Mathematical Statistics

This course is an introduction to mathematical statistics and data analysis. It starts by introducing central concepts of probability theory (events, probability measure, random variables, distributions, joint distributions, and conditional distributions) and then moves on to the development of mathematical foundations of statistical inference. Topics covered in the course include random variables, expectations, parameter estimation (method of moments, method of maximum likelihood, and Bayesian approach), properties of point estimators (bias, variance, consistency, and efficiency), confidence intervals, hypotheses testing, likelihood ratio test, data summary methods, and introduction to linear regression. A class of distributions, including chi-squared, t, and F distributions, the distributions derived from normal that occur in many applications of hypothesis testing and statistical inference, is introduced.