# Statistics and Probability

This is a grouped Moodle course. It consists of several separate courses that share learning materials, assignments, tests etc. Below you can see information about the individual courses that make up this Moodle course.
##### Statistics and Probability (Main course) B6B01PST
 Credits 4 Semesters Summer Completion Assessment + Examination Language of teaching undefined Extent of teaching 2P+2S+1D
Annotation
The students will be introduced to the theory of probability and mathematical statistics, namely to the basic computing methods and their applications in practice. The course covers the basic parts of probability and mathematical statistics. The first part is focused on classical probability, including conditional probability. The next part deals with the theory of random variables and their distributions, examples of the most important types of discrete and continuous distributions, numerical characteristics of random variables, their independence, sums and transformations. Probabilistic knowledge is then used in the description of statistical methods for estimating distribution parameters and testing hypotheses.
Study targets
The students will be introduced to the theory of probability and mathematical statistics, namely to the basic computing methods and their applications in practice.
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 outlines
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
Calculation of basic derivatives and integrals. Basics of combinatorics.
##### Statistics and Probability B0B01STP
 Credits 5 Semesters Summer Completion Assessment + Examination Language of teaching undefined Extent of teaching 2P+2S
Annotation
Cílem předmětu je seznámit studenty se základy teorie pravděpodobnosti a matematické statistiky, jejich výpočetními metodami a aplikacemi těchto matematických nástrojů na praktické příklady.
Course outlines
1. Náhodné jevy, pravděpodobnost, pravděpodobnostní prostor ? definice a základní typy.
2. Podmíněná pravděpodobnost, Bayesova věta, nezávislost jevů.
3. Náhodná veličina - definice, distribuční funkce a její užití.
4. Základní charakteristiky náhodných veličin ? střední hodnota, rozptyl a jiné momenty.
5. Diskrétní náhodná veličina ? definice, popis, příklady diskrétních náhodných veličin.
6. Spojitá náhodná veličina ? definice, popis, příklady spojitých náhodných veličin.
7. Nezávislost náhodných veličin, kovariance a korelace.
8. Rozdělení součtu nezávislých náhodných veličin, konvoluce.
9. Náhodný vektor ? definice, popis, marginální rozdělení, význam ve statistice.
10. Centrální limitní věta - využití pro základní výpočty, význam ve statistice.
11. Základní pojmy ve statistice ? náhodný výběr, výběrový průměr, výběrový rozptyl, kvantil, empirická distribuční funkce, histogram, krabicový graf.
12. Bodové odhady parametrů ? nestrannost, metoda momentů, metoda maximální věrohodnosti.
14. Testování hypotéz ? obecný princip, t-test, test dobré shody, test nezávislosti v kontingenční tabulce.
Literature
[1] Navara, M.: Pravděpodobnost a matematická statistika. ČVUT, Praha 2007.
##### Statistics and Probability B6B01PRA
 Credits 5 Semesters Summer Completion Assessment + Examination Language of teaching undefined Extent of teaching 2P+2S+1D
Annotation
The students will be introduced to the theory of probability and mathematical statistics, namely to the basic computing methods and their applications in practice. The course covers the basic parts of probability and mathematical statistics. The first part is focused on classical probability, including conditional probability. The next part deals with the theory of random variables and their distributions, examples of the most important types of discrete and continuous distributions, numerical characteristics of random variables, their independence, sums and transformations. Probabilistic knowledge is then used in the description of statistical methods for estimating distribution parameters and testing hypotheses.
Study targets
The students will be introduced to the theory of probability and mathematical statistics, namely to the basic computing methods and their applications in practice.
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 outlines
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
Calculation of basic derivatives and integrals. Basics of combinatorics.
Responsible for the data validity: Study Information System (KOS)