Statistics

Year
2
Academic year
2019-2020
Code
01621588
Subject Area
Quantitative Methods
Language of Instruction
Portuguese
Mode of Delivery
Face-to-face
Duration
SEMESTRIAL
ECTS Credits
6.0
Type
Compulsory
Level
1st Cycle Studies

Recommended Prerequisites

Calculus.

Teaching Methods

The presentation will be done through theoretical and practical classes. In the lecture we will present the fundamental results associated with the probability theory, with the presentation of concepts, definitions and theorems, explaining how these results are useful for the calculation of probabilities and in which situations they can be used to understand a particular phenomenon or to take a decision. The tutorials aim to build on the concepts and results presented in lecture, giving examples with a set of practical exercises that will be proposed throughout the semester.

Learning Outcomes

Overall objectives

The overall objective of the curricular unit is that the student recognizes the importance of the concept of probability and also its usefulness as a way to understand different phenomena embedded in an environment of uncertainty.

 

Specific objectives

It is intended to give to students a set of results associated with the concept of probability and statistical inference, allowing them to calculate the probability of events models, namely, through parametric models.

 

Generic competencies

Being approved in this curricular unit, the students must; be able to calculate the probability of simple and complex events by applying the basic rules of probability;  how to use a sample to make inferences.

 

Specific competencies

Being approved in this curricular unit, the students must; know how to calculate probabilities; how to define point estimates;  how to analyse the properties of the estimators;  how to define  interval estimates and hypothesis testing.

Work Placement(s)

No

Syllabus

Probabilities
1.  Random experiments, axioms, probabilities properties, conditional probabilities, independence.
2.  Random variables and their distributions, moments, moments generating function, quantiles.
3.  Statistical models, discrete and continuous laws.
4.  Random vectors, joint distributions, marginal distributions, conditional distributions, conditional moments.
5.  Stochastic convergence, weak law of large numbers, central limit theorem.

Mathematical Statistics
1.  Random sample, sample statistic, sample distributions.
2.  Estimation methods, point estimation, method of moments, maximum likelihood.
3.  Estimators, statistical properties of the estimators.
4.  Pivotal variables, interval estimation.
5.  Hypothesis testing, rejection regions, first and second type errors, Neyman-Pearson's lemma, uniformly most powerful tests, p-value

Head Lecturer(s)

António Alberto Ferreira Santos

Assessment Methods

Assessment
Periodic or by final exam as given in the course information : 100.0%

Bibliography

CASELLA, George ; BERGER, Roger L. - Statistical inference. 2nd ed.. [Pacific Grove,] : Boorks/Cole Cencage Learning, 2002. [BP 519.2 CAS]
DEGROOT, Morris H. ; SCHERVISH, Mark J. - Probability and statistics. 4th ed.. Boston : Pearson, 2012. [BP 519.2 DEG]
INTRODUÇÃO à estatística. Bento Murteira [et al.]. Lisboa : Escolar Editora, 2010. [BP 519.2 INT]
ROHATGI, Vijay K ; SALEH, A. K. Md. Ehsanes - An introduction to probability theory and mathematical statistics. 2nd ed.. New York : John Wiley & Sons, 2001. [BP 519.2 ROH]