Probability and Statistics B

Code:

M2040

Acronym:

M2040

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2024/2025 - 1S

Active?	Yes
Responsible unit:	Department of Mathematics
Course/CS Responsible:	Bachelor in Artificial Intelligence and Data Science

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L:B	0	Official Study Plan	3	-	6	48	162
L:CC	63	study plan from 2021/22	2	-	6	48	162
			3
L:EA	15	The study plan from 2019	2	-	6	48	162
L:F	0	Official Study Plan	2	-	6	48	162
L:G	0	study plan from 2017/18	2	-	6	48	162
			3
L:IACD	78	study plan from 2021/22	2	-	6	48	162
L:M	0	Official Study Plan	3	-	6	48	162
L:Q	0	study plan from 2016/17	3	-	6	48	162

Teaching language

Portuguese

Objectives

An Introductory course in Probability and Statistics: acquisition of basic concepts of Probability and Statistics and their application to concrete situation
Particular attention is paid to the presentation and understanding of the concepts, keeping the mathematical treatment on an medium level.

Learning outcomes and competences

On completing this curricular unit it is expected that the student:

1. can understand the concepts involved in a statistical study and be aware of the various problems that arise in each particular study.
2. can identify and apply appropriate techniques of descritive statistics to organize and summarize data and interpret them;
3. dominates the probability calculus and knows to calculate probabilities associated with the phenomenon under study;
4. be able to characterize random variables/random vectors and identify the respective probability distributions;
5.  be able to make inferences on population parameters applying techniques of point and interval estimation.

Working method

Presencial

Program

1. Basic concepts in Statistics: Populations and samples; the role of randomization; observational and experiment studies; statistical variables.


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

3. Probability Theory: fundamental concepts, probability interpretations, independence of events and conditional probability, Bayes’ and total probability theorems.



2. Random Variables: characterization, discrete and continuous models; function of a random variable, moments; Discrete distributions:  the uniform, binomial and poisson distributions; the uniform, exponentisal, normal distributions, student's t distribution and  chi-squared distribution. Chebyshev's inequality, central limit theorem.

4. Statistical Inference: point estimation, estimators properties, maximum likelihood estimators, interval estimation.


Mandatory literature

Applied Statistics and Probability for Engineers, John Wiley & Sons, 2003; Douglas C. Montgomery, George C. Runger. ISBN: ISBN: 0-471-20454-4
Chance encounters; Wild Christopher J.. ISBN: ISBN: 0-471-32936-3
Introdução à estatística; Murteira Bento & all. ISBN: ISBN: 972-773-116-3
Bento José Ferreira Murteira; Introdução à estatística. ISBN: 972-773-116-3

Complementary Bibliography

Myra L. Samuels; Statistics for the life sciences. ISBN: 978-0-13-122811-5 0-13-122811-0

Teaching methods and learning activities

Software

R

Evaluation Type

Evaluation with final exam

Assessment Components

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

Amount of time allocated to each course unit

designation	Time (hours)
Estudo autónomo	114,00
Frequência das aulas	48,00
Total:	162,00

Eligibility for exams

No requirements.

Calculation formula of final grade

In both evaluation periods, the classification will be that obtained in an exam with a score of 20 points, with the exception descreibed below.

Students with a score greater than or equal to 17.5 values in the final exam must make a complementary written or oral exam in order to obtain a score greater than or equal to 18 values.

Examinations or Special Assignments

Special assessment (TE, DA, ...)

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

Observations

Article 13 of the General Regulation for the Assessment of First Cycle Students, Integrated Master's Study Cycles and Second Cycles of the U.Porto, approved on May 19, 2010 (cf. http://www.fc.up.pt /fcup/documentos/documentos.php?ap=3&ano=2011): "Fraud committed when carrying out a test, in any of its forms, implies its annulment and communication to the statutorily competent body for possible disciplinary proceedings."

 

Any student may be required to take an oral test to clarify any doubts that may have arisen regarding the tests or assessment work.