During World War II the German army used tanks to devastating advantage.

The Allies needed accurate estimates of their tank production and

deployment. They used two approaches to find these values: spies, and

statistics. In this talk we describe the statistical approach and its

generalization. Assuming the tanks are labeled consecutively starting at

1, if we observe $k$ serial numbers from an unknown number $N$ of tanks,

with the maximum observed value $m$, what is the best estimate for $N$?

This is now known as the German Tank Problem, and is a terrific example of

the applicability of mathematics and statistics in the real world. We

quickly review some needed combinatorial identities (which is why we are

able to obtain clean, closed form expressions), give the proof for the

standard problem, discuss the generalization, and show how if we were

unable to do the algebra we could guess the formula by an application of

linear regression, thus highlighting its power and applicability. Most of

the talk only uses basic algebra and elementary knowledge of WWII.

# The German Tank Problem: Math/Stats At War!

Event time:

Friday, September 27, 2019 - 5:00pm

Location:

LOM 206

Speaker:

Steven J Miller

Speaker affiliation:

Williams College, MC'96

Event description: