  We obtain the best possible upper bounds for the moments of a single order
statistic from independent, non-negative random variables, in terms of the
population mean. The main result covers the independent identically distributed
case. Furthermore, the case of the sample minimum for merely independent (not
necessarily identically distributed) random variables is treated in detail.
  Key-words and phrases: order statistics; optimal moment bounds; nonnegative
random variables; sample minimum; reliability systems.
