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Statistics for Data Science II builds on the foundational concepts introduced in Statistics for Data Science I, focusing on advanced statistical problems and their solution approaches. This course dives deeper into statistical modeling, the application of probability distributions, estimation, hypothesis testing, and regression analysis. The course aims to equip students with practical tools for analyzing real-world datasets, further enhancing their skills in statistical methods essential for data science.
Multiple Random Variables: Understanding how multiple random variables interact, including their independence and the functions that link them.
Probability Distributions: Applying probability distributions to datasets to model and analyze random phenomena.
Estimation of Parameters: Mastering the concepts of point and interval estimation, learning how to estimate parameters with confidence.
Hypothesis Testing: Performing hypothesis tests to analyze the mean and variance of data and test assumptions about datasets.
Regression Analysis: Using simple regression models to analyze data and performing hypothesis tests relevant to regression models.
Understand how to analyze multiple random variables and apply probability models to data.
Gain proficiency in estimation techniques such as point and interval estimation.
Master hypothesis testing, including tests for mean and variance.
Learn to apply regression models to analyze data and evaluate the models using hypothesis tests.
WEEK 1: Multiple Random Variables – Two random variables, multiple random variables and their distributions.
WEEK 2: Independence of random variables, functions of random variables, and visualizing them.
WEEK 3: Expectations, covariance, correlation, and basic inequalities in statistics.
WEEK 4: Continuous Random Variables – Density functions, expectations, and the difference between discrete and continuous variables.
WEEK 5: Multiple Continuous Random Variables – Analyzing data like height and weight, applying limit theorems, and building probability models from data.
WEEK 6: Refresher Week – A break week to review concepts and clarify doubts.
WEEK 7 & 8: Estimation and Inference – Focus on parameter estimation and making inferences from data.
WEEK 9: Bayesian Estimation – A deep dive into Bayesian techniques for estimation and inference.
WEEK 10 & 11: Hypothesis Testing – Analyzing and testing hypotheses regarding the mean and variance of datasets.
WEEK 12: Revision Week – A final review of all course material to prepare for the exam.
Professor Andrew Thangaraj, Department of Electrical Engineering, IIT Madras
Professor Thangaraj received his B.Tech in Electrical Engineering from IIT Madras and his Ph.D. from Georgia Tech. He has been a faculty member at IIT Madras since 2004 and specializes in information theory, error-control coding, and cryptography. He is also a key figure in NPTEL and the IIT Madras Online BSc Degree Program.
Real-World Applications: Learn to apply advanced statistical methods to real-world data through hands-on assignments and projects.
Expert Guidance: Gain insights from Professor Andrew Thangaraj, an expert in information theory and cryptography.
Practical Applications: Build skills that are directly applicable to data science, including parameter estimation, hypothesis testing, and regression modeling.
Collaborative Learning: Engage with a community of data science students and professionals, working together to solve complex statistical problems.
Embark on this enriching journey with me and unlock the transformative power of statistics in data science!