  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.
