chapter  4
44 Pages

Functions of Random Variables

ByFrank Beichelt

In view of a random measurement error, the true diameter is not known so that one has to work with an estimate for diameter, namely with the random variable. Computers, even scientific calculators, are equipped with software for the generation of random numbers, i.e., a computer can randomly pick numbers from the interval. More exactly, a computer can generate or simulate arbitrarily frequently and independently of each other realizations of a random variable X, which has a uniform distribution in the interval. In the literature, the terminology 'to simulate a sequence of random numbers from a given distribution' is used equivalently to 'simulate a random variable with a given probability distribution'. The generation of random numbers is the basis for computer-aided modelling of complex stochastic systems in industry, economy, military, science, humanity, or other areas in order to determine properties or relevant parameters of these systems.