Probability and Statistics

Code:

M2022

Acronym:

M2022

Level:

200

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2018/2019 - 1S

Active?	Yes
Web Page:	https://moodle.up.pt/course/view.php?id=460
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	12	Official Study Plan	2	-	6	56	162
L:M	62	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, independence of events 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: estimators properties, confidence intervals for the usual population parameters.

 

Mandatory literature

Montgomery Douglas C.; Applied statistics and probability for engineers. ISBN: 0-471-20454-4
Oliveira J. Tiago de; Probabilidades e estatística. ISBN: 972-9241-20-1 (vol. 1)

Complementary Bibliography

Papoulis Athanasios; Probability and statistics. ISBN: 0-13-711730-2

Teaching methods and learning activities

Lectures: presentation and discussion of the subjects listed in ‘Syllabus’.

Practical classes: solving exercises previously proposed to students; hints to solve exercises not solved in class; support in clarifying theoretical and/or practical problems.

 

keywords

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

Evaluation Type

Distributed 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	106,00
Frequência das aulas	56,00
Total:	162,00

Eligibility for exams

without restrictions

Calculation formula of final grade

The final exam will be divided into two parts, each one scored 10 values.

The first of these parts may be held in a test taking place during the class time. Students who choose to take the test may also take both parts of the first season exam, thus annulating the test score.



In the second season exam (except in cases of improvement), students may use the 1st or 2nd part classifications obtained previously (in the test or in the first seaon exam).

Special assessment (TE, DA, ...)

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