  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.
