CTU FEE Moodle
Probability and Statistics
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.
Probability and Statistics - BD6B01PST
Main course
| Credits | 4 |
| Semesters | Summer |
| Completion | Assessment + Examination |
| Language of teaching | undefined |
| Extent of teaching | 14KP+6KC |
Annotation
No data.
Study targets
No data.
Course outlines
No data.
Exercises outlines
No data.
Literature
No data.
Requirements
No data.
Statistics and Probability - BD5B01STP
| Credits | 6 |
| Semesters | Summer |
| Completion | Assessment + Examination |
| Language of teaching | undefined |
| Extent of teaching | 14KP+6KC |
Annotation
The aim is to introduce the students to the theory of probability and mathematical statistics, and show them the computing methods together with their applications of praxis.
Study targets
Introduction to the theory of probability and mathematical statistics, and show them the computing methods together with their applications of praxis.
Course outlines
1. Random events, probability, probability space.
2. Conditional probability, Bayes' theorem, independent events.
3. Random variable - definition, distribution function.
4. Characteristics of random variables.
5. Discrete random variable - examples and usage.
6. Continuous random variable - examples and usage.
7. Independence of random variables, sum of independent random variables.
8. Transformation of random variables.
9. Random vector, covariance and correlation.
10. Central limit theorem.
11. Random sampling and basic statistics.
12. Point estimation, method of maximum likelihood and method of moments, confidence intervals.
13. Confidence intervals.
14. Hypotheses testing.
2. Conditional probability, Bayes' theorem, independent events.
3. Random variable - definition, distribution function.
4. Characteristics of random variables.
5. Discrete random variable - examples and usage.
6. Continuous random variable - examples and usage.
7. Independence of random variables, sum of independent random variables.
8. Transformation of random variables.
9. Random vector, covariance and correlation.
10. Central limit theorem.
11. Random sampling and basic statistics.
12. Point estimation, method of maximum likelihood and method of moments, confidence intervals.
13. Confidence intervals.
14. Hypotheses testing.
Exercises outlines
1. Random events, probability, probability space.
2. Conditional probability, Bayes' theorem, independent events.
3. Random variable - definition, distribution function.
4. Characteristics of random variables.
5. Discrete random variable - examples and usage.
6. Continuous random variable - examples and usage.
7. Independence of random variables, sum of independent random variables.
8. Transformation of random variables.
9. Random vector, covariance and correlation.
10. Central limit theorem.
11. Random sampling and basic statistics.
12. Point estimation, method of maximum likelihood and method of moments, confidence intervals.
13. Confidence intervals.
14. Hypotheses testing.
2. Conditional probability, Bayes' theorem, independent events.
3. Random variable - definition, distribution function.
4. Characteristics of random variables.
5. Discrete random variable - examples and usage.
6. Continuous random variable - examples and usage.
7. Independence of random variables, sum of independent random variables.
8. Transformation of random variables.
9. Random vector, covariance and correlation.
10. Central limit theorem.
11. Random sampling and basic statistics.
12. Point estimation, method of maximum likelihood and method of moments, confidence intervals.
13. Confidence intervals.
14. Hypotheses testing.
Literature
[1] M. Navara: Pravděpodobnost a matematická statistika. ČVUT, Praha 2007.
[2] V. Dupač, M. Hušková: Pravděpodobnost a matematická statistika. Karolinum, Praha 1999.
[2] V. Dupač, M. Hušková: Pravděpodobnost a matematická statistika. Karolinum, Praha 1999.
Requirements
Basic calculus, namely integrals.