Teaching Guide Information

Presentation

Probability & Statistics is a course sequence spanning over two trimesters. The first trimester covers Probability while the second trimester deals with Statistics.

Probability provides an introduction to probability and its applications. The list of topics covered in the course includes: basic probability concepts; rules and operations in probability; random variables; discrete and continuous distributions; bivariate distributions; conditional distributions and conditional expectation; limit theorems for sums of random variables; appli­cations of limit theorems.

Statistics provides an introduction to statistical inference and its applications. The list of topics covered in the course includes: the notions of population & sample; distribution of sample statistics, point estimation, confidence intervals, hypothesis testing, simple linear regression model.

In each trimester there will be sixteen theory lectures focused on presentation of concepts and applications, and eight seminars dealing with application of the methods learned in class. The course emphasizes both clarity in understanding of the concepts introduced and elementary mathematics involved, as well as an ability to apply these methods in practical settings. Though mathematical background will be kept simple, the student should be aware that thinking and understanding is required. 

Associated skills

Specific competences:

1. Acquisition of the basic concepts of probability and statistical inference.

2. Knowledge and understanding of basic statistical calculations and the software tools used for them.

3. The ability to identify the elements making up a univariate statistical model applied to real situations.

4. The ability to use standard statistical packages and to correctly interpret the produced results.

General competences:

G4. The ability to satisfactorily use the English language for academic purposes (read, write and speak using a medium-high register).

G5. Proficiency in the use of computing tools and their main applications in ordinary academic work.

G9. Consolidated habits as regards self-discipline, personal standards and thoroughness in academic work and in organization and fulfilment of timescales.

G10. A proactive attitude to ascertaining the unknown, essential in all training processes and in all prestigious professional activities.

G11. The ability to apply the knowledge acquired and to adapt it to new situations flexibly and creatively.

G12. The ability to make progress autonomously and continuously in training and learning processes.

G16. Use of the right information in formulating proposals and problem-solving.

G19. Identification of the key factors in a problem. 

Learning outcomes

Students will be able to critically apply basic statistical tools at the end of this course

Sustainable Development Goals

Some tests will be carried out without using paper support and will be delivered online through Aula Global

Prerequisites

There are no prerequisits required to take this course

Contents

Probability

1             Probability: Basic concepts

2             Random Variables

3             Discrete Random variables. Special Discrete Univariate Random Variables.

4             Continuous Random Variables. Special Continuous Univariate Random Variables.

5             Bivariate Random Variables

6.            Asymptotics

Statistics

1             Population & Samples

2             Distribution of Sample Statistics

3             Point Estimation

4             Confidence Intervals

5             Hypothesis Testing

6             1-way ANOVA

7             Simple Regression Model

Teaching Methods

The teaching & learning process is carried out through lectures, seminars and students' personal work.
There will be 16 lectures in theory each semester in large groups, whose duration is 1.5 hours each. In these lectures, basic notions, techniques and main applications will be presented. The range of students' individual work beyong the classroom will also be indicated.
Each semester there will be 8 seminar sessions where the large group will be subdivided into 3 subgroups. These seminars will serve for checking students' progress in learning theory, and exercises will be proposed for the students to work either individually or in small groups. Some seminar sessions will include written controls or online tests wichi will be announced in advance.

The use of statistical software will be made in lectures by the course instructor, in seminars and beyond the classroom by the students.

Students enrolled in the course are expected to carry out the following tasks each week:

• Before lectures in theory: to seach and read the corresponding course materual (individual).
• To attend the lectures (in-classroom).
• To work individually, to analyse the problems solved, to revisit lecture notes and slides, to solve exercises that are posted, to look through textbooks (individual).
• Before the seminars: to solve exercises that are posted. To practice with statistical software (individual).
• To attend the seminars (in-classroom).
• To compare the results obtained while solving exercises to those posted by the course instructor (individual).

Evaluation

Course assessment is based on that in each of two trimesters and a final average grade.

Assessment in each trimester

Continuous assessment (40% of the final trimestral grade):

• Two tests (12.5% of the trimestral grade each)
• First trimester: problems solving (15% of the trimestral grade)
• Second trimester: group project (15% of the trimestral grade)

Final Exam (60% of the final trimestral grade)

Will contain all contents of a trimester and will last between 1 and 2 hours. The Final Exam grade should be of at least 3.5 points over 10, in order for the average with the continuous assessment grade to be calculated. Otherwise, the trimester grade will be that of the Final Exam.

