STATISTICS
Stampa
Enrollment year
2021/2022
2021/2022
Regulations
DM270
MAT/06 (PROBABILITY AND MATHEMATICAL STATISTICS)
Department
DEPARTMENT OF ELECTRICAL,COMPUTER AND BIOMEDICAL ENGINEERING
Course
INDUSTRIAL ENGINEERING
Curriculum
PERCORSO COMUNE
Year of study
Period
2nd semester (07/03/2022 - 17/06/2022)
ECTS
6
Lesson hours
56 lesson hours
Language
Italian
Activity type
WRITTEN AND ORAL TEST
Teacher
Prerequisites

The contents of the course Analisi Matematica I
Learning outcomes

The course introduces students to statistical data analysis. It is intended to provide basic knowledge of descriptive and inferential statistics. Part of the course will be devoted to the study of the basic tools and the probabilistic mathematical language.

At the end of the course the student will be able to understand and interpret basic statistical analyses and should also be aware of the limits of the information obtained from the data.
Course contents

Part I: descriptive statistics.
Data, populations and samples. Frequencies, percentages, histograms. Empirical mean, median, mode, quantiles, variance, standard deviation. Correlation coefficient (Pearson), scatter plots.

Part II: probability.
Definition of probability, elements of combinatorics, conditional probability, independence, Bayes's formula. Applications to clinical tests and genetics.  Discrete random variable: density and distribution function. Mean and variance. Binomial and Poisson distributions.  Random discrete vectors: joint density and independence.  Continuous random variables. Uniform, exponential and Gaussian (or normal) distributions. Density function, mean and variance. Independence. Properties of Gaussian random variables.  Chebychev's inequality and law of large numbers. Central limit theorem and some applications.
Part III: statistical inference.
Random variables associated to a population. Point estimation and confidence interval. Sample mean  random variable and sample standard deviation random variable. Confidence interval for the mean. Use of Student's t random variable. Confidence interval for a proportion.  Hypothesis test for the mean. Null hypothesis. z-test and t-test. p-value. Hypothesis test comparing means  of different populations. Chi-square test goodness of a fit. Chi-square test of independence. p-value.  Linear regression.
Teaching methods

Lectures and sessions of practical exercises aimed at applying in concrete examples the theoretical concepts presented during the lectures.

M. Bramanti. Calcolo delle Probabilità e Statistica. Teoria ed Esercizi. Esculapio.
Assessment methods

There will be a written examination, where the student will be asked to solve some problems on the specific topics treated during the course.
If the student is positively evaluated in the written examination, the commission or the student can ask for an additional oral colloquium.

Note that the final grade of "Complementi di Analisi Matematica e Statistica" will be the mean of the grades of the two parts of the course, "Complementi di Analisi Matematica" and "Statistica''.
Further information

This course is a part of "Complementi di Analisi Matematica e Statistica''
Sustainable development goals - Agenda 2030