# 47732 - STATISTICS

## Conoscenze e abilità da conseguire

At the end of the course students have the basic tools for analysing and describing a set of data through numerical indexes, graphical representations and dependence models for both univariate and bivariate data. The students are able to deal with basic tools of probability theory and its applications. The students will be also able to estimate population parameters from sample data by using standard inferential techniques (point estimation, confidence interval and hypothesis testing).

## Contenuti

The course program is organized in three parts as described below.

1. Exploratory Data Analysis

The data matrix. Types of variables. Frequency tables. Graphical representations. Summary measures of position and dispersion. Linear transformations, standardization and bell-shaped distributions. Association of two quantitative variables, covariance and correlation coefficient. Outline of simple linear regression.

2. Probability Theory

Random experiment, sample space and events, probability measure. Conditional probability, independence, Bayes theorem. Random variables. Expected value and variance of a random variable. Discrete and continuous random variables. Bernoulli and binomial distribution. Exponential distribution. Gaussian distribution. Independent variables. Linear combination of random variables and the central limit theorem.

3. Inferential Statistics

Random sampling. Parametric statistical models. Sampling distributions. Point estimation. Bias and mean squared error. Confidence intervals for the mean of a Gaussian population. The Student t distribution. Approximate confidence interval for a probability. Hypothesis testing on the mean of a Gaussian population. The p-value. Inference on a proportion.

## Testi/Bibliografia

David M Diez, Christopher D Barr, Mine C ̧etinkaya-Rundel (2015). OpenIntro Statistics (Third Edition).

This textbook is available under a Creative Commons license. Visit openintro.org for a free PDF

## Metodi didattici

Teacher's lectures.

## Modalità di verifica dell'apprendimento

Written examination.

## Strumenti a supporto della didattica

Slides of the course, materials for self-assessment.