Probability Calculus26689
- Centre
- Faculty of Science and Technology
- Degree
- Bachelor's Degree In Mathematics
- Academic course
- 2024/25
- Academic year
- 2
- No. of credits
- 6
- Languages
- Spanish
- Basque
- English
- Code
- 26689
TeachingToggle Navigation
Teaching guideToggle Navigation
Description and Contextualization of the SubjectToggle Navigation
In this course, the basic concepts, techniques and results of Probability Calculus are presented.
To learn this course, it is advisable to have studied or being studying with sufficient benefit, the course of Differential and Integral Calculus II.
This course provides basic concepts and techniques for the course Statistical Inference, which is studied at the third level. In addition, the student acquires an intuitive basis of probability theory, which allows for a rigorous formalization of probability theory in the fourth-grade course called Probability and Stochastic Processes.
Skills/Learning outcomes of the subjectToggle Navigation
SPECIFIC ABILITIES
M03CM01-To know the basic concepts and results of probability calculus and statistics.
M03CM02-To be trained in major probability distributions and usual techniques of statistical inference.
M03CM03-A correct use of terminology related to random phenomena and data analysis.
M03CM04-A correctly modeling of common situations about random phenomena.
M03CM05- To be familiar with the adequate informatic resources for the treatment of the mentioned situations and handle some of them correctly
M03CM06- To select correctly the adequate technique of analysis, depending on the goal that is aimed in the study of such situations
M03CM07-To make accurate calculations and / or graphical expressions necessary to study random phenomena, using theoretical and / or computational resources.
M03CM08-To interprete the results of the analyzes carried out with a critical sense.
RESULTS FROM STUDYING THIS COURSE
To know how to solve problems in probability calculus that can be complex, both in the discrete and continuous case.
Carry out estimations of significant quantities (probabilities, means, etc), when the exact calculation is not possible.
Theoretical and practical contentToggle Navigation
1. PROBABILITY: Random phenomena. Events. Probability-space. Examples. Basic rules of probability calculus. Conditional probability. Independent events.
2. RANDOM VARIABLES: Concept. Probability-distribution. Distribution function. Discrete and continuous variables. Main examples of distributions.
3. RANDOM VECTORS: Concept. Probability-distribution. Main examples. Marginal-distributions. Independence between random variables. Conditional distributions.
4. EXPECTATION: Concept and main properties. Calculation of expectectation of discrete and continuous random variables.
5. MOMENTS: Concept. Probability generating function. Moment generating function. Variance. Covariance. Correlation.
6. LAW OF LARGE NUMBERS: Random variables convergence modes. Strong and weak laws of large numbers. Central limit theorem.
MethodologyToggle Navigation
The theoretical content will be explained in master classes, following the references that have been provided in the Bibliography as well as in the materials to be used. To complete these master classes, there are classroom practices where the students solve problems by means of the obtained knowledge in theoretical classes. In the seminars, exercises and examples that are indicative of the subject will be developed. In general, these exercises and examples will be given to the students in advance so that they can practice them themselves as well as to motivate reflection and discussion in the appropriate session. On the other hand, computer skills will be developed in the subject focused on achieving the abilities of the course.
Assessment systemsToggle Navigation
- Continuous Assessment System
- Final Assessment System
- Tools and qualification percentages:
- See orientations (%): 100
Ordinary Call: Orientations and DisclaimerToggle Navigation
CONTINUOUS EVALUATION GUIDELINES:
In this course, presentations, the resolution of theoretical work and practical exercises, computer laboratory practices and written tests will be evaluated.
More precisely:
Final written exam (75%)
Computer laboratory practices, exercises, partial exams, presentation of works (25%)
Evaluation system:
97%: The maximum of the following two results will be calculated: 1) Written exam (97%) and 2) Written exam (75%, it will be necessary to take at least 5 out of 10 to pass the subject) plus work, presentations and partial exams during the semester (% 22)
3%: Examination of computer practices
Students who do not carried out to the final written exam on the day of the regular call will be assessed as “Not Presented”.
Students who do not wish to participate in the continuous evaluation must formally refuse it by presenting a written statement to the teacher in charge of the subject within a period of nine weeks from the beginning of the semester stating that he/she refuses the continuous evaluation.
FINAL EVALUATION GUIDELINES:
On the day of the regular call, there will be a test that assesses all the abilities developed in the subject and this test will be the 100% of the final note (written exam 97%, examination of computer practices 3%).
