Distributions of Random Variables

Abstract

Two different categories of random variables are commonly used in engineering and scientific applications of probability and statistics: discrete and continuous random variables. Every random variable can be described by distribution function and corresponding probability density function. Commonly used distribution functions are defined by a limited number of parameters. Similarly as in the case of sample characteristics, distribution parameters, summarized in Appendix 1, are used to characterise the location, dispersion, asymmetry and peakedness of a distribution. So called standardized random variables, having the means equal to zero and variances equal to 1, are often applied in numerical methods used to analyse the random properties of engineering and scientific systems.