Statistics

The course is intended for students who have a deficiency in probability and statistics. It starts off with the very first principles of probability and quickly passes on to essential statistical techniques. Estimation and testing theory will be reviewed, including maximum likelihood estimators, likelihood ratio test and (least squares) regression. The course is based on John A. Rice, Mathematical Statistics and Data Analysis, Duxbury Press, Belmont, California. All together the topics will be treated in 7 lectures. Students are required to study the corresponding theory and examples in the book as well as to make accompanying exercises.
The topics covered in the course are: Sample spaces, probability measures, distribution functions, random variables with discrete and continuous distributions, functions of random variables, multivariate distributions, random vectors, independent random variables, conditional distributions, functions of random vectors and their distributions, expectation and variance, covariance and correlation, the law of large numbers, central limit theorem, chi-square and t-distributions, estimation, method of moments, maximum likelihood, large sample theory, confidence intervals, Cramer-Rao bound, hypothesis testing, Neyman-Pearson paradigm, likelihood ratio tests, confidence intervals, linear regression, least squares estimation of regression parameters, testing regression hypotheses.