Probability and Statistics
Code  Completion  Credits  Range  Language 

18PST  Z,ZK  5  3+1  Czech 
 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 timeseries 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 (&#61539;2  test, &#61539;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 (chi2  test, chi2  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 timetable 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)