ABSTRACT
Various probabilities Pn and probability densities p(x) were used to illustrate prediction techniques without questioning their particular functional forms and the reasons for using them. There are many methods of choosing probabilities and probability densities. For example, one can use the geometrical relations of events to determine the probabilities with dice. Because an ideal true die is a perfect cube, each of the six sides has an equal chance of appearing. The Dow Jones averages are computed each day, summing the values of some 30 selected stocks that are traded on the New York Stock Exchange and dividing the sum by a number A. A stochastic system for which the average randomness is a maximum subject to the information that is known about the system is called a most random system. The probability that the Gaussian random variable x has values less or equal to w, the distribution functions F(w) of Gaussian stochastic systems, is an often-used quantity.
