Subject description - B0B01PST1
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B0B01PST1 | Probability and Statistics | ||
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Roles: | P | Extent of teaching: | 4P+2S |
Department: | 13101 | Language of teaching: | |
Guarantors: | Hájek P. | Completion: | Z,ZK |
Lecturers: | Helisová K. | Credits: | 6 |
Tutors: | Beck D., Helisová K., Lebeda M., Slavenko M. | Semester: | Z |
Web page:
https://math.fel.cvut.cz/en/people/heliskat/01pst2.htmlAnotation:
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:
[1] | Wasserman, L.: All of Statistics: A Concise Course in Statistical Inference. Springer Texts in Statistics, Corr. 2nd printing, 2004. | |
[2] | Papoulis, A., Pillai, S.U.: Probability, Random Variables, and Stochastic Processes. McGraw-Hill, Boston, USA, 4th edition, 2002. | |
[3] | 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 MathematicsNote:
A necessary condition for the assignment is active participation at seminars and a successful test. More info: 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 |
BPKYR_2021 | Common courses | P | 3 |
Page updated 22.7.2024 17:51:39, semester: Z,L/2024-5, Z,L/2023-4, Send comments about the content to the Administrators of the Academic Programs | Proposal and Realization: I. Halaška (K336), J. Novák (K336) |