Probability and Statistics B

Garant předmětu:

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

It is a basic course of probability theory and mathematical statistics. The probability theory is build gradually beginning with the classical definition and continuing till the Kolmogorov definition. The notions as random variable, distribution function of random variable and characteristics of random variable are treated and basic limit theorems are stated and proved. On the basis of this theory the basic methods of mathematical statistics such as estimation of distribution parameters and hypothesis testing are explained.

Requirements:

Basic course of Calculus (in the extent of the courses 01MAB3, 01MAB4 held at the FNSPE CTU in Prague).

Syllabus of lectures:

1. Classical definition of probability, statistical definition of probability, conditional probability and Bayes's theorem

2. Random variables, distribution functions, discrete and continuous random variables, independent random variables, characteristics of random variable

3. Law of large numbers, central limit theorem

4. Point estimation, confidence intervals

5. Tests of statistical hypotheses, goodness of fit tests

Syllabus of tutorials:

1. Combinatorial rules, classical and geometric probability

2. Conditioned probability and related theorems

3. Distribution function of random variable, discrete and continuous random variables, transformation of random variables

4. Characteristics of random variables, mainly expectation and variance, central limit theorem

5. Point estimation of parameters

6. Hypothesis testing, goodness-of-fit tests

Study Objective:

Knowledge:

Fundamentals of probability theory and overview of simple statistical methods.

Skills:

Application of probability theory to solution of concrete examples, statistical analysis and processing of real data, testing hypothesis about the sets of real data.

Study materials:

Key references:

[1] H. G. Tucker: An introduction to probability and mathematical statistics. Academic Press, 1963

Recommended references:

[2] J. Shao: Mathematical statistics, Springer, 1999

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• BS Matematické inženýrství - Matematické modelování (elective course)
• BS Matematické inženýrství - Matematická fyzika (elective course)
• BS Matematické inženýrství - Aplikované matematicko-stochastické metody (elective course)
• BS Informatická fyzika (elective course)
• BS Aplikace softwarového inženýrství (elective course)
• BS Aplikovaná informatika (elective course)
• BS jaderné inženýrství B (elective course)
• BS Jaderné inženýrství C (elective course)
• BS Dozimetrie a aplikace ionizujícího záření (elective course)
• BS Experimentální jaderná a částicová fyzika (elective course)
• BS Inženýrství pevných látek (elective course)
• BS Diagnostika materiálů (elective course)
• BS Fyzika a technika termojaderné fúze (elective course)
• BS Fyzikální elektronika (elective course)
• BS Jaderná chemie (elective course)
• Jaderná chemie (elective course)