To show the organization of the course that includes this module, follow this link:  Course organization

Learning outcomes

This course aims to provide the students with the fundamental of descriptive statistics, inferential statistics and probability theory.

Program

Part I) descriptive statistics.
Univariate statistics: main chart (pie chart, bar chart, histogram e box-plot), measures of location (mean, mode and median), measure of spread (range, interquartile range, variance, standard deviation), measure of asymmetry (third moment, skewness index, Pearson's skewness coefficient) measure of kurtosis (fourth moment, kurtosis, excess kurtosis).
Bivariate statistics: main representations (contingency tables e shattered plots), main measures (mean, variance and covariance), correlation analysis (linear regression and Pearson's correlation coefficient).

Part II) Probability theory
Probability: probability definition (classic and modern), event taxonomy (independent events, mutually exclusive events, complementary event, union event and intersection event). Conditional probability. Probability of notable events.
Random variables: discrete random variable (discrete probability distribution, expected value and variance), continuous random variable (probability density function, expected value and variance), main continuous distributions (uniform, gaussian, standard normal and chi-square).main discrete distributions (binomial and Bernoulli), central limit theorem, Chebyshev’s inequality, convergence in law of random variables and limit random variable.

Part III) Inferential Statistics.
Estimation theory: estimation problem, main properties of an estimator (unbiased, consistency and efficiency). point estimation (expected value and variance), interval estimation (expected value and variance).
Hypothesis test: Problem statement (first type and second type error, theoretical distribution), testing process, chi-square based independence test.

Part IV) Laboratory
Spreadsheet fundamental: scope and main software. Cells main properties: value, format, absolute and relative reference. Calc for basic statistics: single and double entry table, bar plot, shatter plot and linear regression plot.

Examination Methods

The exam requires two tests. The former test is composed by close questions while the latter is composed by open questions and exercises. To pass the exam, a student has to get a positive mark in both the tests.

Teaching materials

•   0.1 - Informazioni sul corso.   (pdf, it, 79 KB, 05/12/11)
•   0.2 - Concetti introduttivi.   (pdf, it, 89 KB, 05/12/11)
•   1.1 - Statistica descrittiva I - Serie monovariate: principali rappresentazioni e definizioni di frequenze.   (pdf, it, 165 KB, 05/12/11)
•   1.2 - Statistica descrittiva II - Serie monovariate: indici sintetici (posizione, variabilità, simmetria e curtosi) e box-plot.   (pdf, it, 235 KB, 15/07/12)
•   1.3 - Statistica descrittiva III - Serie bivariate: rappresentazioni tabellari e grafiche, indici sintetici e retta di regressione.   (pdf, it, 278 KB, 24/01/12)
•   2.1 - Probabilità I - Calcolo delle probabilità: definizioni introduttive, definzioni di probabilità (classica, assiomatica), probabilità condizionata   (pdf, it, 143 KB, 14/12/11)
•   2.2 - Probabilità II - Variabili casuali discrete: definizioni introduttive , valore atteso, varianza, principali vv.cc.   (pdf, it, 158 KB, 23/12/11)
•   2.3 - Probabilità III - Variabili casuali continue: indici sinteitici, principali vv.cc., Teorema del limite centrale, distribuzione limite.   (pdf, it, 393 KB, 14/12/11)
•   3.1 - Inferenza I - Teoria della stima: problema della stima, proprietà di uno stimatore, stima puntuale, stima per intervallo.   (pdf, it, 223 KB, 23/12/11)
•   3.2 - Inferenza II - Test di ipotesi: costruzione di un test, test sul valore atteso, test di aderenza alla distribuzione, test di indipendenza del Pearson   (pdf, it, 246 KB, 24/01/12)
•   9.1 - Esercizi proposti - (v3.0).   (pdf, it, 588 KB, 05/12/11)