Weighted Trimestral Course Grade

Is equal to 0.4 times the Continuous Assessment Grade plus 0.6 times the Final Exam grade.

Final assessment in Probability and Statistics course (over two trimesters)

The course grade is the average of the two trimester grades, provided that each of the trimester weighted grades is of at least 4 points over 10. Otherwise, the course is considered to be Failed.

Re-Take Exam (one exam per trimester)

In each of the two trimesters, a Re-Take Exam will be scheduled.

In both trimesters, the Re-Take Exam is for all those students who have taken part in at least a half of the continuous assessment activities, have taken part in the Final Exam, and have got a grade less than 5 points over 10 as the trimestral weighted grade.

In the second trimester, moreover, only those students can sit for the Re-Take Exam who have obtained an average grade over both trimesters which is less than 5 points.

The Re-Take Exam will consist of a global exam over all topics covered in the corresponding trimester.

Continuos Assessment grades cannot be improved in a Re-Take Exam.

If a student sits for a Re-Take Exam, the Trimestral Weighted Grade is calculated as a weighted average of the Continuous Assessment Grade (40%) and the Re-Take Grade (60%), given that the Re-Take Exam grade is not less than 3.5 points over 10. Otherwise, the Weighted Trimester Grade remains as it has been before the Re-Take Exam.

Grades of course repeaters

Course repeaters who followed continuous assessment during the previous academic course and who got a final grade of Failed (not those who were graded as Not Shown Up) may be examined (in each of the two trimesters) through two control tests valid 15% each, and a Final Exam valid 70%. A minimum grade of 3.5 points over 10 is required in the Final Exam.

Those students who are interested in taking this assessment itinerary should contact the course instructor before the first seminar control is carried out.

Bibliography and information resources

QA276.18 .N49 2007

Paul Newbold, William L. Carlson, and Betty M. Thorne. Statistics for Business and Economics, Pearson 2019, 9th ed. ISBN 9781292315201 (any edition of the book beginning from the 4th edn. may be used).

QA276.12 .M665 2004
Moore, David S. The Basic Practice of Statistics, W.H. Freeman, New York [N.Y.], 2004, 3rd ed.
 

Información de la Guía Docente

Presentation

Probability & Statistics is a course sequence spanning over two trimesters. The first trimester covers Probability while the second trimester deals with Statistics.

Probability provides an introduction to probability and its applications. The list of topics covered in the course includes: basic probability concepts; rules and operations in probability; random variables; discrete and continuous distributions; bivariate distributions; conditional distributions and conditional expectation; limit theorems for sums of random variables; appli­cations of limit theorems.

Statistics provides an introduction to statistical inference and its applications. The list of topics covered in the course includes: the notions of population & sample; distribution of sample statistics, point estimation, confidence intervals, hypothesis testing, simple linear regression model.

In each trimester there will be sixteen theory lectures focused on presentation of concepts and applications, and eight seminars dealing with application of the methods learned in class. The course emphasizes both clarity in understanding of the concepts introduced and elementary mathematics involved, as well as an ability to apply these methods in practical settings. Though mathematical background will be kept simple, the student should be aware that thinking and understanding is required. 

Associated skills

Specific competences:

1. Acquisition of the basic concepts of probability and statistical inference.

2. Knowledge and understanding of basic statistical calculations and the software tools used for them.

3. The ability to identify the elements making up a univariate statistical model applied to real situations.

4. The ability to use standard statistical packages and to correctly interpret the produced results.

General competences:

G4. The ability to satisfactorily use the English language for academic purposes (read, write and speak using a medium-high register).

G5. Proficiency in the use of computing tools and their main applications in ordinary academic work.

G9. Consolidated habits as regards self-discipline, personal standards and thoroughness in academic work and in organization and fulfilment of timescales.

G10. A proactive attitude to ascertaining the unknown, essential in all training processes and in all prestigious professional activities.

G11. The ability to apply the knowledge acquired and to adapt it to new situations flexibly and creatively.

G12. The ability to make progress autonomously and continuously in training and learning processes.

G16. Use of the right information in formulating proposals and problem-solving.

G19. Identification of the key factors in a problem. 

