*Instructor:*Dr. Marianna BOLLA

*Prerequisite*: Undergraduate Calculus and Basic Probability

*Text*:

G. K. Bhattacharyya, R. A. Johnson: Statistical Concepts and Methods, Wiley.

C. R. Rao: Statistics and Truth, World Scientific, 1997 (only if you have a deeper interest in statistics).

Handouts: tables of notable distributions and percentile values of basic test distributions.

*Course description*

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 chances in everyday life. 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. Applications are also discussed, mainly on a theoretical basis, but we make the students capable of solving numerical exercises by choosing the most convenient method for a given real-life problem.

*Topics:*

- Short introduction to probability theory (sample spaces, random variables, notable distributions, Bayes rule, laws of large numbers, Central Limit Theorem).
- Descriptive study of data. Statistical sample, basic statistics, histograms.
- Basic concepts of testing hypotheses and estimation theory.
- Methods of point estimation, properties of the estimators, confidence intervals.
- Inferences about a population, sampling statistics, theory and applications.
- Parametric inference, comparing two treatments (z, t, F tests).
- Nonparametric inference: Wilcoxon test and sign test.
- Analyzing categorized data (contingency tables), chi-square test.
- Introduction to linear models: regression analysis (linear regression, correlation, model fitting) and analysis of variance.
- If time permits, we will cover the following topics too: sufficiency, efficiency, consistency, Neyman-Fisher factorization, Neyman-Pearson theorem.