Academic year 2015-16
Probability and Stochastic Processes
| Degree: | Code: | Type: |
| Bachelor's Degree in Computer Science | 21408 | Core subject, 2nd year |
| Bachelor's Degree in Telematics Engineering | 21719 | Core subject, 2nd year |
| Bachelor's Degree in Audiovisual Systems Engineering | 21597 | Core subject, 2nd year |
| ECTS credits: | 8 | Workload: | 200 hours | Trimester: | 1st and 2nd |
| Department: | Dept. of Information and Communication Technologies |
| Coordinator: | Xavier Binefa |
| Teaching staff: | Xavier Binefa, Ruben Moreno, Àngel Garcia Cerdaña, Silvana Silva, Petroula Laiou, Murat Demitas.
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| Language: | Catalan, English |
| Timetable: | |
| Building: | Communication campus - Poblenou |
The subject of probability and stochastic processes is one of the mathematical basis for courses in engineering who graduate studies in Computer Engineering, Audiovisual Systems Engineering and Telematics Engineering. He taught in the first and second quarters of the second year, and it requires the use of many mathematical methods acquired in the previous subjects, in particular, mathematical analysis and linear algebra.
The course has two distinct parts. In the first part of the course, some of the fundamentals of probability theory are introduced going into a computer simulation of random variables, stochastic processes and queuing theory. These concepts form the mathematical basis of statistics. In the second part of the course, we focus on statistical inference -comprising both parametric estimation and hypothesis tests- and analysis of variance. This subject can successfully attack both modeling loads in servers and computer networks as well as transmission and signal analysis.
The acquired mathematical knowledge is essential to other parts of the career. In this sense, other subjects need this knowledge basis as artificial intelligence, signal processing, computational linguistics, audio, computer vision, and all those who in one way or another use pattern recognition techniques.
It requires the use of many mathematical methods acquired in the subjects first, in particular mathematical analysis and linear algebra.
Competences to achieve in the subject
A. General
A1. scientific
A1.1 Analysis
1. Interpreting the results of mathematical problems and learn to contextualize within the general framework of a theory.
2. Relate concepts and mathematical results.
A1.2 Understanding
3. Understand mathematical language.
4. Understand the statements of mathematical problems
A2. technological
5. Know how to apply theoretical knowledge to practical problems.
A3 Communication
6. Exhibition of mathematical ideas and results of mathematical problems concisely.
A4. Self-learning Development
7. Knowing how to find and analyze information from different sources.
A5. interpersonal
8. Know discuss and analyze issues in computer and mathematical concepts in order to understand in depth.
A6. specific skills
9. Know and understand the concepts of probability, statistics and stochastic processes.
In the course will be assessed each of the two parties. The grade for the course will be the average of the ratings for the parties if these are all greater than or equal to four out of ten. The subject is passed if the average is greater or equal to five.
For each part
there will be the possibility of continuous evaluation based on controls (15 minutes every two weeks, in sessions of seminars and Issues, and Practices (to be held in one of the seminar sessions). If the controls average is approved and practices with a score equal to or greater than 5 means that you have the right to continuous assessment. This right remains until the end of July.
For each part there will be an examination of the contents of the part.
Controls and practices are not recoverable in the month of July.
The note of the part may be obtained depending on whether it has a right to continuous assessment.
Entitled to continuous assessment: Conduct a Review of the content of the part and if you have a grade equal to or greater than 4 in the exam, the note of the part will be:
A = Maxim (Examination, 0.6*Examination + 0.3*controls+ 0.1 * Practice ).
In the examination of the first quarter and in July there will be an optional question on the novel Report (see bibliography)
No right to continuous assessment: It will consist of a review of all share. It is necessary that this note is equal to five to make the average with the notes of the other parties. The note will be the note will get the part.
If any part is suspended, the student may examine in the month of July the share.
Skills assessment
Assessment of general skills:
Scientific, communication and development of self-learning are assessed throughout the course by practical controls and the final exam.
Interpersonal: the seminars are evaluated by solving problems in groups.
Evaluation of specific skills:
They are assessed throughout the course using the controls, and practice exams.
Part 1: Probability and random variables Content
1) Introduction to Probability
2) Conditional probability
3) Random variables and distributions; discrete, continuous, multiple, conditional
4) Mathematical expectation, variance, and sample Mean; Law of large numbers, Covariance and correlation, conditional expectance
5) Special Distributions, central limit theorem
6) Computer simulation of random variables
7) Queuing Theory and Stochastic Processes
Part 2: Statistical Inference
8) Introduction to statistical inference
9) Parametric inference
10) HypothesisTest
11) Linear Regression and ANOVA
12) Bayesian Estimation
In the lectures the basic concepts of the subject will be presented and illustrated with many examples. The programming section contents a weekly schedule of topics to be discussed at each session.
The seminars are intended for discussion and deepening of the concepts introduced in the lectures by means of examples and problems. Students have two hours to work and discuss with the teacher a list of proposed problems.
In the classes of problems, them will be solved and discussed, and some of which the students have previously made. It will detail in time, what the problems are to be prepared and worked out every week to do the class profitable. Most of the blocks are constituted by a session of theory and seminars or problems.
The course also includes practical sessions (for example, in the first part there will be one, two hours, on simulation of statistical distributions and the central limit theorem).
The teaching subject material will be published weekly during the course. This material consists of the slides class, a collection of problems and practice scripts.
Primary texts of the course are:
Two texts most recommended are:
A detective novel in which the key characters of statistics appears (and its pitfalls):
Charles M. Cuadras Report: una narració científica. Edicions EUV, 2003
Over the course of the teaching material available in the global classroom.