A story is told from World War II, when the Allies were considering a ground invasion of Europe. Critical to their success would be the number of Mark V tanks fielded by the Germans. Intelligence, however, gave contradictory estimates as to the number of tanks that were being produced per month.
It was noticed that captured tanks had serial numbers, which were apparently assigned in order of production. Statisticians came up with a formula which would give an estimate of the total number of tanks produced given a sample of serial numbers. After the war, German production records showed that the estimate was almost exactly correct.
Suppose tanks are numbered 1, 2, 3, 4, 5, ... N, where N is the total number of tanks produced. Given a sample of, say, five serial numbers, how would you estimate the value of N?
Friday, July 18, 2008
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