# MATHEMATICAL STATISTICS

**Brief introduction to the course:**

While probability theory describes random phenomena, mathematical statistics teaches us how to behave in the face of uncertainties, according to the famous mathematician Abraham Wald. Roughly speaking, we will learn strategies of treating randomness in everyday life. Taking this course is suggested between the Probability and Multivariate Statistics courses.

**The goals of the course:**

The course gives an introduction to the theory of estimation and hypothesis testing. The main concept is that our inference is based on a randomly selected sample from a large population, and hence, our observations are treated as random variables. Through the course we intensively use facts and theorems known from probability theory, e.g., the laws of large numbers. On this basis, applications are also discussed, mainly on a theoretical basis, but we make the students capable of solving numerical exercises.

**The learning outcomes of the course:**

Students will be able to find the best possible estimator for a given parameter by investigating the bias, efficiency, sufficiency, and consistency of an estimator on the basis of theorems and theoretical facts. Students will gain familiarity with basic methods of estimation and will be able to construct statistical tests for simple and composite hypotheses. They will become familiar with applications to real-world data and will be able to choose the most convenient method for given real-life problems.

Regular homework, and presentation or final

basic probability