Abstract:

In this article, we present an example of creating new random variables and working with standard random variables in Wolfram Mathematica. This program has recently focused on a very wide range of work with mathematical applications. Probability and statistics are one of the areas where there is an ever-widening development. In the following article, how can it be used to create new random variables that are either a matter of theoretical research or have a broader area of application that students use in subjects PAS and KST - subjects of probability theory and application of statistics.

The basic tools are well-prepared procedures Probability, NProbability, TransformedDistribution, EstimatedDistribution and many others. All these means are used and presented directly in lectures and exercises of these subjects. Students find out the relationships between known random variables, create others hitherto unknown to them and use them in specific application tasks. Using classical methods of probability theory, students cannot directly derive some relationships, but the above procedures allow students to find relationships, for example, between the average of chi-square random variables and the random gamma distribution.

Of course, all new knowledge is also displayed graphically, because Wolfram Mathematica has excellent graphical outputs. Examples of such outputs are of course given in the article. To gain new knowledge, it is their display that is very important and illustrative. Using these graphical procedures, we display the densities, probability functions and distribution functions of newly generated random variables.

Keywords:

Normal distribution, distribution derived from the normal distribution, continuous distribution.