# STATISTICS

The topics covered in the course of Mathematics (code ECO0011)

Obiettivi dell’insegnamento e risultati di apprendimento attesi

Students will acquire a good understanding of the statistical tools and techniques related to descriptive statistics, probability and inferential statistics covered in the course, as well as the ability to employ them in economic and business applications.

Contenuti e programma del corso

DESCRIPTIVE STATISTICS

−Classification of the variables

−Absolute, relative and percentage frequencies.

−Graphical representation of the variables:

1. Pie charts, bar charts, histograms.

2. Cumulative distribution function.

−Numerical description of the variables:

−Measures of central tendency: analytic means (arithmetic and geometric mean); median and quartiles, mode.

−Measures of variability.

−Concentration measures.

−Bivariate analysis:

−Scatter plot and contingency table. Joint, marginal, conditional distributions. Conditional mean.

−Independence.

−Chi-square measure of association

−Linear dependence between two variables: covariance and correlation coefficient.

- Simple linear Regression:

- Ordinarily least square estimators

- Prediction

- R2 coefficient of determination.

PROBABILITY

−Review of Bayes theorem.

−Random variables (r.v.):

- Review of Bernoulli, Binomial, Poisson distributions.

−Review of uniform, normal, exponential distributions.

INFERENTIAL STATISTICS

Point estimation

−Random sample, estimator and estimate: definition.

−Sample mean and sample variance: definition and properties.

−Central Limit Theorem

−Properties of estimators: unbiasedness, asymptotic unbiasedness, efficiency, consistency.

Confidence Intervals

−Definition of Confidence Intervals (C.I.)

−.

−C.I. for the mean of the normal population: variance known and unknown; Student T distribution.

−C.I. for the proportion of a Bernoulli population.

−C.I. for the difference in the means of two normal populations: variance known and unknown.

Test of Hypothesis

−- Introduction

−Test for the mean of the normal population: variance known and unknown

−Test for the proportion of the Bernoulli population.

−Test for the variance of the normal population.

−Test for the difference in the means of two normal populations: variance known and unknown.

Tipologia delle attività didattiche

The theoretical lessons will be accompanied by weekly exercises classes.

Testi e materiale didattico

• Cicchitelli, G. STATISTICA. PRINCIPI E METODI, Pearson, 2012

Modalità di verifica dell’apprendimento

Students will be evaluated in their knowledge and understanding through the means of a written exam concerning theory and exercises.