Characterizations of finite sequences \(\beta _{1}<\cdots <\beta _{n}\) representing expected values of order statistics from a random sample of size n are given. As a by-product, a characterization of binomial mixtures, when the mixing random variable is supported in the open interval (0, 1), is presented; this enables the exact description of the convex hull of the open binomial curve, as well as the open moment curve.
