# Subject description - B6B01PST

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

B6B01PST | Statistics and Probability | ||
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Roles: | P | Extent of teaching: | 2P+2S+1D |

Department: | 13101 | Language of teaching: | |

Guarantors: | Helisová K. | Completion: | Z,ZK |

Lecturers: | Helisová K., Staněk J. | Credits: | 4 |

Tutors: | Helisová K., Korbelář M., Staněk J. | Semester: | L |

**Web page:**

**Anotation:**

**Study targets:**

**Content:**

**Course outlines:**

1. | Random events, probability, probability space. | |

2. | Conditional probability, Bayes' theorem, independent events. | |

3. | Random variable - definition, distribution function, probability function, density. | |

4. | Characteristics of random variables - expected value, variance and other moments. | |

5. | Discrete random variable - examples and usage. | |

6. | Continuous random variable - examples and usage. | |

7. | Independence of random variables, covariance, correlation. | |

8. | Transformation of random variables, sum of independent random variables (convolution). | |

9. | Random vector, covariance and correlation. | |

10. | Central limit theorem. | |

11. | Random sampling and basic statistics. | |

12. | Point estimates, maximum likelihood method and method of moments. | |

13. | Confidence intervals. | |

14. | Hypotheses testing. |

**Exercises outline:**

1. | Combinatorics, random events, probability, probability space. | |

2. | Conditional probability, Bayes' theorem, independent events. | |

3. | Random variable - construction and usage of distribution function, probability function and density. | |

4. | Characteristics of random variables - expected value, variance. | |

5. | Discrete random variable - examples and usage. | |

6. | Continuous random variable - examples and usage. | |

7. | Independence of random variables, covariance, correlation. | |

8. | Transformation of random variables, sum of independent random variables (convolution). | |

9. | Random vector, joint and marginal distribution. | |

10. | Central limit theorem. | |

11. | Random sampling and basic statistics, point estimates, maximum likelihood method and method of moments. | |

12. | Confidence intervals. | |

13. | Hypotheses testing. | |

14. | Reserve. |

**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:**

**Keywords:**

**Subject is included into these academic programs:**

Program | Branch | Role | Recommended semester |

BPSIT | Common courses | P | 4 |

Page updated 7.6.2023 17:50:17, semester: L/2022-3, Z/2023-4, Z/2024-5, Send comments about the content to the Administrators of the Academic Programs | Proposal and Realization: I. Halaška (K336), J. Novák (K336) |