- Department of Digital Systems - https://www.ds.unipi.gr/en -

# Probability Theory

### Learning Outcomes

This course attempts to enhance the knowledge gained in the course Probability Theory explain the fundamental concepts and to provide an appropriate mathematical background that enables the students to study the fields of computers and computers networks. The course directly supports most of the curriculum subjects and lessons: Note that during the lesson, specific examples of application are discussed in some of the above curricular subjects such as applications in telecommunication systems, cryptography, digital services such as e- learning, e-health using new technologies with the help of programs such as Matlab, Octave, SPSS, R. After successfully attending this course, students are expected to have acquired the basic ones that are necessary in Information Technology. In conclusion, the students through the course process develop mathematical thinking and analyze, adapt their acquired knowledge to apply them to a variety of subjects in the field of study or the field of study, as well as to acquire new knowledge. In addition, they learn to solve complex or new problems in their scientific field of study by developing integrated as well as creative or innovative solutions and approaches while supporting their solutions and views in a methodical and scientific way. Finally, they learn to analyze and critically and responsibly choose ideas and information about those elements that concern them.

### Course Contents

• Accidental experiment, samples and possibilities.
• Definitions of possibilities.
• Finite samples with results of equal possibilities.
• Provisions, combinations, binomial theorem.
• Committed probability.
• The multiplicative theorem.
• Total probability and Bayes theorem.
• Independent trials.
• Random variables, probability distributions.
• Parameters of distributions, interrelation of distribution accidental variables.
• One-dimensional distributions.
• Continuous distributions.
• Discrete distributions
• Generators of proneness; probabilities generators.
• Two-dimensional distributions.
• Marginal distributions distributions, Average-Committed distributions
• Transformations of random variables-Stochastic independence of two random variables.

• M. Filippakis-T. Papadoggonas, Probability Theory and Business Statistics, Tsotras Publications, Athens 2017, 1rst Edition.
• M. Koutras, Probability Theory and applications, tsotras publications, Athens 2015.
• Durrett R. (2004): Probability: Theory and Examples, 3rd Edition, Duxbury Press.
• Teaching Notes.