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Single discipline educational activity
Course Sheet Academic Year of enrolment:
Disciplinary Sector:
Probability and Mathematical Statistics
Professor and Collaborators:
CAROLI COSTANTINI Cristina
Hours of classroom activity:
Prerequisites:
Basic notions of differential and integral calculus and of vectors and matrices.
Objectives
Contents Probability spaces. Elements of combinatorics and uniform, finite probability spaces. Conditional probability and independence. Discrete and absolutely continuous random variables. Pairs of discrete and jointly absolutely continuous random variables. Jointly Gaussian random variables. Law of large numbers, central limit theorem.
Extended Syllabus 1. Probability spaces and their properties. Finite, uniform probability spaces. Combinatorics. extractions without replacement.
2. Conditional probability and its properties. Bayes formula. Independent events and conditionally independent events. Bernouli trials.
3. Discrete random variables: binomial, hypergeometric, geometric and Poisson laws.
4. Continuous random variables: uniform, exponential and Gaussian laws. Distribution function.
5. Expectation and its properties. Variance. Quantiles.
6. Joint laws of random variables: marginals, independence, conditional density. Density of the sun of two random variables. Sum of independent Gaussian random variables.
8. Joint Gaussian distributions.
9. Law of large numbers and Central Limit Theorem.
Recommended Bibliography S. Ross: Calcolo delle probabilità 3/ed, Apogeo, 2014
Notes and exercises available on the web page of the teacher (https://economia.unich.it/ ). The textbook is also available in English and the on-line material is available in English, upon request.
Methods of Provision
Teaching Methods The course is organized in at least 48 hours of lectures on the theory, with applications and examples.
The course has a companion course of Probability Laboratory where exercises and problems are worked out.
Evaluation methods Verification of learning:
There will be a final exam for the courses of Probability and Laboratory of Probability. The final exam will consist of both a written test (or an intermediate test and a final one, according to the student's choice) and an oral exam. The written test will be composed of exercises and problems. Both the written text and the oral exam can be taken in English.
Contacts/More Information