriptive Statistics and Sampling Distributions
Week 10: Point and Interval Estimations
Week 11: Testing of Hypothesis
Week 12: Analysis of Correlation and Regression

### Books and references

1. Introduction to Probability and Stochastic Processes with Applications, Liliana Blanco Castaneda, Viswanathan Arunachalam, Selvamuthu Dharmaraja, Wiley, Asian Edition, Jan. 2016.
2. Introduction to Statistical Methods, Design of Experiments and Statistical Quality Control, Selvamuthu Dharmaraja, Dipayan Das, Springer, 2018.
3. An Introduction to Probability and Statistics, Vijay K. Rohatgi and A.K. Md. Ehsanes Saleh, John Wiley, second edition, 2001.

### Prof. S Dharmaraja

IIT Delhi
Prof. S. Dharmaraja earned his M.Sc. degree in Applied Mathematics from Anna University, Madras, India, in 1994 and Ph.D. degree in Mathematics from the Indian Institute of Technology Madras, in 1999. From 1999 to 2002, he was a post-doctoral fellow at the Department of Electrical and Computer Engineering, Duke University, USA. From 2002 to 2003, he was a research associate at the TRLabs, Winnipeg, Canada. He has been with the Department of Mathematics, IIT Delhi, since 2003, where he is currently a Professor, Department of Mathematics and joint faculty of Bharti School of Telecommunication Technology and Management. During July 2014 and August 2017, he served as Head, Department of Mathematics. He appointed as 'Jaswinder & Tarvinder Chadha Chair Professor' for teaching and research in the area of Operations Research from May 2010 to July 2015. He has held visiting positions at the Duke University, USA, Emory University, USA, University of Calgary, Canada, University of Los Andes, Bogota, Colombia, National University of Colombia, Bogota, Colombia, University of Verona, Verona, Italy, Sungkyunkwan University, Suwon, Korea and Universita degli Studi di Salerno, Fisciano, Italy. His research interests include applied probability, queueing theory, stochastic modeling, performance analysis of computer and communication systems and financial mathematics. He has published over 45 papers in refereed international journals and over 20 papers in refereed international conferences in these areas. He is an Associate Editor of International Journal of Communication Systems and an Associate Editor of Opsearch. He is co-author of a text book entitled "Introduction to Probability and Stochastic Processes with Applications" in John Wiley (US Edition, New Jersey, June 2012) and (Asian Edition, New Delhi, Jan. 2016) and co-author of a text book entitled "Financial Mathematics: An Introduction" in Narosa, Nov. 2012.

### Course certificate

The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.
The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).
Date and Time of Exams: 30 October 2022 Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.
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. If there are any changes, it will be mentioned then.
Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.

CRITERIA TO GET A CERTIFICATE

Average assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course.
Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.

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 Madras. It will be e-verifiable at nptel.ac.in/noc.

Only the e-certificate will be made available. Hard copies will not be dispatched.

Once again, thanks for your interest in our online courses and certification. Happy learning.

- NPTEL team