INSTITUTO TECNOLÓGICO DE CERRO AZUL INGENIERÍA INDUSTRIAL (Sistema Abierto)
DOCENTE
LIC. SERGIO MARTÍNEZ ORTIZ
MATERIA
SIMULACIÓN 2da. UNIDAD
GENERACIÓN DE NÚMEROS ALEATORIOS
ESTUDIANTE
ALARADO CASTILLO ROGER ALE!ANDRO A"#$%%&'
1
CONTENIDO INTRODUCCIÓN ................................................................................................... 3 2.1. NÚMEROS ALEATORIOS: DEFINICIÓN, PROPIEDADES, GENERADORES Y TABLAS................................................................................................................ 4 2.2. PROPIEDADES DE LOS NÚMEROS PSEUDOALEATORIOS ................................6 2.3. PRUEBAS ESTADÍSTICAS DE ALEATORIEDAD PARA LOS NÚMEROS PSEUDOALEATORIOS: DE MEDIAS, DE VARIANZA, DE INDEPENDENCIA Y DE BONDAD DE AJUSTE..................................................................................... ....... 7 2.. OBTENCIÓN DE NÚMEROS PSEUDOALEATORIOS UTILIZANDO PA!UETES COMPUTACIONALES.................................................................................... ...... 10 2.". M#TODO DE MONTE CARLO .........................................................................12 CONCLUSIÓN ..................................................................................................... 15 BIBLIOGRAFÍA .................................................................................................... 16
INTRODUCCIÓN
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L* %&)/*&80 ( M$0'(*+$ =*( +(-(+(0&* * eperimentos que involucran el uso de números pseudoaleatorios. )l requisito clave de esta t*cnica es que los resultados de todas las variables de inter*s deben ser seleccionados aleatoriamente.
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
13
CONCLUSIÓ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
BIBLIOGRAF+A
='':KK(%.%&(%=*+(.0('K$+1K0/)(+$%*(*'$+&$%111 =''%:KK(%.%+&9.$)K$K133^KP+$9()*%(S&)/*&$0A/ ='':KK&'*&*./%.(%K*%&70*'/+*%KS&)/*&$0K(?(+&&$%K)$(*$2.=')
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