# Subject description - B6B01PST

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B6B01PST Probability and Statistics
Roles:P Extent of teaching:2P+2S+1D
Department:13101 Language of teaching:
Guarantors:Helisová K. Completion:Z,ZK
Lecturers:Helisová K. Credits:4
Tutors:Helisová K. Semester:L

Anotation:

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.

Study targets:

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

Content:

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.

Course outlines:

 1 Random events, probability, probability space. 2 Conditional probability, Bayes' theorem, independent events. 3 Random variable - definition, distribution function, density. 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. 13 Confidence intervals. 14 Hypotheses testing.

Exercises outline:

 1 Random events, probability, probability space. 2 Conditional probability, Bayes' theorem, independent events. 3 Random variable - definition, distribution function, density. 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. 13 Confidence intervals. 14 Hypotheses testing.

Literature:

 [1] Papoulis, A.: Probability and Statistics, Prentice-Hall, 1990. [2] Stewart W.J.: Probability, Markov Chains, Queues, and Simulation: The Mathematical Basis of Performance Modeling. Princeton University Press 2009.

Requirements:

Calculation of basic derivatives and integrals.

Webpage:

http://math.feld.cvut.cz/helisova/01pstA7B01PST.html

Keywords:

Probability, statistics.

Subject is included into these academic programs:

 Program Branch Role Recommended semester BPSIT Common courses P 4

 Page updated 25.5.2020 05:52:04, semester: Z,L/2020-1, Z,L/2019-20, Send comments about the content to the Administrators of the Academic Programs Proposal and Realization: I. Halaška (K336), J. Novák (K336)