This year’s Awards Day Ceremony will take place on Friday April 26th at 3:30pm in Schenker Lecture Hall, followed by a talk given by Dr. Steven Miller.

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

**Steven J Miller**

*Carnegie Mellon and Williams College*

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.