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Unformatted text preview: MIE360: System Modeling and Simulation Lecture Notes Daniel Frances© 2010 1 Lecture 9 – Are the Actuals significantly different than the Simulated Data Observation Actual Simulated 1 3.5 4.1 2 4.2 1.7 3 3.2 2.3 4 5.1 1.9 5 2.8 0.5 Normally it can be assumed that these two sets of data are independent, as the sequence of the runs was entirely random (generated from different seeds) The approach is then to develop a confidence interval for the difference of the means, referred to as a Modified 2samplet” or “Welsh’s” Confidence Interval. Let’s refer to X as the Real data and Y as the simulated data. Let’s assume for now that 5 is large enough for the CLT (to be revised later) Then the average of the Actuals is normally distributed with mean X = 3.76 and x S = 0.907/ √ 5=0.41 Similarly the average of the Simulated results is normally distributed with Y = 2.1 and Y S =0.58 Theorem: Any linear combination a 1 X 1 + a 2 X 2 + … + a n X n of independently and normally distributed...
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 Fall '10
 D.Frances
 Normal Distribution, Standard Deviation, Probability theory, System Modeling and Simulation, Daniel Frances©

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