Extraordinary Call: Orientations and DisclaimerToggle Navigation
On the day of the extraordinary call, there will be an exam that assesses all the abilities developed in the subject. This test will be evaluated as follows:
97%: The maximum of the following two results will be calculated: 1) Written exam (97%) and 2) Written exam (75%, it will be necessary to take at least 5 out of 10 to pass the subject) plus work, presentations and partial exams during the semester (% 22)
3%: Examination of computer practices
If the average mark of the computer laboratory exam is 4 out of 10 or higher, it is not necessary to take the computer laboratory exam in the non-regular call.
BibliographyToggle Navigation
Basic bibliography
G. GRIMMETT y D. WELSH, Probability: an introduction, Oxford Science Publications.
J. PITMAN, Probability, Springer-Verlag.
S.M. ROSS, A First Course in Probability, Prentice Hall.
Web addresses
R Core Team (2018). R: A language and environment for statistical
computing. R Foundation for Statistical Computing, Vienna, Austria.
URL http://www.R-project.org/
GroupsToggle Navigation
16 Teórico (Spanish - Tarde)Show/hide subpages
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16-16 | 14:00-15:00 (1) | ||||
16-29 | 15:00-16:00 (2) | ||||
16-30 | 16:00-17:00 (3) |
16 Seminar-1 (Spanish - Tarde)Show/hide subpages
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18-28 | 17:00-18:00 (1) |
16 Applied classroom-based groups-1 (Spanish - Tarde)Show/hide subpages
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17-28 | 14:00-15:00 (1) | ||||
17-29 | 17:00-18:00 (2) | ||||
30-30 | 17:00-18:00 (3) | 15:00-16:00 (4) |
16 Applied computer-based groups-1 (Spanish - Tarde)Show/hide subpages
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25-25 | 10:30-11:30 (1) 12:00-13:00 (2) | ||||
26-26 | 12:00-13:00 (3) |
46 Teórico (Basque - Tarde)Show/hide subpages
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16-16 | 15:00-16:00 (1) | ||||
16-17 | 16:00-17:00 (2) | ||||
16-28 | 14:00-15:00 (3) | ||||
17-24 | 17:00-18:00 (4) | ||||
25-29 | 16:00-17:00 (5) | ||||
26-28 | 17:00-18:00 (6) | ||||
30-30 | 16:00-17:00 (7) |
46 Seminar-1 (Basque - Tarde)Show/hide subpages
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18-28 | 16:00-17:00 (1) |
46 Seminar-2 (Basque - Tarde)Show/hide subpages
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18-28 | 15:00-16:00 (1) |
46 Applied classroom-based groups-1 (Basque - Tarde)Show/hide subpages
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17-30 | 15:00-16:00 (1) | ||||
19-23 | 16:00-17:00 (2) | ||||
25-29 | 17:00-18:00 (3) | ||||
30-30 | 17:00-18:00 (4) |
46 Applied computer-based groups-1 (Basque - Tarde)Show/hide subpages
Weeks | Monday | Tuesday | Wednesday | Thursday | Friday |
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25-25 | 10:30-11:30 (1) 12:00-13:00 (2) | ||||
26-26 | 12:00-13:00 (3) |
46 Applied computer-based groups-2 (Basque - Tarde)Show/hide subpages
Weeks | Monday | Tuesday | Wednesday | Thursday | Friday |
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25-25 | 10:30-11:30 (1) 12:00-13:00 (2) | ||||
26-26 | 10:30-11:30 (3) |
66 Teórico (English - Tarde)Show/hide subpages
Weeks | Monday | Tuesday | Wednesday | Thursday | Friday |
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16-16 | 16:00-17:00 (1) | 14:00-15:00 (2) | |||
16-29 | 15:00-16:00 (3) | ||||
17-27 | 16:00-17:00 (4) | ||||
18-26 | 17:00-18:00 (5) | ||||
28-28 | 17:00-18:00 (6) | ||||
29-30 | 16:00-17:00 (7) |
66 Seminar-1 (English - Tarde)Show/hide subpages
Weeks | Monday | Tuesday | Wednesday | Thursday | Friday |
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18-28 | 16:00-17:00 (1) |
66 Applied classroom-based groups-1 (English - Tarde)Show/hide subpages
Weeks | Monday | Tuesday | Wednesday | Thursday | Friday |
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17-28 | 14:00-15:00 (1) | ||||
17-29 | 17:00-18:00 (2) | ||||
30-30 | 17:00-18:00 (3) | 15:00-16:00 (4) |
66 Applied computer-based groups-1 (English - Tarde)Show/hide subpages
Weeks | Monday | Tuesday | Wednesday | Thursday | Friday |
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25-25 | 10:30-11:30 (1) 12:00-13:00 (2) | ||||
26-26 | 12:00-13:00 (3) |