- Docente: Pietro Rigo
- Crediti formativi: 6
- SSD: MAT/06
- Lingua di insegnamento: Inglese
- Modalità didattica: Convenzionale - Lezioni in presenza
- Campus: Bologna
- Corso: Laurea in Scienze statistiche (cod. 8873)
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dal 19/09/2023 al 25/10/2023
Conoscenze e abilità da conseguire
By the end of the course the student should know the basic theory of multidimensional random variables and sequences of random variables. In particular the student should be able: - to derive the distribution of transformed random variables - to derive joint, conditional and marginal probability density functions - to state the definition and recall the properties of multivariate normal distributions to investigate converge properties of sequences of random variables
Contenuti
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Probability spaces and their elementary properties
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Various definitions of probability (just a hint)
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Random variables and their distributions
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Independence
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Probability measures on R and R^n (including distribution functions, and, in case of R, discrete, singular continuous, and absolutely continuous probability laws)
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List of the main probability measures on R and normal distribution on R^n
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Transform of random variables
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Moments
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Conditional distributions
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Convergence of random variables
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Laws of large numbers
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Central limit theorems
Testi/Bibliografia
In order to prepare the exam, the notes are (more than) enough, provided obviously they are taken in a exhaustive and correct way. For those who don't like notes, and/or for those who want to deepen some topics, the following text books are suggested:
Bertsekas D.P. and Tsitsikli J.N., Introduction to Probability, 2nd Edition, ISBN: 978-1-886529-23-6
Grimmett G. and Stirzaker D. (2001) Probability and random processes, Oxford University Press.
Dall'Aglio G. (1987) Calcolo delle probabilita', Zanichelli.
Metodi didattici
Regular lectures and tutorials
Modalità di verifica e valutazione dell'apprendimento
One-hour-a-half written exam, consisting of 3/4 exercises, followed by an oral examination. The exercises are obvious versions of the ones discussed in class, and attain to elements of the syllabus covered by the course lectures. The aim of the written test is to assess the student's ability to use definitions, properties and theorems of probability theory when facing with some simple problems. Finally, the oral part of the exam is subjected to the overcoming of the written part.
Strumenti a supporto della didattica
Notes and the text-books quoted above
Orario di ricevimento
Consulta il sito web di Pietro Rigo