- Docente: Andrea Cosso
- Credits: 6
- SSD: MAT/06
- Language: Italian
- Teaching Mode: Traditional lectures
- Campus: Bologna
- Corso: Second cycle degree programme (LM) in Mathematics (cod. 8208)
Learning outcomes
At the end of the course, the student knows basic concepts and methods of probability and mathematical statistics. The student can solve simple problems of probability and statistical inference.
Course contents
○ Descriptive statistics: historical background; population and sample, types of data, frequencies, tabular and graphical representations; measures of central tendency, measures of variability; boxplot; normal samples and measures of shape.
○ Bivariate data: joint frequencies and two-way tables; scatter plot; covariance and linear correlation coefficient; method of least squares and linear regression.
○ Introduction to Probability: interpretations of probability, beyond the scheme classical/frequentist/subjectivist; a brief history of Probability.
○ Mathematical model of a random experiment: primitive notions and axioms of probability, sample space, events, consequences of axioms; geometric probability.
○ Conditional probability and independence: chain rule, total probability rule, Bayes' rule; tree diagram.
○ Combinatorics and finite uniform probability spaces.
○ Random variables and random vectors of discrete type.
○ Introduction to Statistical inference: recalls of continuous random variables and Gaussian distribution; recalls of Law of large number and Central limit theorem; statistical model of a random experiment; elements of point estimation theory; biased and unbiased estimators, mean square error, asymptotical properties of estimators; Bayesian approach to Statistical inference.
Readings/Bibliography
Lectures notes and sheets of exercises prepared by the teacher (available on virtuale.unibo.it in Italian).
Supplementary textbook: Sheldon M. Ross, Introduction to Probability and Statistics for Engineers and Scientists, fifth edition, Academic Press.
Teaching methods
Lectures and exercises will be alternated in order to explain theoretical concepts through examples.
Lectures and exercises will be delivered in mixed mode, with the possibility to follow them in the classroom or remotely.
Lectures are in Italian.
Assessment methods
Written and oral examination.
Teaching tools
Website of the course available on virtuale.unibo.it, where the student can find: lecture notes, sheets of exercises, as well as other useful material for the course.
Office hours
See the website of Andrea Cosso