| Code |
16670
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| Year |
1
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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 |
This course has no prerequisites. Mathematical maturity at the level of Integral Calculus is recommended but not mandatory.
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Mode of delivery |
Theoretical and practical lessons. Face-to-face teaching
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Work placements |
Not aplicable.
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Learning outcomes |
•To provide the student the basic knowledge in probability theory, random variables and the most important theoretical distributions.
•To familiarize the student with the most important concepts and methods in statistical inference, allowing him to apply these to real situations.
After approval at this UC, the Student should be able to:
O1. Formalize correctly problems involving the result of randomized trials.
O2. Identify the probabilistic models, their properties and relation to other models.
O3. Formalize correctly problems involving the result of randomized trials.
O4. Demonstrate knowledge in the field of the statistical inference, with emphasis on parametric inference.
O5. Demonstrate strong predisposition for individual and group learning.
O6. Demonstrate the ability to interpret and analyze the results obtained using a statistical software resulting from the application of acquired knowledge.
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Syllabus |
1 - Theory of probability: conditional probability and independence. Theorem of total probability and Bayes Theorem.
2 - Random variables. Probability distributions.
3 - Theoretical Distributions: Discrete distributions. Continuous distributions.
4 - Point and Interval Estimation.
4.1 - Point estimation. Some properties of the estimators.
4.2 - Definition of confidence interval. Confidence intervals for means, variances and proportions.
5 - Hypotheses testing: Fundamental concepts. Tests for means, proportions and variances.
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Main Bibliography |
•Pedrosa, A. e Gama, S. (2004). Introdução computacional à Probabilidade e Estatística. Fundação Calouste Gulbenkian. Lisboa
•Murteira, B. (1990). Probabilidades e Estatística. Vol I e II(2ª ed.) McGraw-Hill.
•Pestana, D. D. e Velosa, S. F. (2006). Introdução à Probabilidade e à Estatística. Volume I, 2ª Edição, Fundação Calouste Gulbenkian.
•Rohatgi, V. K. (1976). An Introduction to Probability Theory and Mathematical Statistics. J. Wiley & Sons, New York.
•Ross, S. M. (1987). Introduction to Probability Theory for Engineers and Scientists. J. Wiley & Sons, New York.
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Teaching Methodologies and Assessment Criteria |
1. Student achievement of the intended learning outcomes is assessed within the teaching and learning process through two assessment components (Test 1 and Test 2), each graded on a 0–10 scale.
2. The Continuous Assessment Grade (CEA) is calculated as the sum of the marks obtained in both components, as follows: CEA = Test 1 + Test 2.
3. Students who obtain a CEA of 9.5 or higher (on a 0–20 scale) are exempt from the final examination.
4. The status of «Attendance» is granted to students who cumulatively fulfil the following requirements:
a) Attendance of at least 50% of the scheduled contact hours;
b) In case of unsuccessful completion, a CEA of at least 5.
5. The attendance requirement does not apply to students covered by special status provisions, in accordance with national legislation and applicable institutional regulations.
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Language |
Portuguese. Tutorial support is available in English.
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