Probability and Statistics

Scholar Year: 2018/2019 - 2S

Courses

Head Teacher Responsability António José Moeda Sardinha Head

Weekly workload Hours/week T TP P PL L TC THE EL OT OT/PL TPL S Type of classes 4 Lectures Type Teacher Classes Hours Theorethical and Practical classes Totals 1 4,00

Teaching language

Portuguese

Intended learning outcomes (Knowledges, skills and competencies to be developed by the students)

- Apply the concepts of random variable and its distribution;
- Solve problems involving models and probability distributions with discrete variables and with continuous variables;
- Understand the concept of random sample and solve problems involving sampling distributions;
- Characterize and apply estimators;
- Construct and interpret confidence intervals;
- Identify and apply the appropriate hypothesis test;
- Identify the relation between hypothesis testing and confidence intervals;
- Build and analyze a simple linear regression model.

Syllabus

1. Random Variables: Concept of r.v. Functions for discrete and continuous r.v Expected value, variance and standard deviation, characterization and properties
2. Theoretical Distributions (TD): Discrete DT; Binomial and Poisson; Characterization. Continuous DT; Exponencial, Uniform and Normal. Brief reference to the Student-t, Chisquare and Snedecor F DT properties
3. Elements of Sampling Theory: Population and sample. Random Sample and Statistic. Sampling. Distribution.
4. Elements of Estimation Theory: Concept of Estimator; properties. Point and Interval Estimates. Confidence intervals.
5. Hypothesis Testing (HT): Null and alternative hypothesis, critical region, significance level, decision rule of the test, errors type I and type II and power of the test. Parametric HT of normal populations.
6. Simple Linear Regression: Regression line. Parameter estimation of best linear fit using the least squares approach. Concept of residuals. Empirical linear correlation coefficient.

Demonstration of the syllabus coherence with the UC intended learning outcomes

The curricular unit contents are structured, regarding its suitability for the intended learning outcomes.
Therefore, each subject approaches fundamentals concepts and practical applications by solving problems using the basic tools of Probability and Statistics to enable students to analyze certain phenomena of random nature, framed in the context of technology, particularly in the recognition and enforcement of probabilistic models, the deduction and application of confidence intervals and hypothesis testing, and the construction and analysis of simple linear regression models.

Teaching methodologies

- Classroom lectures through a combination of lecture method and problem solving;
- E-learning in the Moodle platform, providing access to the contents of UC through slides, videos, and solved and proposed exercises, promoting the holding of weekly activities.

Demonstration of the teaching methodologies coherence with the curricular unit's intended learning outcomes

Methodologies used are centered on knowledge of concepts and their applications.
With the classroom lectures are promoted the transmission of probability and statistical contents and its application through problem solving, mostly in contexts related to technology.
E-learning methodology, promotes discipline and autonomous work throw the weekly activities proposed, deepening the probability and statistical contents covered.

Assessment methodologies and evidences

There are two ways of assessment: by Tests and by Exam.

The assessment by Tests is based on the accomplishment of two tests.
The conditions of approval in the evaluation by Tests are as follows:
1. If the average (rounded to the units) of the test scores is greater than or equal to 10 and less than 17, the student is approved with a final grade equal to said average, provided that in any of the tests the grade was higher or equal to 6.5 (the mean of the tests is calculated from the scores of these rounded to tenths);
2. If the student obtains a grade of 6.5 or higher but has not passed the test assessment, then the student may choose to take a recovery test instead of the Exam in the Normal Exam Period. If the student misses one of the tests, he can also choose to recover this test instead of the Exam, provided that in the other test he has obtained a mark of 6.5 or higher;
3. If the average (rounded to the units) of the test scores is greater than or equal to 17, the student will have to take an oral test, the final grade being the average of these two marks. If it does not appear in the oral test the final classification will be 16 values.

Schedule of tests:
1st test: April 17, 2019 (Wednesday) at 7:00 pm *;
2nd test: June 19, 2019 (Wednesday) at 7:00 pm *.
* - Schedule to be confirmed by the Pedagogical Council (CP).

Assessment by Exam is based on an examination, and the approval conditions are as follows:
1. If the exam grade (rounded to the units) is greater than or equal to 10 and less than 17, the student is approved with a final grade equal to the grade of the exam (rounded to the units);
2. If the exam grade (rounded to the units) is greater than or equal to 17, the student will have to take an oral test, obtaining as a final mark the average of the classifications of said oral test and the exam. If you do not attend the oral test the final grade will be 16 points.

Primary Bibliography

Secondary Bibliography

Observations

• Students must be enrolled in the Moodle platform of ESTSetúbal, in order to have access to the support materials and all the information about the UC of Probabilities and Statistics.

• Face-to-face support: the timetable is available on the PE page in Moodle and in the window of PE in Maths Dept.;
• Permanent Moodle Forum.

Test and Examination Standards
• Moodle registration for tests and exams is required up to one week before each evaluation (students will receive email information about the opening and term of these registrations).
• On the day of the evaluation, before entering the room, the student will have to give the teacher a test / examination book (totally blank). The purchase of the test / examination notebook (consisting of a cover and five sheets, which remains blank) is made previously in the bookstore.
• Students may consult a handwritten A4 sheet, either on tests or on exams (photocopies of handwritten sheets are not allowed).
• It is necessary to present an identification document.
• The room can only be abandoned after one hour from the start of the test / examination. The abandonment of the room will imply the final delivery of the test / examination.
• Individual use of calculating machines is permitted.
• You can consult the tables provided by teachers on the day of the tests or exams.
• The handling or display of mobile phones during the test is not allowed.