Probability and Mathematical Statistics

Grading of the course requires grading of the following courses:

Linear Algebra and Differential Calculus (17ABBLAD)

Lecturer:

Tutor:

Supervisor:

Department of Biomedical Technology

Synopsis:

Introduction into probability theory and mathematical statistics. Classical, geometrical and Kolmogorov definitions of probability. Random variables, their distributions, characteristics, transformations. Population and sample. Parameter estimators. Statistical tests.

Requirements:

Written exam, 6 tasks, at least 50% success

Syllabus of lectures:

1. Motivation. Introduction into probability theory and mathematical statistics. Basic ideas of the mathematical model. Population and sample.

2.Classical, geometrical and Kolmogorov definitions of probability. Random variables.

3.Discrete random variables, their distributions, characteristics.

4.Continuous random variables, their distributions, characteristics.

5. Calculations with random variables.

6. Estimators. Confidence intervals for normal distribution.

7. Testing statistical hypotheses. Tests abot normal distribution parameters. Chi-square test. Non-parametric tests.

Syllabus of tutorials:

1.Classical probability theory. Combinatorial problems (coin throw, dice throw, Loto). Geometrical probability - meeting problem

2.Random phenomenon, conditional probability. Total probability. Bayesian theorem and its applications.

3.Discrete random variable. Probability function, distribution function - evaluation, graphical representation. Some discrete distributions and their characteristics - alternative, binomial. Mean and variance, quantils

4.Continuous random variable. Density, distribution function - evaluation, graphical representation. Mean and variance, quantils. Normal distribution.

5.Random vector, marginal distribution, correlation. Transformations of random variables and vectors.

6.Transformations of random variables and vectors, their distribution, means, variations, quantils - calculation training

7.Mathematical statistics - confidence intervals, testing mathematical hypotheses, t-tests, F-tests, chi-square test. Repetition.

Study Objective:

To learn basics of the mathematical model of random phenomena description. The course has two parts: (i) probability theory, obove all the notion of a random variable and its description; (ii) two basic methods of mathematical statistics - parameter estimators and testing statistical hypotheses.

Study materials:

[1] Chatfield Ch.: Statistics for Technology, 3rd ed., Chapman & Hall, London, 1992

[2] Altman D.G.: Practical Statistics for Medical Research, 2nd ed., Chapman & Hall, London, 1994

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Bakalářský studijní obor Biomedicínský technik v AJ (compulsory course)