Analysis of Experimental Data 1
Code  Completion  Credits  Range 

14AED1  Z,ZK  3  2 
 Lecturer:
 Petr Kopřiva (guarantor)
 Tutor:
 Petr Kopřiva (guarantor)
 Supervisor:
 Department of Materials
 Synopsis:

The course gives an overwiew of the probability theory with respect to applications in technical sciences.
 Requirements:

Calculus, algebra.
 Syllabus of lectures:

1.Random events and operations with events.
2.Probability definitions.
3.Conditional probability, independence of events, probability of union and intersection of events.
4.Total probability theorem, Bayes` theorem.
5.Random variable (distribution function, probability function, density function).
6.Time to failure, reliability function, hazard rate function.
7.Multiple random variables.
8.Functions of random variables.
9.Characteristics of random variables (measures of central tendency, variability, and skewness).
10.Markov inequality, Chebyshev inequality.
11.Characteristics of multivariate random variable (covariance, correlation).
12.Characteristics of linear forms.
13.Moment generating function, characteristic function.
14.Basic models of discrete random variable (alternative, binomial, geometric, hypergeometric, Poisson, multinomial).
15.Continuous random variable, types of parameters.
16.Reduced,standardized, and truncated distributions,probability paper.
17.Basic models of continuous random variable (rectangular, normal, lognormal, exponential, gamma, Weibull, beta, multinomial normal).
18.Limit theorems (laws of large numbers, central limit theorem).
 Syllabus of tutorials:

1. Basic probability calculations.
2. Conditional probability, probability of union and intersection of events.
3. Bayes' theorem.
4. Functions describing distribution od random variables.
5. Characteristics of random variables.
6. Distributions of discrete random variable.
7. Distribution of continuous random variable.
 Study Objective:

Knowledge:
Fundamentals of the probability theory.
Skills:
To solve problems in the field od probability.
 Study materials:

Key references:
[1] BENAROYA,H.  HAN,S.M.: Probability Models in Engineering and Science. Taylor & Francis, 2005.
Recommended references:
[1] LEONGARCIA,A.: Probability and Random Processes for Electrical Engineering. AddisonWesley, Reading, Mass., 1994.
[2] HINES,W.V.  MONTGOMERY,D.C.: Probability and Statistics in Engineering and Management Science. John Wiley & Sons, New York, 1980.
 Note:
 Further information:
 No timetable has been prepared for this course
 The course is a part of the following study plans:

 Diagnostika materálů (compulsory course of the specialization)