MC_transformation - Monte Carlo simulations (MCS) are often...

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about functions of random variables, including mean, distributions, and probability of failure. The distribution of the response of a system can be found for a random input using a Monte Carlo simulation. The response, for example stress, may depend on several random variables, such as force and area. Using MCS to generate a large sample of x values and the corresponding values transfers a histogram of ) ( x r x to a histogram of r . Figure 1 illustrates the transformation of the random input variable, x , into the response, r . Figure 1 – Transformation of distribution of random input, x , with PDF, , to random response, , characterized by PDF, . Histograms show the Monte Carlo approximations. ) ( x f x ) ( x r ) ( r f r The dashed line plots of and are the probability density functions (PDF) of the random input and response, respectively. Random numbers for ) ( x f x ) ( r f r x are generated according to the input’s PDF,
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This note was uploaded on 06/06/2011 for the course EAS 4240 taught by Professor Peterifju during the Spring '08 term at University of Florida.

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MC_transformation - Monte Carlo simulations (MCS) are often...

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