Probability and Statistics

Code:

M2022

Acronym:

M2022

Level:

200

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2019/2020 - 1S

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

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L:F	10	Official Study Plan	2	-	6	56	162
L:M	66	Official Study Plan	2	-	6	56	162

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 infer population parameters from a sample of that population applying techniques of  interval estimation.

Working method

Presencial

Program

1. Probability Theory: review of fundamental concepts, probability space (sample space, sigma-algebra, probability measure), independence  and conditional probability, Bayes’ and total probability theorems.



 

2. Random Variables: characterization, discrete and continuous models, bidimensional random variables, function of a random variable, moments, Chebyshev's inequality, central limit theorem and law of large numbers.



 

3. Descriptive Statistics: fundamental concepts and tecniques for summarizing data.

 

4. Statistical Inference: sample distributions, estimators properties, confidence intervals for the usual population parameters.

 

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.

keywords

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

Evaluation Type

Distributed evaluation without final exam

Assessment Components

designation	Weight (%)
Teste	100,00
Total:	100,00

Amount of time allocated to each course unit

designation	Time (hours)
Estudo autónomo	106,00
Frequência das aulas	56,00
Total:	162,00

Eligibility for exams

without restrictions

Calculation formula of final grade

1. In the first call the final mark will be the sum of the scores obtained in two assessments: 

Assessment 1: with a total of 8 points, will take place in a date to be settled with students. 

Assessment 2: with a total of 12 points, will take place during the period settled for conclusion of distributed evaluation. 


2. In the second call, the final mark will be obtained in an exam with a total of 20 points. 
This exam will be divided in two parts, allowing the students which have not yet been aproved in the course (and only these students) to substitute the score in any of the two parts by the score obtained in the corresponding assessment. 

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

Improvement in the classification can be obtained in the second call only.