Applied Mathematical Statistics: Theory and Problem Solving

Mathematical statistics provides the essential theoretical framework for data science, quantitative research, and rigorous decision-making. Without a solid understanding of its principles, interpreting complex data models is guesswork. This course empowers you to master the core theoretical tools necessary to understand, derive, and apply fundamental statistical methods, transforming raw data into meaningful, defensible insights. ### What you'll learn * Understand the foundational axioms of probability, conditional probability, and independence. * Master the properties and applications of common discrete and continuous probability distributions. * Apply various methods for point estimation, including Maximum Likelihood Estimation (MLE) and the Method of Moments. * Practice deriving sampling distributions and constructing confidence intervals for parameters. * Configure and execute rigorous hypothesis testing procedures, including likelihood ratio tests. * Learn to evaluate the efficiency and consistency of estimators using criteria like the Cramer-Rao Lower Bound. * Interpret statistical results rigorously, connecting theoretical models to practical conclusions in data contexts. This course guides you through the progression of statistical knowledge, starting with foundational probability and random variables, advancing through distribution theory, and culminating in comprehensive coverage of estimation and hypothesis testing methods. It emphasizes both conceptual clarity and structured problem-solving through written examples and exercises. This course is designed for absolute beginners and assumes no prior knowledge of statistics, only familiarity with basic calculus. Start building your analytical and theoretical foundation today.