In this final work, important concepts from probability and statistics are explained, and various examples are given to help illustrate this mathematical discipline. Random variables are described in more detail, which are divided into discrete and continuous random variables. For both types of random variables, their distributions, density and distribution functions, and basic numerical indicators and their properties are defined. The largest part of the paper is devoted to basic discrete distributions. Despite the large number of different distributions used in statistics, this work describes the most commonly used discrete distributions. As such distributions are considered to be: uniform, Bernoulli, binomial distribution, Poisson distribution, geometric distribution and hypergeometric distribution. For each of these distributions, several examples have been solved to facilitate the understanding and application of a particular distribution. Basic expressions are derived for each distribution and graphs are given that are characteristic of each distribution and very often easier to identify with. This paper also emphasizes the use of software tools such as Excel and Python. These software tools allow you to solve problems related to random variables more accurately and easily. They can be used to clarify problems more easily and quickly, with the ability to create tables and graphs.