CTU FEE Moodle
Statistics and Probability
B232 - Summer 23/24
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 - B6B01PST
Main course
| 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.
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.
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.
[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
No data.
Study targets
No data.
Course outlines
No data.
Exercises outlines
No data.
Literature
No data.
Requirements
No data.
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.
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.
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.
[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.