Activities

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Activities

• Capture Recapture, Tanks

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Capture Recapture

• I have gone out to a pristine Mn lake and marked
  and released M50 fish.
• Take a SRS of n20 fish and note how many of
  these fish have been previously marked.
• Call this number out of 20, m.
• We denote the unknown number of fish in the lake
  as N.
• How should we estimate N?

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Capture Recapture
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Capture Recapture
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WW II Tanks

• In WW II the German tanks were discovered to have
  serial numbers that were simply consecutive like
  1, 2, 3, etc.
• The Allies figured they could determine how many
  tanks the Germans had manufactured, N, from the
  captured tank serial numbers.
• How could this be done?

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WW II Tanks
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WW II Tanks

• The first estimator is an estimator known as a
  Method of Moments estimator.
• The second estimator is based on the largest
  value in the sample, X_(n), or X_(max). This is
  called a Maximum Likelihood Estimator.
• It can also be derived as the biggest number plus
  the average gap.
• MLEs are superior to MOMs by stat theory.

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Military Intelligence ?