  The critical behavior of a quenched random hypercubic sample of linear size
$L$ is considered, within the ``random-$T_{c}$'' field-theoretical mode, by
using the renormalization group method. A finite-size scaling behavior is
established and analyzed near the upper critical dimension $d=4-\epsilon$ and
some universal results are obtained. The problem of self-averaging is clarified
for different critical regimes.
