Probability and Statistics

Code:

M2034

Acronym:

M2034

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2022/2023 - 2S

Active?	Yes
Responsible unit:	Department of Mathematics
Course/CS Responsible:	Bachelor in Mathematics

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L:M	81	Official Study Plan	2	-	9	84	243
L:MA	0	Official Study Plan	2	-	9	84	243

Teaching language

Portuguese

Objectives

Acquisition of basic concepts of Probability and Statistics and their application to concrete situations.

Learning outcomes and competences

On completing this curricular unit it is expected that the student

a.dominates the probability calculus and  knows to calculate probabilities associated with the phenomenon under study;

b.
be able to characterize random variables and identify the respective probability distributions;

c.
can identify appropriate techniques of descritive statistics to organize and summarize data and interpret them;

d.
be able to make inferences on population parameters applying techniques of  interval estimation.

Working method

Presencial

Program

1. Random experiments and statistical regularity.
Probability spaces (sample space, sigma-algebra, probability measure). Conditional probability and independence.


2. Random variables: measurable functions, characterization of random variables; moments; some relevant inequalities.
Discrete and continuous distributions.
Random vectors and their characterization, independence and conditioning. Moments. Examples of multivariate distributions.
Stochastic convergence (in probability, mean square, almost sure, in distribution). Laws of large numbers and the central limit theorem.

3. Exploratory data analysis. Descriptive statistics and statistical inference. Sampling, statistics, sample distributions.

4. Point estimation. General properties of an estimator. Estimation methods (moments and maximum likelihood).
 Confidence intervals for the usual population parameters.
Introduction to hypothesis testing.

Mandatory literature

Morris H. DeGroot & Mark J. Schervish; Probability and Statistics, Fourth Edition, Addison-Wesley , 2012. ISBN: 978-0-321-50046-5

Complementary Bibliography

Montgomery Douglas C.; Applied statistics and probability for engineers. ISBN: 0-471-20454-4
Papoulis Athanasios; Probability and statistics. ISBN: 0-13-711730-2

Teaching methods and learning activities

The contents of the syllabus are mainly presented in the lectures, providing examples in order to illustrate and motivate the concepts and methods considered. Some specific  topics are only presented in the classes, where exercises and related problems are solved and discussed.

All resources are available for the students at the unit’s web page.

Software

R project

keywords

Physical sciences > Mathematics > Statistics
Physical sciences > Mathematics > Probability theory

Evaluation Type

Distributed evaluation without final exam

Assessment Components

designation	Weight (%)
Teste	90,00
Trabalho prático ou de projeto	10,00
Total:	100,00

Amount of time allocated to each course unit

designation	Time (hours)
Estudo autónomo	159,00
Frequência das aulas	80,00
Trabalho escrito	4,00
Total:	243,00

Eligibility for exams

There are no restrictions.

Calculation formula of final grade

Assessment will be based on two tests (90%) and project work (10%)(with dates to be defined at the beginning of the semester). To be approved, a minimum rate of 30% is required in each of the tests.

The final mark corresponds to the average of the marks obtained in the tests added to the classification obtained in the project work. 

There will be an exam at the time of appeal (época de recurso), accessible to any student who has not passed in the regular time (época normal).

In both the regular and the appeal exam periods, a complementary test may be required to assign a mark higher than 17 values.

Special assessment (TE, DA, ...)

Exams under speacial conditions will consist of a written test which can be preceded by an oral eliminatory exam.

Classification improvement

Exam. Students who are improving the mark cannot do so through tests.