In this thesis our goal is to study pseudorandom numbers. We will investigate how to produce pseudorandom samples from the uniform distribution with a method called the linear congruential method. Another method we will look at is the inverse sampling method which gives us the possibility to generate samples from other distributions that are not the uniform distribution. When generating pseudorandom samples quality is an important aspect, therefore we are going to take a look at a discrepancy which is a tool to determine quality of uniformly distributed samples. We implement the methods in Python and perform numerical experiments to test some quality aspects of the output.