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Generació de suuccessions aleatòries i aplicacions

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Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2016, Director: Àngel Jorba i Monte

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This work consists to simulate random sequences with computer and see some of its applications. We say simulate because is impossible the sequences to be completely random because computers are deterministic machines that only do, line after line, a set of preset instructions.
In this work will discuss the generation of pseudo-random sequences with computer. The pseudo-random sequences are sequences that qualify as random sequences. The work is divided into three parts. In the first we see methods to generate pseudo-random sequences. The second part consists of pass statistical tests to see what really simulate this randomness. Finally, the third part, we will see two of the many applications that we found interesting.
The generators are linear and multiplicative congruence. Also we talk about what it means to have maximum periods and streaks a sequence of random numbers. The methods we have implemented to generate these numbers are three: the randu, the minimum standard and the shuffling.
The randomness tests to will pass the sequence numbers generated by the above methods are the following statistical tests: χ 2 , the Kolmogorov-Smirnov and test to see streaks. All implemented to check the condition of the inheritance lining the interval [0, 1]. In addition, the χ 2 will see the cube unit [0, 1] 3.
The applications that we have implemented make the calculation of integrals and encryption. We will see with random sequences a very approximate result with the Monte Carlo method and how we can transform text into a uniform sequence.

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Treballs Finals de Grau (TFG) - Matemàtiques

# metadata.dc.title[].value
Generació de suuccessions aleatòries i aplicacions