## M378K INTRODUCTION TO MATHEMATICAL STATISTICS

**Prerequisite and degree relevance:**Mathematics 362K with a grade of at least C. Students taking this course are usually majoring in mathematics, actuarial science, or one of the natural sciences. M362K, 358K, and 378K form the core sequence for students in statistics.

**Course description:**Sampling distributions of statistics, estimation of parameters (confidence intervals, method of moments, maximum likelihood, comparison of estimators using mean square error and efficiency, sufficient statistics), hypothesis tests (p-values, power, likelihood ratio tests), and other topics.

This is the first course in mathematical statistics and is taught from a classical viewpoint. The major topics are: estimation of parameters, including maximum likelihood estimation; sufficient statistics, and confidence intervals; testing of hypotheses including likelihood ratio tests and the Neyman Pearson theory; the distributions and other properties of some statistics that occur in sampling from normal populations such as the gamma, beta, chi-squared, Students t, and F distributions; and fitting straight lines. The course is designed to give students some insight into the theory behind the standard statistical procedures and also to prepare continuing students for the gradu ate courses. Within the limits of the prerequisites, students are expected to reproduce and apply the theoretical results; they are also expected to be able to carry out some standard statistical procedures.