Title:  Statistics and Probability 

Code:  MSP 

Ac.Year:  2019/2020 

Sem:  Winter 

Curriculums:  

Language of Instruction:  Czech 

Credits:  6 

Completion:  examination (written) 

Type of instruction:  Hour/sem  Lectures  Seminar Exercises  Laboratory Exercises  Computer Exercises  Other 

Hours:  26  39  0  0  0 

 Exams  Tests  Exercises  Laboratories  Other 

Points:  70  30  0  0  0 



Guarantor:  Žák Libor, Doc. RNDr., Ph.D. (UM OSO) 

Deputy guarantor:  Češka Milan, RNDr., Ph.D. (DITS) 

Lecturer:  Češka Milan, RNDr., Ph.D. (DITS) Žák Libor, Doc. RNDr., Ph.D. (UM OSO) 
Instructor:  Češka Milan, RNDr., Ph.D. (DITS) Žák Libor, Doc. RNDr., Ph.D. (UM OSO) 

Faculty:  Faculty of Mechanical Engineering BUT 

Department:  Department of Mathematics, section of Statistics and Optimalization FME BUT 

Schedule: 

  Learning objectives: 

  Introduction
of further concepts, methods and algorithms of probability theory, descriptive
and mathematical statistics. Development of probability and statistical topics
from previous courses. Formation of a stochastic way of thinking leading to
formulation of mathematical models with emphasis on information fields.  Description: 

  Summary
of elementary concepts from probability theory and mathematical statistics.
Limit theorems and their applications. Parameter estimate methods and their
properties. Scattering analysis including post hoc analysis. Distribution
tests, tests of good compliance, regression analysis, regression model
diagnostics, nonparametric methods, categorical data analysis. Markov
decisionmaking processes and their analysis, randomized algorithms.  Knowledge and skills required for the course: 

  Foundations
of differential and integral calculus.
Foundations
of descriptive statistics, probability theory and mathematical statistics.  Learning outcomes and competencies: 

  Students
will extend their knowledge of probability and statistics, especially in the
following areas:  Parameter
estimates for a specific distribution
 simultaneous
testing of multiple parameters
 hypothesis
testing on distributions
 regression
analysis including regression modeling
 nonparametric
methods
 Markov
processes
 Why is the course taught: 

  The
society development desires also technology and, in particular, information
technology expansion. It is necessary to process information  data in order to
control technology. Nowadays, there is a lot of devices that collect data
automatically. So we have a large amount of data that needs to be processed.
Statistical methods are one of the most important means of processing and
sorting data, including their analysis. This allows us to obtain necessary
information from your data to evaluate and control.  Syllabus of lectures: 

  Summary
of basic theory of probability: axiomatic definition of probability,
conditioned probability,
dependent and independent events, Bayes formula.
 Summary
of discrete and continuous random variables: probability, probability
distribution density, distribution function and their properties, functional
and numerical characteristics of random variable, basic discrete and continuous distributions.
 Discrete
and continuous random vector (distribution functions, characteristics,
multidimensional distribution). Transformation of random variables.
Multidimensional normal distribution.
 Limit
theorems and their use (Markov and Chebyshev Inequalities, Convergence, Law of
Large Numbers, Central Limit Theorem)
 Parameter
estimation. Unbiased and consistent estimates. Method of moments, Maximum
likelihood method, Bayesian approach  parameter estimates.
 Analysis
of variance (simple sorting, ANOVA). Multiple comparison (Scheffy and Tukey
methods).
 Testing
statistical hypotheses on distributions. Goodness of fit tests.
 Regression
analysis. Creating a regression model. Test hypotheses on regression model
parameters. Comparison of regression models. Diagnostics.
 Nonparametric
methods for testing statistical hypotheses.
 Analysis
of categorical data: contingency table, chisquare test, Fisher test.
 Markov
processes with discrete and continuous time and their analysis and
applications.
 Markov
decision processes and their analysis. Hidden Markov Models
 Introduction
to randomized algorithms and their use (Monte Carlo, Las Vegas, applications).
 Syllabus of numerical exercises: 

  Probability
theory repetition: probability, conditioned probability, dependent and
independent events, Bayes formula.
 Random
variables repetition: discrete and continuous random variables, functional and
numerical characteristics of random variable, basic discrete and continuous
distributions.
 Random
vector repetition: functions and numerical characteristics, distribution.
Multidimensional normal distribution.
 Limit
theorems and their use.
 Parameter
estimate: properties, methods
 Analysis
of variance (simple sorting, ANOVA), post hos analysis.
 Testing
statistical hypotheses on distributions. Goodness of fit tests.
 Regression
analysis. Creating a regression model. Test hypotheses on regression model
parameters. Diagnostics.
 Nonparametric
methods for testing statistical hypotheses.
 Analysis
of categorical data: contingency table, chisquare test.
 Markov
processes with discrete and continuous time and their analysis and applications.
 Markov
decision processes and their analysis.
 Introduction
to randomized algorithms
 Fundamental literature: 

  Anděl, Jiří. Základy matematické statistiky. 3., Praha: Matfyzpress, 2011. ISBN 9788073780012.
 Meloun M., Militký J.: Statistické zpracování experimentálních dat, 1994.
 FELLER, W.: An Introduction to Probability Theory and its Applications. J. Wiley, New York 1957. ISBN 990000147X
 Hogg, V.R., McKean J.W. and Craig A.T. Introduction to Mathematical Statistics. Seventh Edition, 2012. Macmillan Publishing Co., INC. New York. ISBN13: 9780321795434 2013
 Zvára K.. Regresní analýza, Academia, Praha, 1989
 D. P. Bertsekas, J. N. Tsitsiklis. Introduction to Probability, Athena, 2008. Scientific
 Controlled instruction: 

  Participation
in lectures in this subject is not controlled
Participation
in the exercises is compulsory. During the semester two abstentions
are tolerated. Replacement of missed lessons is determined by the leading exercises.  Progress assessment: 

  Two tests will be written during the semester  6th and 12th week. The
exact term will be specified by the instructor. The test duration is 45
minutes. The rating of each test is 015 points.
Final written exam  70 points  Exam prerequisites: 

  The
credit will be awarded to the one who meets the attendance conditions and whose
total test scores will reach at least 15 points. The points earned in the
exercise are transferred to the exam.  
