Probability and Mathematical Statistics
Code  Completion  Credits  Range  Language 

17ABBPMS  Z,ZK  4  2P+2C  English 
 Grading of the course requires grading of the following courses:
 Linear Algebra and Differential Calculus (17ABBLAD)
 Garant předmětu:
 Marek Piorecký
 Lecturer:
 Marek Piorecký
 Tutor:
 Filip Černý, Marek Piorecký, Jan Štrobl
 Supervisor:
 Department of Biomedical Technology
 Synopsis:

Introduction to probability theory and mathematical statistics. Determinism and chance. Axiomatic definition. Random variable and its distribution function. Discrete and continuous distributions. Quintiles. Random vectors. Conditioning and independence. Functions of random variables. Characteristics of random variables, weak law of large numbers. The role of mathematical statistics, the population and sample. Random selection. Point and interval estimates. Hypothesis testing. Goodness. Nonparametric tests.
 Requirements:

Testimonial:
1) Three small tests during the semester (typical examples), tests together must be passed with at least 75 %.
2) Active participation in seminars, doing homework.
3) Allowed to be absent 3 times during the semester.
Exam:
Only students that have got testimonial and who have already passed the course 17ABBLAD (prerequisity).
Oral exam  decides about the grade (AF).
 Syllabus of lectures:

1. Motivational lecture. Determinism and randomness.
2. Random variable and 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.
9. Testing hypotheses in a normal distribution.
10. Nonparametric tests.
11. Analysis of variance.
12. Principles of experimental design.
 Syllabus of tutorials:

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

The objective is to familiarize students with the basic principles of modern statistics based on the (Kolmogorov) theory of probability.
 Study materials:

1. Chatfield C.: Statistics for Technology, 3rd edition, Chapman and Hall, London, 1992.
2. Rogalewicz V.: Pravděpodobnost a statistika pro inženýry. Skriptum ČVUT, 2. vydání, 2007. (in Czech)
 Note:
 Timetable for winter semester 2022/2023:

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 2022/2023:
 Timetable is not available yet
 The course is a part of the following study plans:

 Biomedical Technician  full time study in English (compulsory course)