# 85159 - Fundamental Concepts of Statistics

• Docente: Cinzia Viroli
• Credits:: 10
• SSD: SECS-S/01
• Language: English
• Campus: Bologna
• Corso: Second cycle degree programme (LM) in Statistical Sciences (cod. 9222)
• from Sep 19, 2022 to Dec 05, 2022

## Learning outcomes

By the end of the course the student acquires the fundamental notions of theory of probability and statistical inference. In particular, the student is able to investigate the properties of random variables, including transformations and convergence, and to solve estimation problems and hypothesis testing by classical parametric inference in an effective and coherent way.

## Course contents

1. Fundamental concepts of probability: univariate and multivariate random variables, conditional and marginal distributions, independent random variables
2. Transformations of univariate and multivariate random variables
3. Moment generating Functions and Characteristic Functions
4. Inequalities
5. Convergence of random variables
6. Introduction to Bayesian and frequentist statistical inference: models and learning
7. Parametric inference: method of moments, maximum likelihood and properties, optimization methods
8. Hypothesis testing and p-values: the Wald test, Chi-square distribution, Likelihood Ratio Test, Multiple Testing
9. Bootstrap
10. Nonparametric hypothesis testing about one and two samples

Used course material consists of lecture notes and slides provided by the teacher.

Background information can be found in several chapters of the following books:

• George Casella, Roger L. Berger, Statistical Inference, 2nd Edition, 2002, Duxbury Pr (Cengage)
• All of Statistics, A Coincise Course in Statistical Inference, Larry Wasserman, Springer.

## Teaching methods

Lectures and tutorials

## Assessment methods

The learning assessment is composed by two components.

1. About 27/30 marks are assigned to a 2 hours exam comprising of theoretical and practical exercises, aimed at assessing the student's ability to use the learned definitions, properties and theorems. During the written exam, students can make use of the text book, personal notes and a calculator. Students are not permitted to use a mobile phone (and smart watch or similar electronic data storage or communication device). The written exam is based on a quiz consisting of a set of multiple-choice with 4 possible answers.
2. About 6/30 marks are assigned to regular homework activity. Three homeworks will be given and they will consist of a data analysis project developed with R.

## Teaching tools

Blackboard and slides

## Office hours

See the website of Cinzia Viroli