Description
The purpose of the the course “Probability Theory & Statistics” is to provide the students with the essential knowledge, skills and techniques of probability and statistics which may be of great importance in selected problems in the field of computer science.
Content
The outline of the course is as follows:
Basic Concepts: Random Experiments, Events Space – Sample Space, Discrete – Continuous Sample Spaces, Operations of events, Classical definition of Probability – Frequencies – Axioms of Probability and consequences, Preliminary results.
Discrete Probability and Combinatorics: Finite Sample spaces, equiprobable events, Basic Combinatorial techniques, Counting and Probability.
Conditional Probability: Tree Diagrams, Conditional Probability, A priori probability, A posteriori probability, Law of Total Probability, Chain Rule, Bayes Theorem, Stochastic Independence, Applications.
Random Variables: Definition of Random variables, Examples of Random variables, Discrete – Continuous variables, Probability (Density) Function, Cumulative Distribution Function, Expected Value and Variance.
Common discrete distributions: Bernoulli, Binomial, Geometric, Hypergeometric, Negative Binomial, Poisson
Common coninuous distributions: Uniform, Exponential, Normal (Gaussian).
Applied Statistics on PSPP (Laboratory): Descriptive Statistics, Frequency tables, Statictics, Graphs, Statistical Hypothesis Testing of Mean Values, Crosstabs, Independence – Homogeneity Tests, Linear Correlation Coefficients, Linear Regression.
Structure
The course is structured as follows:
Teaching: 3hrs/week theory
2hrs/week lab exercise
Total workload per semester (13 weeks):
Lectures (theory): 3 x 13 = 39 hrs
Lectures (lab): 2 x 13 = 26 hrs
Home exercises: 2 x 13 = 26 hrs
Homework (study): 18 x 4.5 = 81 hrs
Collaboration/Communication: 8 hrs
Total: 180 hrs
Evaluation
I. The theoretic part of the final exam (weight 60%) is comprised of 4-5 problems involving the following topics:
Event space determination, operations with events and computation of probabilities.
Application of combinatorics for the computation of probability on discrete finite event spaces.
Conditional probability – Independence and related results
Experiment modeling using random variables.
Application of common random variable distributions.
II. Laboratory practice (40%)
Lab exercises are presented, solved and evaluated on a weekly basis.
The final exam of the laboratory part, involves 3-4 statistical problems posed on a given dataset which in turn are solved by the students using the software package PSPP.
The above evaluation scheme is announced to the students (a) through the course’s homepage, (b) during the first lectures in the class (theory and lab).
Oral Exams
The purpose of the the course “Probability Theory & Statistics” is to provide the students with the essential knowledge, skills and techniques of probability and statistics which may be of great importance in selected problems in the field of computer science. With the completion of the course the student should be able to:
Recognize the difference between stochastic and deterministic models.
Describe all the possible outcomes and sample space of stochastic experiment.
Recognize the difference between discrete and continuous sample spaces.
Understand and apply the axioms of probability theory and the basic techniques regarding the events of the sample space.
Calculate the probability of events in discrete, finite event spaces, using combinatorial enumeration techniques.
Apply tree diagrams for the analysis of successive experiments.
Evaluate and explain the significance of conditional probability.
Recognize the difference between “a priori” and “a posteriori” probabilities.
Evaluate and explain the concept stochastic independence
Understand and apply the theorem of Bayes, Law of Total Probability and the Chain rule.
Understand and describe the concept of random variable. Distinguish between probability and cumulative distribution function.
Calculate characteristic values (expectation, variance) of given random variables
Recognize and evaluate the role of known distributions in theoretical and practical level.
Apply the correct known distributions in a given practical problem.
Calculate probabilities using known distributions.
Understand and recognized basic concepts of statistics (population – sample, parameter – statistic)
Create data sheets in the statistical software package PSPP.
Understand and apply basic techniques of descriptive statistics in PSPP (frequency tables, statistics, graphs)
Recognize different types of statistical tests and apply the corresponding procedure in PSPP.
Understand the notion of linear linear correlation and apply the procedure of the determination of a linear regression model. Furthermore, the student should be able to evaluate the significance of the model and variables involved.
Recognize the type of statistical analysis to be applied given a particular dataset, according to the nature of the variables involved.
Papoulis A., S. Unnikrishna Pillai, Πιθανότητες Τυχαίες Μεταβλητές & Στοχαστικές Διαδικασίες, Εκδόσεις Τζιόλα, 4η έκδοση, 2007, ISBN 978-960-418-127-8.
Dekking F.M., Kraaikamp, C., Lopuhaa, H.P., Meeseter, L.E., A Modern Indroduction to Probability and Statistics, Understanding Why and How, Springer Verlang, 2005
Kinney J. John, Probability, An Introduction with Statistical Applications, John Wiley, 1997
Montgomery Douglas C., Runger George C., Applied Statistics and Probability for Engineers, John Wiley & Sons Inc, 2002.
Papoulis A. and S.Unnikrishna Pillai, Probability, Random Variables and Stochastic Processes, 4th edition, McGraw Hill, 2002.
Baron M., Probability and Statistics for Computer Scientists, Second Edition, Chapman and Hall/CRC, 2013, ISBN 978-1439875902.
Johnson J.L., Probability and Statistics for Computer Science, Wiley-Interscience, 2003, ISBN 978-0471326724.
