Foundations of Mathematical Statistics for IIT JAM

Preparing for a highly competitive postgraduate statistics entrance exam requires a deep, conceptual understanding of mathematical foundations rather than just memorizing formulas. This text-based course guides you systematically through the core tenets of probability and mathematical statistics, helping you develop the analytical skills needed to solve complex exam-level problems with confidence. What you'll learn: - Understand fundamental probability, conditional probability, and Bayes' theorem. - Analyze univariate and multivariate random variables, joint distributions, and expectation. - Apply limit theorems, including the Weak Law of Large Numbers and the Central Limit Theorem. - Master estimation theory, focusing on unbiasedness, consistency, and maximum likelihood estimators. - Evaluate statistical hypotheses using the Neyman-Pearson lemma and likelihood ratio tests. - Explore modern computational statistics concepts, including basic resampling and bootstrap methods. The course begins with foundational probability definitions and set theory before progressing to random variables, probability distributions, and advanced statistical inference. You will work through structured written derivations, step-by-step proofs, and practice problems designed to mirror the rigor of the exam. This course is designed for university students and aspirants preparing for the IIT JAM Mathematical Statistics exam, requiring only a basic background in college-level calculus. Start reading today to master the mathematical principles behind statistical inference.