# Subject description - B0B01PST

Summary of Study |
Summary of Branches |
All Subject Groups |
All Subjects |
List of Roles |
Explanatory Notes
Instructions

B0B01PST | Probability and Statistics | Extent of teaching: | 4P+2S | ||
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Guarantors: | Navara M. | Roles: | P | Language of teaching: | |

Teachers: | Navara M. | Completion: | Z,ZK | ||

Responsible Department: | 13101 | Credits: | 7 | Semester: | Z,L |

**Anotation:**

**Study targets:**

**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:**

**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:**

**Keywords:**

**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) |