Analysis of Experimental Data 1
- Department of Materials
The course gives an overwiew of the probability theory with respect to applications in technical sciences.
- Syllabus of lectures:
1.Random events and operations with events.
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, log-normal, 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:
Fundamentals of the probability theory.
To solve problems in the field od probability.
- Study materials:
 BENAROYA,H. - HAN,S.M.: Probability Models in Engineering and Science. Taylor & Francis, 2005.
 LEON-GARCIA,A.: Probability and Random Processes for Electrical Engineering. Addison-Wesley, Reading, Mass., 1994.
 HINES,W.V. - MONTGOMERY,D.C.: Probability and Statistics in Engineering and Management Science. John Wiley & Sons, New York, 1980.
- Further information:
- No time-table has been prepared for this course
- The course is a part of the following study plans:
- Diagnostika materálů (compulsory course of the specialization)