Learning outcomes

Students will be able to critically apply basic statistical tools at the end of this course

Sustainable Development Goals

Some tests will be carried out without using paper support and will be delivered online through Aula Global

Prerequisites

There are no prerequisits required to take this course

Contents

Probability

1             Probability: Basic concepts

2             Random Variables

3             Discrete Random variables. Special Discrete Univariate Random Variables.

4             Continuous Random Variables. Special Continuous Univariate Random Variables.

5             Bivariate Random Variables

6.            Asymptotics

Statistics

1             Population & Samples

2             Distribution of Sample Statistics

3             Point Estimation

4             Confidence Intervals

5             Hypothesis Testing

6             1-way ANOVA

7             Simple Regression Model

Teaching Methods

The teaching & learning process is carried out through lectures, seminars and students' personal work.
There will be 16 lectures in theory each semester in large groups, whose duration is 1.5 hours each. In these lectures, basic notions, techniques and main applications will be presented. The range of students' individual work beyong the classroom will also be indicated.
Each semester there will be 8 seminar sessions where the large group will be subdivided into 3 subgroups. These seminars will serve for checking students' progress in learning theory, and exercises will be proposed for the students to work either individually or in small groups. Some seminar sessions will include written controls or online tests wichi will be announced in advance.

The use of statistical software will be made in lectures by the course instructor, in seminars and beyond the classroom by the students.

Students enrolled in the course are expected to carry out the following tasks each week:

• Before lectures in theory: to seach and read the corresponding course materual (individual).
• To attend the lectures (in-classroom).
• To work individually, to analyse the problems solved, to revisit lecture notes and slides, to solve exercises that are posted, to look through textbooks (individual).
• Before the seminars: to solve exercises that are posted. To practice with statistical software (individual).
• To attend the seminars (in-classroom).
• To compare the results obtained while solving exercises to those posted by the course instructor (individual).

Evaluation

Course assessment is based on that in each of two trimesters and a final average grade.

Assessment in each trimester

Continuous assessment (40% of the final trimestral grade):

• Two tests (12.5% of the trimestral grade each)
• First trimester: problems solving (15% of the trimestral grade)
• Second trimester: group project (15% of the trimestral grade)

Final Exam (60% of the final trimestral grade)

Will contain all contents of a trimester and will last between 1 and 2 hours. The Final Exam grade should be of at least 3.5 points over 10, in order for the average with the continuous assessment grade to be calculated. Otherwise, the trimester grade will be that of the Final Exam.

Weighted Trimestral Course Grade

Is equal to 0.4 times the Continuous Assessment Grade plus 0.6 times the Final Exam grade.

Final assessment in Probability and Statistics course (over two trimesters)

The course grade is the average of the two trimester grades, provided that each of the trimester weighted grades is of at least 4 points over 10. Otherwise, the course is considered to be Failed.

Re-Take Exam (one exam per trimester)

In each of the two trimesters, a Re-Take Exam will be scheduled.

In both trimesters, the Re-Take Exam is for all those students who have taken part in at least a half of the continuous assessment activities, have taken part in the Final Exam, and have got a grade less than 5 points over 10 as the trimestral weighted grade.

In the second trimester, moreover, only those students can sit for the Re-Take Exam who have obtained an average grade over both trimesters which is less than 5 points.

The Re-Take Exam will consist of a global exam over all topics covered in the corresponding trimester.

Continuos Assessment grades cannot be improved in a Re-Take Exam.

If a student sits for a Re-Take Exam, the Trimestral Weighted Grade is calculated as a weighted average of the Continuous Assessment Grade (40%) and the Re-Take Grade (60%), given that the Re-Take Exam grade is not less than 3.5 points over 10. Otherwise, the Weighted Trimester Grade remains as it has been before the Re-Take Exam.

Grades of course repeaters

Course repeaters who followed continuous assessment during the previous academic course and who got a final grade of Failed (not those who were graded as Not Shown Up) may be examined (in each of the two trimesters) through two control tests valid 15% each, and a Final Exam valid 70%. A minimum grade of 3.5 points over 10 is required in the Final Exam.

Those students who are interested in taking this assessment itinerary should contact the course instructor before the first seminar control is carried out.

Bibliography and information resources

QA276.18 .N49 2007

Paul Newbold, William L. Carlson, and Betty M. Thorne. Statistics for Business and Economics, Pearson 2019, 9th ed. ISBN 9781292315201 (any edition of the book beginning from the 4th edn. may be used).

QA276.12 .M665 2004
Moore, David S. The Basic Practice of Statistics, W.H. Freeman, New York [N.Y.], 2004, 3rd ed.