Confidence Limits on Simulation Averages 2.

• Imagine repeating this experiment many (infinity) times, each time taking a sample of size n.

• If we say “67% of all the sample means <m> lie within [some value] of the true mean.”…

• …then [some value] serves as a confidence limit

• According to the Central Limit Theorem, the distribution of observations of the sample mean <m> will follow a gaussian, with

  • mean
  • variance

• Our confidence limit is then

• We can only estimate this using the sample variance

p(<m>)

<m>

= 0.12

(true value)

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