Law of Probability Distribution Function of The Module of Difference of Discrete Random Variables

The use of the absolute value symbol in theoretical studies often leads to difficulties in analytical operations. However, from a practical point of view, transformations based on absolute differences are the most visual and effective. The article discusses functional transformations, which are modules of the differences of discrete random variables. The concept of the first difference modulus is given. The laws of the probability distribution of random variables obtained as the modulus of the difference of two independent random variables that have the same discrete distribution (Bernoulli or geometric), as well as the distribution laws of new random variables that are the sums of the moduli of the first difference, have been found. The main numerical characteristics of new random variables are calculated.