Probabilistic Methods and Statistics 510-IS1-2PST-23
Course profile: General Academic
Form of study: Full-time studies
Course type: Obligatory
Field of science: natural sciences,
Discipline of science: mathematics
Year/semester of study: year 2/semester 4
Prerequisites (sequential system of courses and exams): Mathematical Analysis 2, Mathematical Analysis 3, Linear Algebra with Analytic Geometry
Lecture: 30 hours
Exercises classes: 30 hours
Laboratory classes: 15 hours
Teaching methods: delivery method: lecture, searching methods, i.e. problem-based, situational, exchange of ideas, accounting exercises, laboratories, consultations, work with literature, solving homework tasks, discussions in problem groups.
ECTS credits: 5
Balance of student workload:
Class attendance:
- lecture 30 hours
- exercises classes 30 hours
- laboratory classes 15 hours
Course preparation:
- exercises 15 hours
- laboratory classes 10 hours
Literature study: 5 hours
Projects: 15 hours
Preparation for the test: 15 hours.
Preparation for tests, the exams: 8 hours
Exam duration: 4 hours
Individual consultation with the teacher: 4 hours
Student workload:
- student workload related to the activities requiring the teacher's direct participation: 83h, 3.3 ECTS
- student workload that does not require the teacher's direct participation: 68h, 2.7 ECTS
Type of course
Mode
Prerequisites
Mathematical Analysis 2
Mathematical Analysis 3
Discrete Mathematics
Course coordinators
Term 2024: | Term 2025: |
Learning outcomes
The student knows:
1. the fundamental concepts, definitions, and theorems in the theory of probability - KP6_WG2
2. the fundamental concepts of mathematical statistics and methods of statistical inference - KP6_WG2
The student can:
1. use the concept of probabilistic space; is able to build and analyze a mathematical model of a random experiment - KP6_UW3
2. discuss selected random experiments and mathematical models in which typical probability distributions occur and are used - KP6_UW3
3. use the formula for the total probability and Bayes' formula and selected schemes of probability theory - KP6_UW3
4. determine the parameters of the distribution (discrete and continuous); can use limit theorems and laws of large numbers to estimate probabilities - KP6_UW3
5. use statistical characteristics of the population and their sample equivalents - KP6_UW3
6. estimate parameters - KP6_UW3
7. test hypotheses about means, variances, and other parameters - KP6_UW3
8. make simple statistical inferences, also with the use of computer tools - KP6_UW3
9. use computer programs in the field of data analysis - KP6_UW3
The student knows:
1. the limitations of their own knowledge and understands the need for further education - KP6_UU1
Assessment criteria
Final assesment: exam.
Bibliography
1. Borovkov A.A., Probability Theory, Springer 2013.
2. Klenke A., Probability Theory. A Comprehensive Course, Springer 2020.
3. Shao J., Mathematical Statistics: Exercises and Solutions, Springer 2005.
4. Shao J., Mathematical Statistics, Springer Texts in Statistics, Springer 2003.
Additional information
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: