Sample mean and sample variance: Their covariance and their (in)dependence

It is of interest to know what the covariance of sample mean and sample variance is without the assumption of normality. In this article we study such a problem. We show a simple derivation of the formula for computing covariance of sample mean and sample variance, and point Out a way of constructing examples of "zero covariance without independence." A small example is included to help teachers explain to students.