Generació de nombres aleatoris i les seves aplicacions

Abstract

[en] In this project, as its name indicates, we will study the generation of random numbers by doing tests to verify its validity and by seeing its applications. Firstly, in the first chapter we will introduce the topic where, for example, we will define how the random sequences work. In the second chapter we will start by explaining the generators of linear congruence, multiplicative congruence and different important concepts, then to study thoroughly the generation of the uniform distribution. To continue with, we will study the most used examples: minimum standard, RANDU and the method of shuffling; we will implement them in C language and finally we will discuss other important methods. In the third chapter we will study the most common statistical tests used to detect whether a succession is of independent random variables with uniform distribution: the test $x^{2}$ and the test of Kolmogorov – Smirnov. Then, in the fourth and fifth chapter, we will see the different applications of the generation of random numbers. After that, we will examine the Monte Carlo method through a simple example and we will apply this method to the calculation of integrals. Following on, we will see two different methods in order to reduce the variance since it is a way to reduce the estimation error of this method. To conclude, we will apply the generation of random numbers in simulation techniques to handle queues. In order to study these simulation techniques, we will introduce it through a simple example of the management of a single queue and we will also define the concepts of event and agenda. In this way, we will be able to apply these techniques in more complex applications which are also more useful in real life.