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.

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.

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.

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%).

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.