Probability and Statistics

Garant předmětu:

Lecturer:

Tutor:

Supervisor:

Department of Software Engineering

Synopsis:

The course of Probability and Statistics introduces basic theory of probability and statistic theory for bachelor?s students of SOFE. Upon successful completion of this course students will be able to apply introduced theory to their bachelor's thesis and econometric courses, as well as to advanced study of applied statistics, econometrics and time-series theory.

Requirements:

Knowledge of matematical analysis and algebra.

Syllabus of lectures:

1.Probability (definition, probability calculation)

2.Probability of events (union and intersection of events), the conditional probability

3.Random variable and its distribution (distribution function, probability function, density of probability)

4.Characteristics of random variable (expected value, variance, moments, covariance, correlation)

5.Basic distributions of discrete random variable (alternative, binomial, Poisson?s, hypergeometric)

6.Basic distributions of continuous random variable (normal and related distribution, exponential, uniform)

7.Basic terms of mathematical statistics (basic set, random sample, descriptive statistics, the law of large numbers, central limit theorem)

8.Basic statistics of sample (arithmetic mean, sample variance, properties, median, quantiles)

9.Point and interval estimations of parameters for given distributions

10.Tests of statistic hypothesis for given distributions

11.Tests of a good match (2 - test, 2 - test for contingency tables)

12.Regress analysis (basic linear regress model, point and interval estimations of regress parameters)

13.Correlation analysis (sample covariance and correlation, estimation of correlation coefficient)

Syllabus of tutorials:

1.Probability (definition, probability calculation) - examples

2.Probability of events (union and intersection of events), the conditional probability - examples

3.Random variable and its distribution (distribution function, probability function, density of probability) - examples

4.Characteristics of random variable (expected value, variance, moments, covariance, correlation) - examples

5.Basic distributions of discrete random variable (alternative, binomial, Poisson?s, hypergeometric) - examples

6.Basic distributions of continuous random variable (normal and related distribution, exponential, uniform) - examples

7.Basic terms of mathematical statistics (basic set, random sample, descriptive statistics, the law of large numbers, central limit theorem) - examples

8.Basic statistics of sample (arithmetic mean, sample variance, properties, median, quantiles) - examples

9.Point and interval estimations of parameters for given distributions - examples

10.Tests of statistic hypothesis for given distributions - examples

11.Tests of a good match (chi-2 - test, chi-2 - test for contingency tables) - examples

12.Regress analysis (basic linear regress model, point and interval estimations of regress parameters) - examples

13.Correlation analysis (sample covariance and correlation, estimation of correlation coefficient) - examples

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:

Key references:

1. Jarušková, D.: Pravděpodobnost a matematická statistika, Stavební fakulta ČVUT, 2006

2. Jarušková, D.: Pravděpodobnost a matematická statistika - příklady, Stavební fakulta ČVUT, 2006

Recommended references:

3. Kožíšek, J.: Statistická analýza, Stavební fakulta ČVUT, 1996

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• BS Aplikace softwarového inženýrství (compulsory course of the specialization)