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Probability

* Exchange students do not have to consider this information when selecting suitable courses for an exchange stay.

Course Unit Code470-2405/01
Number of ECTS Credits Allocated7 ECTS credits
Type of Course Unit *Compulsory
Level of Course Unit *First Cycle
Year of Study *Second Year
Semester when the Course Unit is deliveredWinter Semester
Mode of DeliveryFace-to-face
Language of InstructionCzech
Prerequisites and Co-Requisites Course succeeds to compulsory courses of previous semester
Name of Lecturer(s)Personal IDName
KRA0220Ing. Jan Kracík, Ph.D.
Summary
Probability theory provides a framework for treating uncertainty and is a foundation for mathematical statistics. Students will gain knowledge of fundamental notions of probability theory at a level not requiring knowledge of measure theory.
Learning Outcomes of the Course Unit
Students will understand basic concepts and relations in probability theory needed for mathematical statistics.
Course Contents
Lectures:

Probability space
Conditional probability, independent random events, law of total probability, Bayes' theorem
Conditional independence of random events
Random variable, probability distribution, numerical characteristics
Selected discrete distributions
Selected continuous distributions
Multivariate random variable, probability distribution, numerical characteristics
Independece of random variables, conditional independence
Multivariate normal distribution
Convergence of random variables
Limit theorems
Transformations of random variables, sum of random variables, sampling

Excercises will follow the content of the lectures. During the excercises students will learn basics of R language.



Recommended or Required Reading
Required Reading:
RAO, C. RADHAKRISHNA. Linear statistical inference and its applications. 2. ed., paperback ed. New York: Wiley, 2002. ISBN 0471218758.
ANDĚL, Jiří. Matematická statistika. Praha: SNTL - Nakladatelství technické literatury, 1985.

RAO, C. RADHAKRISHNA. Linear statistical inference and its applications. 2. ed., paperback ed. New York: Wiley, 2002. ISBN 0471218758.
Recommended Reading:
TEETOR, Paul. R cookbook. Sebastopol, CA: O'Reilly, 2011. ISBN 9780596809157
TEETOR, Paul. R cookbook. Sebastopol, CA: O'Reilly, 2011. ISBN 9780596809157


Planned learning activities and teaching methods
Lectures, Tutorials, Project work
Assesment methods and criteria
Task TitleTask TypeMaximum Number of Points
(Act. for Subtasks)
Minimum Number of Points for Task Passing
Credit and ExaminationCredit and Examination100 (100)51
        CreditCredit30 10
        ExaminationExamination70 35