Let k be a non-negative integer, and let r1, r2,..., rk be non-negative real numbers satisfying r1 + r2 + ... + rk [less-than-or-equals, slant] 1 and ri+1 + ... + rk (k - i)/k for all i = 1,...,k - 1. It is proved that there exists a constant c such that for any X1,X2,...,Xk non-negative i.i.d....