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Answer: Standard error for the first simulation: 3%; Standard error for the second simulation: 2.25%
The standard error is calculated using the formula: $$\text{Standard error} = \frac{\text{Standard deviation}}{\sqrt{n}}$$ **For the first simulation (n = 81):** $$\text{Standard error} = \frac{27}{\sqrt{81}} = \frac{27}{9} = 3\%$$ **For the second simulation (n = 144):** $$\text{Standard error} = \frac{27}{\sqrt{144}} = \frac{27}{12} = 2.25\%$$ Therefore, the standard errors are: - First simulation: 3% - Second simulation: 2.25% This demonstrates that as the number of simulations increases, the standard error decreases, improving the accuracy of the Monte Carlo simulation.
Author: Tanishq Prabhu
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Tim Yang, FRM, is working on building a model using a Monte Carlo simulation. However, he is concerned about the accuracy of the simulation which is measured by its standard error. Tim initially runs a model with 81 simulations and the standard deviation was found to be 27%. He then runs the model with 144 simulations and the standard deviation is still 27%. What are the standard errors for the simulations?
A
Standard error for the first simulation: 0.33%; Standard error for the second simulation: 0.19%
B
Standard error for the first simulation: 27%; Standard error for the second simulation: 27.00%
C
Standard error for the first simulation: 2.25%; Standard error for the second simulation: 3%
D
Standard error for the first simulation: 3%; Standard error for the second simulation: 2.25%
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