Probability and Statistics

Garant předmětu:

Lecturer:

Tutor:

Supervisor:

Department of Software Engineering

Synopsis:

This one-semester course covers probability of random events in various probability spaces, conditional probability, properties of random variables, distribution function of random variables, mean value, variance and quantile of random variables, fundamental probability distribution of discrete and continuous random variables. Overview of basic statistics methods -confidence intervals, statistical hypothesis, linear regression, contingency table.

Requirements:

Syllabus of lectures:

1.Overview of basic principals of probability

2.Random variables, probability density, probability functions, distribution functions, basic characteristics

3.Discrete and continuous probability distribution, properties and application

4.Specialized statistical probability distribution - Pearson, Student, Fischer

5.Random samples

6.Random sampling from a normal probability distribution

7.Confidence intervals and their construction

8.Hypothesis testing of normal distribution - single sample

9.Hypothesis testing of normal distribution - two samples

10.Hypothesis testing of other distributions. Dependent- and independent-sample t-test. Tests of correlation

11.Theoretical analysis of linear regression, methods of least squares, determination of systems of normal equations. Coefficient estimation.

12.Correlation analysis, co-variance, correlation coefficients, Spearman's coefficient

13.Contingency tables

14.Connectivity and application

Syllabus of tutorials:

Study Objective:

The goal of the study is to gain knowledge of probability and mathematic statistics theory, and also their corect application to real problems.

Study materials:

Cihlář, J., Pelikán, Š.: Pravděpodobnost - cvičení, PF UJEP Ústí n/L 1996, skriptum

Cihlář, J.: Statistika, PF Ústí n/L 1982, skriptum

Cihlář, J., Pelikán, Š.: Statistika - cvičení, PF UJEP Ústí n/L 1987, skriptum

McClave, J. T., Dietrich, F.H.: Statistics, Dellen Publishing Compeny, San Francisco 1988

Hebák, P., Hustopecký, J.: Průvodce moderními statistickými metodami,SNTL Praha 1990

Riečan, B. a kol: Pravděpodobnosť a matematická štatistika, SNTL Praha 1984

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: