Where to reinforce planes given survivor damage

Question

Engineers study the bullet damage on bombers that made it back from missions. Based on where those holes are, where should extra armour go?

Short answer

Where the returning planes have no holes. This is survivorship bias (Wald's insight): planes hit in those areas, such as engines and cockpit, did not come back, so they are missing from the data. Holes on survivors mark places a plane can absorb hits.

Adapted from Wilmott, Frequently Asked Questions in Quantitative Finance, ch. 10 brainteaser 'Aircraft armour', p.356; question and answer rewritten by SelfMadeQuant.com.

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Lessons behind this question

Maximum Likelihood Estimation: Score and Log-Likelihood
Bias, Variance, and Mean Squared Error
Populations, Samples, and Sampling Distributions

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