# STATISTICS

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

ï‚· Obiettivi dellâ€™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.

ï‚· Contenuti e programma del corso

DESCRIPTIVE STATISTICS

âˆ’Classification of the variables

âˆ’Absolute, relative and percentage frequencies.

âˆ’Graphical representation of the variables:

1. Pie charts, bar charts, histograms.

2. Cumulative distribution function.

âˆ’Numerical description of the variables:

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

âˆ’Measures of variability.

âˆ’Concentration measures.

âˆ’Bivariate analysis:

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

âˆ’Independence.

âˆ’Chi-square measure of association

âˆ’Linear dependence between two variables: covariance and correlation coefficient.

- Simple linear Regression:

- Ordinarily least square estimators

- Prediction

- R2 coefficient of determination.

PROBABILITY

âˆ’Review of Bayes theorem.

âˆ’Random variables (r.v.):

- Review of Bernoulli, Binomial, Poisson distributions.

âˆ’Review of uniform, normal, exponential distributions.

INFERENTIAL STATISTICS

Point estimation

âˆ’Random sample, estimator and estimate: definition.

âˆ’Sample mean and sample variance: definition and properties.

âˆ’Central Limit Theorem

âˆ’Properties of estimators: unbiasedness, asymptotic unbiasedness, efficiency, consistency.

Confidence Intervals

âˆ’Definition of Confidence Intervals (C.I.)

âˆ’.

âˆ’C.I. for the mean of the normal population: variance known and unknown; Student T distribution.

âˆ’C.I. for the proportion of a Bernoulli population.

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

Test of Hypothesis

âˆ’- Introduction

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

âˆ’Test for the proportion of the Bernoulli population.

âˆ’Test for the variance of the normal population.

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

ï‚· Tipologia delle attivitÃ didattiche

The theoretical lessons will be accompanied by weekly exercises classes.

ï‚· Testi e materiale didattico

â€¢ Cicchitelli, G. STATISTICA. PRINCIPI E METODI, Pearson, 2012

ï‚· ModalitÃ di verifica dellâ€™apprendimento

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