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| MATH0062-1 | Elements of probability calculus
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| Duration : | 15h Th, 10h Pr, 25h Proj. |
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| Number of credits : |
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| Lecturer : | Louis Wehenkel |
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Language(s) of instruction :
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| French language |
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Organisation and examination :
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| Teaching in the second semester |
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Course contents :
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| - Motivations: reasoning under uncertainties, modeling of stochastic systems, data analysis.
- Basics: random experiment, events, Kolmogorov axioms, conditional probability, Bayes theorem, independence, interpretations of the notion of probability.
- Discret and continuous random variables: probability distribution, repartition function, density, expectation, variance, moments, characteristic and generating functions, usual distributions, functions of a random variable.
- Pairs and vectors of random variables: joint, marginal, and conditional distributions, conditional expectation and variance, independence, covariance/correlation, functions of random variables, linear and nonlinear regression.
- Convergence of sequences of random variables, central limit theorem, laws of large numers.
- Notion of random function |
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Learning outcomes of the course :
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| The student shall be able to apply probabilistic methods to problems of reasoning under uncertainty, by being able to model them and identify the main resolution steps. He will also be knowledgeable about the main analytical and computational techniques useful in order to compute numerical solutions. |
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Prerequisites and co-requisites/ Recommended optional programme components :
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| Calculus, algebra, geometry, and elements of computer science and applied mathematics. |
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Planned learning activities and teaching methods :
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| The course is composed of about 10 hours of theoretical lectures, 10 hours of classroom exercises, and 10 hours of assistance to the realization of a practical project with the computer. |
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Mode of delivery (face-to-face ; distance-learning) :
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| Presential |
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Recommended or required readings :
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| Course notes, slides, and exercise notes.
See http://www.montefiore.ulg.ac.be/~lwh/Probas/ |
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Assessment methods and criteria :
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| 20% for the practical work and 80% for the written exam. |
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Work placement(s) :
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| NIL |
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Organizational remarks :
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| To be announced later on. |
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Contacts :
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| mailto:L.Wehenkel@ulg.ac.be(L.Wehenkel@ulg.ac.be) |
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