75339 - Mathematical Statistics

Course Unit Page

Academic Year 2018/2019

Learning outcomes

The aim of the course is to give students the basic knowledge of statistics for data-analysis and of statistical elementary methods that can be applied to other mathematical areas. In the end of the course, the student possesses the ability to study the behavior of samples of a random variable and to apply statistical elementary methods to some problems of analysis, number theory and mathematical physics.

Course contents

Samples. Statistics.

Tests of hypotheses. Neyman-Pearson lemma. Tests of hypotheses for normally distributed populations. Chi square test. Chi square test for independence.

Regression. Linear regression for normally distributed populations. Analysis of variance.

Test di ipotesi. Lemma di Neyman-Pearson. Test di ipotesi per popolazioni distribuite normalmente. Test chi quadro. Test chi quadro per l'indipendenza.

Regressione lineare. Regressione normale.Analisi della varianza.

Non-parametric tests.

Glivenko-Cantelli lemma. Kolmogorov-Smirnov test.

Readings/Bibliography

Wiebe R. Pestman. Mathematical Statistics. De Gruyter.

Teaching methods

Lectures.

Assessment methods

Final verification consists in an oral test.

The oral tests is based on three questions. In answering them the student will have to show that he/she masters the basic concepts of the course and that he/she is able to develop arguments and to solve simple exercises on the content of the course.

Office hours

See the website of Massimo Campanino