In this paper we derive sharp lower and upper bounds for the covariance of two bounded random variables when knowledge about their expected values, variances or both is available. When only the expected values are known, our result can be viewed as an extension of the Bhatia-Davis Inequality for variances. We also provide a number of different ways to standardize covariance. For a binary pair random variables, one of these standardized measures of covariation agrees with a frequently used measure of dependence between genetic variants.

翻译：在本文中,当了解了两个封闭的随机变量的预期值、差异或两者同时存在时,我们得出了两个封闭的随机变量的共差的下下限和上限。当只知道预期值时,我们的结果可以被视为Bhatia-Davis差异不平等的延伸。我们还提供了一些不同的方法来规范共差。对于双对随机变量,这些标准化的共差计量方法之一同意遗传变量之间经常使用的依赖度。