Introduction to Probability 1

Course guarantor:

Jiří Franc

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

1.Random trial with finite set of possible results, classical probability, independent random events

2.Probability and combinatorics

3.Probability and geometry, Bertrands paradox

4.Conditional probability, Bayes theorem, medical diagnosis, Simpsons paradox

5.Random variable with discrete state space, its distribution and mean value

6.Problems involving the calculation of mean value

7.Probabilistic method in graph theory

8.Random algorithms, Morris algorithm and its variants

Requirements:

Syllabus of lectures:

1.Random trial with finite set of possible results, classical probability, independent random events

2.Probability and combinatorics

3.Probability and geometry, Bertrands paradox

4.Conditional probability, Bayes theorem, medical diagnosis, Simpsons paradox

5.Random variable with discrete state space, its distribution and mean value

6.Problems involving the calculation of mean value

7.Probabilistic method in graph theory

8.Random algorithms, Morris algorithm and its variants

Syllabus of tutorials:

Study Objective:

Study materials:

Key references:

[1] M. Aigner, G. M. Ziegler: Proofs from the book, Springer, 2018

[2] N. Alon, J. H. Spencer: The probabilistic method, Wiley-Interscience, 4. vydání, 2016

Recommended references:

[3] J. Bewersdorff : Luck, Logic, and White Lies: The Mathematics of Games, CRC Press, 2005

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: