Estimating Tanks - Communication in Mathematical Statistics

Communication skills are critical for statisticians, but in our curricula emphasis on communication tends to be in applied courses. After providing historical context around the traditional mathematical statistics course, this article introduces a project for the course allowing students to engage in writing about theoretical results. This project is one of two used in the course with writing components, and was introduced in the Spring of 2015 and revised for Spring of 2024. The project combines theoretical derivations, computation (via a simulation study) and practice with written communication skills into a single assignment. It was based on the historical German tank problem, estimating the number of tanks, N, produced based on assuming serial numbers on tanks were labeled 1 to N, and sampling a set of k tanks found in the field. Example student work and feedback are included. Students found learning to perform a simulation study particularly useful. Potential adaptations, improvements, and adjustments are discussed for the project.