# 81660 - Probability and Mathematical Statistics Complements

• Docente: Elena Bandini
• Credits: 6
• SSD: MAT/06
• Language: Italian
• Campus: Bologna
• Corso: Second cycle degree programme (LM) in Mathematics (cod. 5827)
• from Feb 21, 2024 to May 29, 2024

## Learning outcomes

At the end of the course, the student knows basic concepts and methods of probability and mathematical statistics. The student can solve simple problems of probability and statistical inference.

## Course contents

○ Descriptive statistics: historical background; population and sample, types of data, frequencies, tabular and graphical representations; measures of central tendency, measures of variability; boxplot; normal samples and measures of shape.

○ Bivariate data: joint frequencies and two-way tables; scatter plot; covariance and linear correlation coefficient; method of least squares and linear regression.

○ Introduction to Probability: interpretations of probability, beyond the scheme classical/frequentist/subjectivist; a brief history of Probability.

○ Mathematical model of a random experiment: primitive notions and axioms of probability, sample space, events, consequences of axioms; geometric probability.

Conditional probability and independence: chain rule, total probability rule, Bayes' rule; tree diagram.

Random variables: recalls of discrete and continuous random variables.

Markov Chains: introduction to stochastic processes; definition of Markov chain and basic properties; graphical representation, transition probabilities; communicating classes and irreducible Markov chains; invariant distribution, asymptotic behavior.

Introduction to Statistical inference: recalls of Law of large number and Central limit theorem; statistical model of a random experiment; elements of point estimation theory; biased and unbiased estimators, mean square error, asymptotical properties of estimators; Bayesian approach to Statistical inference.

Lectures notes and sheets of exercises prepared by the teacher (available on virtuale.unibo.it in Italian).

Supplementary textbook:

Quentin Berger, Francesco CaravennaPaolo Dai Pra, Probabilità. Un primo corso attraverso esempi, modelli e applicazioni, second edition, Springer-Verlag (2021).

## Teaching methods

Lectures and exercises will be alternated in order to explain theoretical concepts through examples.

Lectures are in Italian.

## Assessment methods

Written and oral examination

## Teaching tools

Website of the course available on virtuale.unibo.it, where the student can find: lecture notes, sheets of exercises, as well as other useful material for the course.

## Office hours

See the website of Elena Bandini