# Statistics and Probability

##### 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.
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.
Literature
 M. Navara: Pravděpodobnost a matematická statistika. ČVUT, Praha 2007.
 V. Dupač, M. Hušková: Pravděpodobnost a matematická statistika. Karolinum, Praha 1999.
Requirements
Basic calculus, namely integrals.
Responsible for the data validity: Study Information System (KOS)