Courses » Statistical Inference

Statistical Inference


This course aims at giving the foundation knowledge of Probability and Statistical Inference. In particular, it gives details of theory of Estimation and testing of hypothesis. Both theoretical aspect will be discussed and practical problems will be dealt with in great detail. This course will help students and practitioners of statistics at both UG and PG level. This course will also serve as a foundation course for students workingon Machine Learning.

Important For Certification/Credit Transfer:

Weekly Assignments and Discussion Forum can be accessed ONLY by enrolling here

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Final Exam (in-person, invigilated, currently conducted in India) is mandatory for Certification and has INR Rs. 1100 as exam fee.

Students and practitioners of Statistics, Mathematics


UG/PG: UG and PG

PREREQUISITES: Background of Probability, Basic Knowledge of Data its collection and descriptive statistics

INDUSTRY SUPPORT: Parameter Estimation and Testing of Hypothesis are basic requirements


Current position: Professor, Department of Mathematics, Indian Institute of Technology, Delhi. Education: Ph.D. Computer Science, University of London, England(1995), M.Tech. Computer Science, Indian Statistical Institute, Calcutta(1986), M.Stat. Statistics, Indian Statistical Institute, Calcutta(1984), B.Stat. Statistics, Indian Statistical Institute, Calcutta(1982) Ph.D. Thesis: Title : Contributions to time-bounded Problem Solving using Knowledge-based Approach., Supervisor: Prof. J. A. Campbell, Dept. of computer Science, University College London.


Week 1  :  Revision of Probability, Different Discrete and Continuous Distributions
Week 2  :   Functions of Random Variables and their distributions, T, Chi-sq, F distributions and their Moments
Week 3  : Introduction of statistics and the distinction between Data and its properties, and probabilistic models
Week 4  :  Estimator and methods of estimation, Properties of an estimator: Consistency, Unbiasedness, Efficiency and Sufficiency
Week 5  :  Neyman Factorization, Cramer-Rao Bound
Week 6  :  Confidence Intervals, Concepts of hypothesis testing, Characteristics of Good Hypothesis, null and Alternative Hypotheses, Types of Errors
Week 7  :  Inference on Population mean, Comparing two population means, Inference on Variance, Comparing two population variance
Week 8  :  Neyman Pearson Lemma


1) Probability and Statistics for engineers and scientists, Ed 4, Anthony J Hayter, Brroks/Cole, Cengage Learning.
2) Statistical Methods, R.J.Freund, W.J. Wilson and D.L Mohr, (Ed 3) Elsevier.
3) Mathematical Statistics: A Textbook, S. Biswas and G.L.Sriwastav, Narosa
  • The exam is optional for a fee.
  • Date and Time of Exam: October 7, 2018 (Sunday)
  • Time of Exams: Morning session 9am to 12 noon; Afternoon session: 2pm to 5pm.
  • Exam for this Course will be available in both morning & afternoon sessions.
  • 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  Best 6 out of 8 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 Madras.It will be e-verifiable at http://nptel.ac.in/noc/