An Alternate Proof of Stirling's Formula

• Activity Number: 340 - Teaching Statistics and Data Ethics in the Health Sciences
• Type: Contributed
• Date/Time: Tuesday, August 9, 2022 : 2:00 PM to 3:50 PM
• Sponsor: Section on Teaching of Statistics in the Health Sciences
• Author(s): ILHAN M. IZMIRLI*
• Companies: 5559500017
• Keywords: Stirling’s formula; central limit theorem; independent and identically distributed (iid) random variables

Abstract

In this paper, we will give a short proof of Stirling’s formula using, essentially, nothing more than the central limit theorem.

It is our contention that this approach, which stresses the probabilistic nature of the formula, is pedagogically more suitable for students taking a mathematical probability course.