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arXiv · 2504.05766

On raw moments of the binomial distribution

Kalle Leppälä
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Abstract

We study the $k$:th raw moment of a variable $R$ following the binomial distribution $\text{B}(n, p)$, where $n/k \rightarrow \beta > 0$. It is known that $\mathbb{E}(R^k)$ is bounded both from below and from above by functions of the form $k^k \Psi^k$. We solve the asymptotically optimal value of $\Psi$ as a function of $p$ and $\beta$.

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Kalle Leppälä. 2025-04-08. On raw moments of the binomial distribution. https://arxiv.org/abs/2504.05766

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