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Monte Carlo simulation

Monte Carlo simulation estimates an uncertain outcome by drawing thousands of random samples from assumed probability distributions and studying the resulting distribution of results.

ByHoang TruongUpdated

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Monte Carlo simulation draws thousands of random values from assumed distributions and studies the full range of results. If simulated project profits have a standard deviation of €2,000 across 10,000 trials, the standard error of the simulated mean is €2,000 ÷ √10,000 = €20 — the reported average is precise to roughly plus or minus €20. Running more trials tightens this error, but does nothing to fix a badly specified input distribution.

Where it fits
TopicProbability & DistributionsAdvancedSubjectData Analysis & StatisticsAdvanced

The formula

LaTeX
SE=σnSE = \frac{\sigma}{\sqrt{n}}

Variables

Standard error of the simulated mean ()
Standard deviation of the simulated outcomes ()
Number of simulation trials

Shows how much the simulated average could differ from the true mean, and how it shrinks as more trials are run.

Check yourself

PracticeCORE

A Monte Carlo simulation of a project's possible profit produces outcomes with a standard deviation of €3,000, run over 90,000 trials. What is the approximate standard error of the simulated mean profit?

Select an answer to check your understanding.