Raw and central moments of binomial random variables via Stirling numbers

Abstract

We consider here the problem of calculating the moments of binomial random variables. It is shown how formulae for both the raw and the central moments of such random variables may be obtained in a recursive manner utilizing Stirling numbers of the first kind. Suggestions are also provided as to how students might be encouraged to explore this application of mathematical techniques to statistical notions yet further.

Keywords:

• binomial distribution
• central moments
• random variable
• raw moments
• Stirling numbers of the first kind

Acknowledgements

The author thank one referee for a number of suggestions that have to led improvements in the clarity of this article.