SimulationPreliminariesSlide 3Slide 4Slide 5ExampleMonte Carlo MethodSlide 8Slide 9SimulationThe Monte Carlo MethodPreliminaries ElementAn item having characteristics or attributes that have logical or numerical values. SystemA set of related elements that may interactTwo types:InternalExternalPreliminariesHow do we study Systems?ModelsA model is an abstraction of a real system that can be used for prediction and control.The purpose of a model is to enable one to determine how one or more changes in variables effect the system.SimulationWhat is simulation?A numerical technique for studying models of systems, typically on a digital computer.What types of models can we simulate? Abstract modelsPhysical modelsEx: Theme Park line – Abstract Solar System - PhysicalSimulationWhere does simulation exist?ArmyNavyAir ForceWackadoosRockysDisney QuestAt home!ExampleNuclear Power Plant SimulationMonte Carlo MethodWhat is it?A stochastic technique – uses random numbers and statistical techniquesMethod of using independent random variables (pseudo random numbers) to study the outcomes of a system. Where did it originate?Term “Monte Carlo” was introduced by von Neumann and Ulam during World War II as a code word for the secret work at Los Alamos.The method was named after a city in the Monoco principality, because a roulette, a simple random number generator.Monte Carlo MethodHow does it work?With respects to problem solvingLets attempt to calculate PI by a “hit and miss” integration.Can it be used to solve other problems?Buffon’s Needle Problem:Simply stated: Given a needle and two lines, determine the probability of the needle crossing one of the lines on the page.Monty Halls 3-Door ProblemMonte Carlo MethodCan it be used to solve other problems?Traveling Salesman problemNumerical Integration - Estimating the value of a definite integral or sumKnapsack Problem – Estimating the most valuable subset of items that will fit into a
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