# Subject description - BE5B01PRS

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BE5B01PRS Probability and Statistics
Roles:P Extent of teaching:4P+2S
Department:13101 Language of teaching:EN
Guarantors:Helisová K. Completion:Z,ZK
Lecturers:Helisová K. Credits:7
Tutors:Helisová K. Semester:Z

Anotation:

Introduction to the theory of probability, mathematical statistics and computing methods together with their applications of praxis.

Study targets:

The aim is to introduce the students to the theory of probability and mathematical statistics, and show them the computing methods together with their applications of praxis.

Content:

The students are introduce to the theory of probability and mathematical statistics. Random events, conditional probability and random variables are defined, examples of the most common random variables are mentioned, and estimating parameters and hypotheses testing is explained. All the computing methods are shown on practical examples.

Course outlines:

 1 Random events, probability, probability space. 2 Conditional probability, Bayes' theorem, independent events. 3 Random variable - definition, distribution function. 4 Characteristics of random variables. 5 Discrete random variable - examples and usage. 6 Continuous random variable - examples and usage. 7 Independence of random variables, sum of independent random variables. 8 Transformation of random variables. 9 Random vector, covariance and correlation. 10 Central limit theorem. 11 Random sampling and basic statistics. 12 Point estimation, method of maximum likelihood and method of moments, confidence intervals. 13 Confidence intervals and hypotheses testing. 14 Markov chains.

Exercises outline:

 1 Random events, probability, probability space. 2 Conditional probability, Bayes' theorem, independent events. 3 Random variable - definition, distribution function. 4 Characteristics of random variables. 5 Discrete random variable - examples and usage. 6 Continuous random variable - examples and usage. 7 Independence of random variables, sum of independent random variables. 8 Transformation of random variables. 9 Random vector, covariance and correlation. 10 Central limit theorem. 11 Random sampling and basic statistics. 12 Point estimation, method of maximum likelihood and method of moments, confidence intervals. 13 Confidence intervals and hypotheses testing. 14 Markov chains.

Literature:

  Papoulis, A.: Probability and Statistics, Prentice-Hall, 1990.  Stewart W.J.: Probability, Markov Chains, Queues, and Simulation: The Mathematical Basis of Performance Modeling. Princeton University Press 2009.

Requirements:

Basic calculus, namely integrals.

Webpage:

http://math.feld.cvut.cz/helisova/01pstimfe.html

Keywords:

Probability, statistics.

Subject is included into these academic programs:

 Program Branch Role Recommended semester BEECS Common courses P 3 BPEECS_2018 Common courses P 3

 Page updated 24.9.2021 19:52:30, semester: L/2021-2, L/2020-1, Z,L/2022-3, Z/2021-2, Send comments about the content to the Administrators of the Academic Programs Proposal and Realization: I. Halaška (K336), J. Novák (K336)