Probability and Mathematical Statistics
Code  Completion  Credits  Range  Language 

F7ABBPMS  Z,ZK  4  2P+2C  English 
 Vztahy:
 The course F7ABBPMS can be graded only after the course F7ABBLAD has been successfully completed.
 Garant předmětu:
 Marek Piorecký
 Lecturer:
 Marek Piorecký, Jan Štrobl
 Tutor:
 Filip Černý, Michaela Mrázková, Marek Piorecký
 Supervisor:
 Department of Biomedical Technology
 Synopsis:

Objectives: to familiarize students with the basic principles of the theory of probability and mathematical statistics.
Prerequisites and entry requirements of the course: Knowledge of mathematics (linear algebra, differential and integral calculus) in the range of F7PBBLAD and F7PBBITP courses taught in the first year of study.
Knowledge, skills, abilities and competencies: The student is acquainted with the probabilistic model, basic definitions of Kolmogorov theory of probability and inductive statistics. The student can apply these definitions to practical problems that arise in other areas of professional work and can explain them sufficiently (e.g. doctors). The student is familiar with the basic methods of inductive statistics and can choose a suitable method for standard statistical problems.
 Requirements:

Testimonial/credit:
1) Getting at least 70 % from the total number of points of 3 small tests during the semester (typical examples are shown at the tutorials).
2) Allowed to be absent 3 times during the semester.
3) Active participation in seminars/tutorials, doing homework.
Exam:
Only students that have got testimonial and who have already passed course F7ABBLAD (prerequisite).
Oral exam  2 open questions on topics / issues from the lectures.
 Syllabus of lectures:

1. Motivational lecture. Determinism and randomness.
2. Random variable and its distribution function.
3. Discrete distributions.
4. Continuous distributions.
5. Random vectors, conditioning and independence.
6. Random vectors, characteristics, functions of random variables.
7. The role of mathematical statistics.
8. Parameter estimation. Point estimation of basic characteristics, interval estimation in normal distribution.
9. Methods for construction of point estimations, method of moments, maximum likelihood method. Introduction to Bayesian statistics.
10. Testing hypotheses in normal distribution (one or two selections).
11. Analysis of variance (one way and two way). Testing hypothesis on type of distribution, normality testing.
12. Nonparametric tests.
13. Evaluation of dependence. Correlation and regression analysis.
14. Principles of experimental design.
 Syllabus of tutorials:

1. Classical and geometric probability.
2. Combinatorial problems.
3. Discrete variables.
4. Continuous variables.
5. Variable with normal distribution.
6. Conditional and marginal distributions.
7. Bayes' theorem.
8. Point estimation parameters.
9. Interval estimation of parameters.
10. Onesample test of hypothesis.
11. Onesample test of hypothesis about the mean value compared with an interval estimate.
12. Twosample paired and unpaired test of hypotheses about the mean value.
13. Nonparametric tests.
14. Chisquared test of hypotheses.
 Study Objective:

The objective is to familiarize students with the basic principles of the theory of probability and mathematical statistics.
 Study materials:

[1] CHATFIELD, Christopher. Statistics for technology: a course in applied statistics. 3rd ed. Boca Raton: Chapman & Hall/CRC, 1998. ISBN 0412253402
[2] Probability and statistics EBook [online]. USA, University of California, 2005 [cit. 20190316] Last update [20140309]. Available at: http://wiki.stat.ucla.edu/socr/index.php/EBook
[3] Vladimír Rogalewicz: Pravděpodobnost a statistika pro inženýry, skriptum FBMI, Nakladatelství ČVUT, Praha, 2007 (in Czech).
 Note:
 Timetable for winter semester 2024/2025:

06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon Tue Wed Thu Fri  Timetable for summer semester 2024/2025:
 Timetable is not available yet
 The course is a part of the following study plans:

 Prospectus  bakalářský (!)
 Biomedical Technology (compulsory course)
 Biomedical Technology (compulsory course)