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Master's Dissertation
DOI
10.11606/D.55.2018.tde-29102018-115306
Document
Author
Full name
Dimas Francisco Rocha
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2018
Supervisor
Committee
Rodriguez, Pablo Martin (President)
Grisi, Rafael de Mattos
Montoya, Mary Luz Rodiño
Ribeiro, Hermano de Souza
Title in Portuguese
Pontos aleatórios na natureza: uma introdução aos processos de Poisson e suas aplicações
Keywords in Portuguese
Distribuição de Poisson
Processos de Poisson
Teoria das probabilidades
Variáveis Aleatórias
Abstract in Portuguese
Neste trabalho é apresentado o processo de Poisson, através de exemplos existentes e identificados na natureza e em situações presentes no cotidiano. A distribuição de Poisson foi desenvolvida pelo matemático Siméon Denis Poisson com o intuito de aplicar a teoria das probabilidades em julgamentos criminais. Atualmente é possível aplicar este conceito em problemas que envolvem de modo geral fenômenos aleatórios de chegadas, desenvolvimento em colônia de bactérias, dentre outros. O processo de Poisson consiste em um modelo probabilístico adequado para um grande número de fenômenos observáveis e é de grande importância no estudo da teoria das filas. Ao longo do texto serão apresentadas e discutidas definições, axiomas e condições a fim de esclarecer e facilitar o entendimento do assunto. Uma série de exemplos são detalhados, demonstrando assim o amplo número de possibilidades de aplicações dessa teoria.
Title in English
Random points in nature: An introduction to Poisson processes and their Applications
Keywords in English
Poisson distribution
Poisson processes
Probability theory
Random variables
Abstract in English
This work the Poisson process was presented and some examples exist and identified in the nature and in situations present in the daily. The Poisson distribution was developed by the mathematician Siméon Denis Poisson in order to apply Probability Theory in criminal trials. At present, it is possible to apply these concep to problems that involve, in general, random phenomena of arrivals, development in colony of bacteria, among others. The Poisson process consists of a suitable probabilistic model for a large number of observable phenomena and is of great importance in the study of queue theory. Throughout the text will be presented and discussed definitions, axioms and conditions in order to clarify and facilitate the understanding of the subject. Some examples that were detailed, thus demonstrating the larger number of possibilities of applications of this theory.
 
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Publishing Date
2018-10-29
 
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