Probability and Statistics

Code:

M2014

Acronym:

M2014

Level:

200

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2022/2023 - 2S

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

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L:B	1	Official Study Plan	3	-	6	56	162
L:G	1	study plan from 2017/18	2	-	6	56	162
			3
L:Q	0	study plan from 2016/17	3	-	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 and 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	102,00
Frequência das aulas	56,00
Trabalho escrito	4,00
Total:	162,00

Eligibility for exams

There are no restrictions.

Calculation formula of final grade

Assessment will be based on two tests (90%) and a 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 of 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).

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

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