# Subject description - B0B01PST

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 B0B01PST Probability and Statistics Extent of teaching: 4P+2S Guarantors: Navara M. Roles: P Language ofteaching: Teachers: Navara M. Completion: Z,ZK Responsible Department: 13101 Credits: 7 Semester: Z,L

Anotation:

Basics of probability theory and mathematical statistics. Includes descriptions of probability, random variables and their distributions, characteristics and operations with random variables. Basics of mathematical statistics: Point and interval estimates, methods of parameters estimation and hypotheses testing, least squares method. Basic notions and results of the theory of Markov chains.

Study targets:

Basics of probability theory and their application in statistical estimates and tests. The use of Markov chains in modeling.

Course outlines:

 1 Basic notions of probability theory. Kolmogorov model of probability. Independence, conditional probability, Bayes formula. 2 Random variables and their description. Random vector. Probability distribution function. 3 Quantile function. Mixture of random variables. 4 Characteristics of random variables and their properties. Operations with random variables. Basic types of distributions. 5 Characteristics of random vectors. Covariance, correlation. Chebyshev inequality. Law of large numbers. Central limit theorem. 6 Basic notions of statistics. Sample mean, sample variance. Interval estimates of mean and variance. 7 Method of moments, method of maximum likelihood. EM algorithm. 8 Hypotheses testing. Tests of mean and variance. 9 Goodness-of-fit tests. 10 Tests of correlation, non-parametic tests. 11 Discrete random processes. Stationary processes. Markov chains. 12 Classification of states of Markov chains. 13 Asymptotic properties of Markov chains. Overview of applications.

Exercises outline:

 1 Elementary probability. 2 Kolmogorov model of probability. Independence, conditional probability, Bayes formula. 3 Mixture of random variables. 4 Mean. Unary operations with random variables. 5 Dispersion (variance). Random vector, joint distribution. Binary operations with random variables. 6 Sample mean, sample variance. Chebyshev inequality. Central limit theorem. 7 Interval estimates of mean and variance. 8 Method of moments, method of maximum likelihood. 9 Hypotheses testing. Goodness-of-fit tests. 10 Tests of correlation. Non-parametic tests. 11 Discrete random processes. Stationary processes. Markov chains. 12 Classification of states of Markov chains. 13 Asymptotic properties of Markov chains.

Literature:

  Wasserman, L.: All of Statistics: A Concise Course in Statistical Inference. Springer Texts in Statistics, Corr. 2nd printing, 2004.  Papoulis, A., Pillai, S.U.: Probability, Random Variables, and Stochastic Processes. McGraw-Hill, Boston, USA, 4th edition, 2002.  Mood, A.M., Graybill, F.A., Boes, D.C.: Introduction to the Theory of Statistics. 3rd ed., McGraw-Hill, 1974.

Requirements:

Linear Algebra, Calculus, Discrete Mathematics

Note:

 A necessary condition for the assignment is active participation at seminars, successful test, and one homework. More info: http://cmp.felk.cvut.cz/~navara/stat/

Webpage:

http://cmp.felk.cvut.cz/~navara/stat/

Keywords:

probability theory, statistical estimate, hypotheses testing, Markov chain

Subject is included into these academic programs:

 Program Branch Role Recommended semester BPOI_BO_2018 Common courses P 3 BPOI4_2018 Computer Games and Graphics P 3 BPOI3_2018 Software P 3 BPOI2_2018 Internet things P 3 BPOI1_2018 Artificial Intelligence and Computer Science P 3 BPOI1_2016 Computer and Information Science P 3 BPOI_BO_2016 Common courses P 3 BPOI4_2016 Computer Games and Graphics P 3 BPOI3_2016 Software P 3 BPOI2_2016 Internet things P 3 BPKYR_2016 Common courses P 4

 Page updated 6.12.2019 17:52:32, semester: Z,L/2020-1, L/2018-9, 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)