We study the effects of rounding on the moments of a random variable. Specifically, given a random variable $X$ and its rounded counterpart $\operatorname{rd}(X)$, we study $|\mathbf{E}[X^k] - \mathbf{E}[\operatorname{rd}(X)^{k}]|$ for non-negative integer $k$. We consider the case that the rounding function $\operatorname{rd} : \mathbb{R}\to\mathbb{F}$ corresponds either to (i) rounding to the nearest point in some discrete set $\mathbb{F}$ or (ii) rounding randomly to either the nearest larger or smaller point in this same set with probabilities proportional to the distances to these points. In both cases, we show, under reasonable assumptions on the density function of $X$, how to compute a constant $C$ such that $|\mathbb{E}[X^k] - \mathbb{E}[\operatorname{rd}(X)^{k}]| < C \epsilon^2$, provided $\operatorname{rd}(x) - x| \leq \epsilon E(x)$. Asymptotic and non-asymptotic bounds for the absolute moments $\mathbb{E}[ |X^k-\operatorname{rd}(X)^{k}| ]$ are also given.

翻译：我们研究对随机变量时刻的四舍五入效果。 具体地说, 根据一个随机变量{ X$ 及其四舍五入对应方$\Operatorname{rd}(X)$, 我们研究的是 $\mathbf{E}[X} -\mathbf{E} -\mathbf{E} [\opatorname{rd{(X)\k}} $对于非负整数的整数整数值。 在这两种情况下, 我们考虑的情况是, 在对 $X$ 的密度函数的合理假设下, 我们如何计算一个不变的 $C$, $\mathb{Rto\mab{F}F} $ (一) 绝对值折合于(一) 某离散数 $\\\\\\\\\\\\\\\\\\ x}E}\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ a>ator$。