Statistics-2

About the Course 

Bio

Andrew Thangaraj received his B.Tech in Electrical Engineering from the Indian Institute of Technology (IIT), Madras, India in 1998 and a PhD in Electrical Engineering from the Georgia Institute of Technology, Atlanta, USA in 2003. He was a post-doctoral researcher at the GTL-CNRS Telecom lab at Georgia Tech Lorraine, Metz, France from August 2003 to May 2004. From June 2004, he has been with the Department of Electrical Engineering, IIT Madras, where he is currently a professor. From Jan 2012 to Jan 2018, he served as Editor for the IEEE Transactions on Communications. From July 2018 to July 2022, he served as an Associate Editor for Coding Techniques for the IEEE Transactions on Information Theory.

Since Oct 2011, he has been serving as NPTEL coordinator at IIT Madras. He has played a key role in initiating and running NPTEL online courses and certification. He is currently the PI of the SWAYAM project of the Ministry of Education, Government of India.

Since May 2020, he has been serving as Coordinator for the BS (Data Science) Program at IIT Madras. Since May 2024, he has been serving as Chair for the Centre for Outreach and Digital Education (CODE) at IIT Madras.

For more details on the philosophy and impact of NPTEL and IITM's BS (Data Science) program, see the keynote talk below in a G20 Education Summit held at IIT Madras Research Park in Jan 2023.

ABOUT THE COURSE 

The Statistics-2 course in IIT Madras  BS Degree in Data Science typically covers intermediate concepts in Statistics focusing on both theoretical understanding and practical applications.

Key Topics Covered (in points):

• Probability Distributions:

  • Discrete and continuous distributions (Binomial, Poisson, Normal, Exponential, etc.)

  • Moment generating functions and their use
    
    

• Sampling Distributions:

  • Sampling theory, distribution of sample mean and variance

  • Central Limit Theorem and its applications
    
    

• Estimation Theory:

  • Point estimation methods (Method of Moments, Maximum Likelihood Estimation)

  • Properties of estimators (unbiasedness, consistency, efficiency)

  • Confidence intervals for means, proportions, variances
    
    

• Hypothesis Testing:

  • Null and alternative hypotheses

  • Type I and Type II errors

  • Tests for means, proportions, and variances (z-test, t-test, chi-square test, F-test)

  • p-values and significance levels
    
    

• Regression and Correlation:

  • Simple linear regression and correlation analysis

  • Least squares estimation

  • Interpretation and inference for regression coefficients
    
    

• Analysis of Variance (ANOVA):

  • One-way and two-way ANOVA models

  • Testing for differences among group means
    
    

• Non-parametric Methods:

  • Tests that do not assume specific distributions (e.g., sign test, Wilcoxon tests)
    
    

• Bayesian Statistics (optional, depending on syllabus):

  • Introduction to Bayesian inference and prior/posterior distributions