汕头大学学报（自然科学版）

随机变量函数的分布和概率计算是实践中经常碰到的问题，也是概率论教学中的一个重要知识点；一维随机变量差的绝对值函数在计算机科学、信息科学等学科中也具有广泛应用.本文主要研究均匀分布随机变量差的绝对值函数，得到了连续型的概率密度函数和离散型的分布律，并介绍该函数在图像信息安全领域的一个具体应用，用实例验证理论的相关结果.

The distribution and probability calculation of functions of random variables are frequently encountered problems in practice and constitute an important knowledge point in probability theory education. The absolute value function of the difference of one-dimensional random variables is also widely used in disciplines such as computer science and information science. This paper focuses on studying the absolute value function of the difference of uniformly distributed random variables, obtaining the probability density function for the continuous case and the distribution law for the discrete case. Furthermore, it introduces a specific application of this function in the field of image information security, using practical examples to validate the theoretical findings.