| Code |
13919
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| Year |
2
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| Semester |
S2
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| ECTS Credits |
6
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| Workload |
TP(60H)
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| Scientific area |
Mathematics
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Entry requirements |
N.A.
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|
Learning outcomes |
To develop probability models for variables on measurable spaces of different dimensions; identify and apply the properties of probability laws in problem solving; characterize a stochastic process; identify and apply various modes of stochastic convergence.
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Syllabus |
1. Probability spaces: axiomatic, conditional probability and independence in a family of events.
2. Laws of probability on IR: classification and integration.
3. Probability laws on IRn: independent random variables, transformation of random vectors, conditional distributions and moments.
4. Probability laws on C: random variables with complex values, characteristic function of a real random vector and Normal vectors.
5. Stochastic processes: characterization, independence of increments, Markovian property, autocorrelation and autocovariance, stationarity, Poisson processes, processes of counting renewals.
6. Stochastic convergences: convergence in law, functional convergences, laws of large numbers and the central limit theorem.
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Main Bibliography |
Billingsley, P. (1986). Probability and Measure, Wiley.
Durrett, R. (1996). Probability: Theory and Examples, Duxbury Press.
Feller, W. (1971). An Introduction to Probability Theory and its Applications, Vol. 2, Wiley.
Kallenberg, O. (1997). Foundations of Modern Probability, Springer.
Resnick, S.I. (1999).A Probability Path, Birkh ¨auser.
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Language |
Portuguese. Tutorial support is available in English.
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